Error analysis in a mathematics examination works by locating the first point where a valid mathematical state became invalid. A wrong final answer may begin with a misread target, wrong model, missing theorem condition, sign error, calculator mode, premature rounding or incomplete interpretation. Treating all of these as “careless mistakes” hides the mechanism that must be repaired.
Understanding how to analyse maths mistakes, correct exam errors and use feedback turns marked work into a repair system. The goal is not to rewrite every solution from the beginning. It is to preserve correct work, isolate the earliest failing transition, fix the smallest responsible component, retest it on fresh questions and verify that the correction survives mixed exam conditions.
This world-facing guide extends How to Use Maths Past Papers, How to Check Maths Answers, and Maths Mark Schemes, Method Marks, Working and Partial Credit. It owns the mathematics-specific post-response error-to-repair loop.
The 50-second answer
OBSERVE WRONG OUTPUT → TRACE BACKWARD → FIND FIRST INVALID TRANSITION → CLASSIFY FAILURE → PRESERVE CORRECT WORK → REPAIR MINIMUM COMPONENT → RETEST UNSEEN → REGRESSION-CHECK DEPENDANTS → RETURN TO MIXED PAPER.
1. The final wrong line is often not the first error
If a student writes the wrong equation and then solves it perfectly, the arithmetic is not the repair target. Rebuilding the algebra without fixing the model wastes effort. Trace the dependency chain backward until the last unquestionably valid state.
2. “Careless” is not yet a diagnosis
“Careless” can mean copied a negative sign incorrectly, omitted a unit, skipped a root, misread “at least,” entered a calculator expression without brackets or rounded too early. Replace the label with an observable action.
3. Preserve correct blocks
If the diagram, equation and first three transformations are correct, keep them. Repair should begin at the first invalid transition. This protects working knowledge and makes the true weakness visible.
4. Error categories should lead to different drills
A method-selection error needs contrast practice; a multiplication-fact bottleneck needs fluency; a theorem-condition error needs configuration discrimination; a checking failure needs an independent verification routine. One generic correction worksheet cannot repair every mechanism equally well.
5. Feedback is useful only when it changes the next attempt
Reading “watch your signs” does little unless the next practice includes a concrete sign-control behaviour such as bracketed substitution or line-to-line coefficient checks. Feedback should compile into an action.
6. Immediate correction can create false confidence
Once the solution is visible, reconstruction feels easy. Close the model, wait, and use a fresh question. Independent delayed success is stronger evidence of repair than fluent copying.
7. Repair can create regression elsewhere
A student who learns to add more working may become slower; a student who changes a formula may introduce a unit error; a corrected parameter can alter several later parts. Recheck dependent outputs after a repair.
8. Error frequency and error cost are different
A rare wrong model can destroy an entire multi-part question, while frequent tiny arithmetic slips may each cost little. Repair priority should consider both recurrence and downstream harm.
9. A good error log gets shorter over time
Do not collect mistakes forever. When a mechanism survives delayed unseen transfer repeatedly, retire it from the active queue. Keep attention available for residual weaknesses.
10. The repair is complete only when it survives disguise
A reverse-percentage correction is not secure if the learner succeeds only when the heading says “reverse percentage.” Put the same structure into a mixed paper with different nouns and numbers. Transfer closes the loop.
Part II. One hundred fifty error mechanisms
11. Misread target
When the failure is misread target, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
12. Command-word error
When the failure is command-word error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
13. Reference-whole error
When the failure is reference-whole error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
14. Wrong model
When the failure is wrong model, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
15. Wrong variable definition
When the failure is wrong variable definition, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
16. Missing condition
When the failure is missing condition, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
17. Wrong theorem
When the failure is wrong theorem, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
18. Wrong formula
When the failure is wrong formula, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
19. Wrong method selection
When the failure is wrong method selection, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
20. Representation error
When the failure is representation error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
21. Diagram assumption
When the failure is diagram assumption, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
22. Scale-reading error
When the failure is scale-reading error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
23. Table correspondence error
When the failure is table correspondence error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
24. Graph extraction error
When the failure is graph extraction error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
25. Unit mismatch
When the failure is unit mismatch, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
26. Conversion error
When the failure is conversion error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
27. Algebra sign error
When the failure is algebra sign error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
28. Bracket error
When the failure is bracket error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
29. Coefficient copying error
When the failure is coefficient copying error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
30. Fraction denominator error
When the failure is fraction denominator error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
31. Illegal cancellation
When the failure is illegal cancellation, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
32. Division by zero risk
When the failure is division by zero risk, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
33. Lost restriction
When the failure is lost restriction, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
34. Extraneous root
When the failure is extraneous root, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
35. Missing root
When the failure is missing root, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
36. Inequality reversal error
When the failure is inequality reversal error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
37. Endpoint error
When the failure is endpoint error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
38. Domain error
When the failure is domain error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
39. Range error
When the failure is range error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
40. Function-order error
When the failure is function-order error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
41. Sequence indexing error
When the failure is sequence indexing error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
42. Calculator mode error
When the failure is calculator mode error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
43. Calculator bracket-entry error
When the failure is calculator bracket-entry error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
44. Calculator transcription error
When the failure is calculator transcription error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
45. Premature rounding
When the failure is premature rounding, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
46. Wrong significant figures
When the failure is wrong significant figures, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
47. Wrong decimal places
When the failure is wrong decimal places, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
48. Exactness error
When the failure is exactness error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
49. Bounds error
When the failure is bounds error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
50. Whole-number interpretation error
When the failure is whole-number interpretation error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
51. Probability denominator error
When the failure is probability denominator error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
52. Replacement-state error
When the failure is replacement-state error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
53. Independence assumption error
When the failure is independence assumption error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
54. Double counting
When the failure is double counting, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
55. Complement misuse
When the failure is complement misuse, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
56. Weighted-mean error
When the failure is weighted-mean error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
57. Histogram density error
When the failure is histogram density error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
58. Sample-population overclaim
When the failure is sample-population overclaim, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
59. Correlation-causation error
When the failure is correlation-causation error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
60. Geometry correspondence error
When the failure is geometry correspondence error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
61. Trigonometric side-label error
When the failure is trigonometric side-label error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
62. Bearing-reference error
When the failure is bearing-reference error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
63. Circle-theorem condition error
When the failure is circle-theorem condition error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
64. Proof by examples
When the failure is proof by examples, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
65. Converse error
When the failure is converse error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
66. Necessary-sufficient error
When the failure is necessary-sufficient error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
67. Quantifier error
When the failure is quantifier error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
68. Proof conclusion gap
When the failure is proof conclusion gap, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
69. Derivative algebra error
When the failure is derivative algebra error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
70. Stationary-point classification error
When the failure is stationary-point classification error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
71. Integral constant error
When the failure is integral constant error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
72. Signed-area error
When the failure is signed-area error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
73. Distance-displacement error
When the failure is distance-displacement error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
74. Optimisation feasibility error
When the failure is optimisation feasibility error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
75. Model-assumption error
When the failure is model-assumption error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
76. Extrapolation error
When the failure is extrapolation error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
77. Interpretation error
When the failure is interpretation error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
78. Missing unit
When the failure is missing unit, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
79. Missing final form
When the failure is missing final form, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
80. Incomplete subpart
When the failure is incomplete subpart, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
81. Missing solutions
When the failure is missing solutions, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
82. Working hidden
When the failure is working hidden, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
83. Working redundant
When the failure is working redundant, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
84. Restart error
When the failure is restart error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
85. Overchecking
When the failure is overchecking, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
86. Underchecking
When the failure is underchecking, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
87. Pacing fixation
When the failure is pacing fixation, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
88. Move-on failure
When the failure is move-on failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
89. Return failure
When the failure is return failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
90. Confidence error
When the failure is confidence error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
91. Answer-change error
When the failure is answer-change error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
92. Dependency propagation
When the failure is dependency propagation, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
93. Carry-forward confusion
When the failure is carry-forward confusion, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
94. Mark-scheme misunderstanding
When the failure is mark-scheme misunderstanding, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
95. Solution-copying
When the failure is solution-copying, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
96. Recognition illusion
When the failure is recognition illusion, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
97. Repeat-paper familiarity
When the failure is repeat-paper familiarity, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
98. Feedback ignored
When the failure is feedback ignored, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
99. Feedback too vague
When the failure is feedback too vague, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
100. Repair too broad
When the failure is repair too broad, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
101. Repair wrong component
When the failure is repair wrong component, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
102. Repair without retest
When the failure is repair without retest, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
103. Retest too soon
When the failure is retest too soon, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
104. Retest same question
When the failure is retest same question, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
105. Transfer failure
When the failure is transfer failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
106. Mixed-practice failure
When the failure is mixed-practice failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
107. Timed-transfer failure
When the failure is timed-transfer failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
108. Regression after repair
When the failure is regression after repair, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
109. New error introduced
When the failure is new error introduced, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
110. Error recurrence
When the failure is error recurrence, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
111. Error clustering
When the failure is error clustering, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
112. High-frequency low-cost error
When the failure is high-frequency low-cost error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
113. Low-frequency high-cost error
When the failure is low-frequency high-cost error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
114. Prerequisite gap
When the failure is prerequisite gap, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
115. Fluency bottleneck
When the failure is fluency bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
116. Retrieval bottleneck
When the failure is retrieval bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
117. Selection bottleneck
When the failure is selection bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
118. Execution bottleneck
When the failure is execution bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
119. Checking bottleneck
When the failure is checking bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
120. Language bottleneck
When the failure is language bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
121. Notation bottleneck
When the failure is notation bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
122. Attention bottleneck
When the failure is attention bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
123. Tool bottleneck
When the failure is tool bottleneck, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
124. Knowledge gap
When the failure is knowledge gap, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
125. Concept misconception
When the failure is concept misconception, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
126. Procedural misconception
When the failure is procedural misconception, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
127. Conditional-knowledge gap
When the failure is conditional-knowledge gap, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
128. Scope error
When the failure is scope error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
129. Precision error
When the failure is precision error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
130. State-update error
When the failure is state-update error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
131. Invariant error
When the failure is invariant error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
132. Constraint error
When the failure is constraint error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
133. Correspondence error
When the failure is correspondence error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
134. Dependency error
When the failure is dependency error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
135. Evidence-type error
When the failure is evidence-type error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
136. Communication error
When the failure is communication error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
137. Legibility error
When the failure is legibility error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
138. Final-answer ambiguity
When the failure is final-answer ambiguity, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
139. Two-answer ambiguity
When the failure is two-answer ambiguity, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
140. Crossed-out evidence
When the failure is crossed-out evidence, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
141. Blank response
When the failure is blank response, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
142. Partial response
When the failure is partial response, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
143. False correction
When the failure is false correction, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
144. Unverified correction
When the failure is unverified correction, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
145. Overcorrection
When the failure is overcorrection, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
146. Error-log overload
When the failure is error-log overload, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
147. Stale error log
When the failure is stale error log, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
148. Retirement failure
When the failure is retirement failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
149. Mastery false positive
When the failure is mastery false positive, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
150. Transfer false positive
When the failure is transfer false positive, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
151. Score-only diagnosis
When the failure is score-only diagnosis, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
152. Careless label
When the failure is careless label, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
153. Teacher-feedback mismatch
When the failure is teacher-feedback mismatch, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
154. Self-marking mismatch
When the failure is self-marking mismatch, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
155. Peer-marking mismatch
When the failure is peer-marking mismatch, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
156. Official-scheme mismatch
When the failure is official-scheme mismatch, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
157. Examiner-report overgeneralisation
When the failure is examiner-report overgeneralisation, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
158. Repair priority error
When the failure is repair priority error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
159. Repair sequencing error
When the failure is repair sequencing error, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
160. Checkpoint missing
When the failure is checkpoint missing, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
161. Regression test missing
When the failure is regression test missing, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
162. Release criterion missing
When the failure is release criterion missing, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
163. Freshness criterion missing
When the failure is freshness criterion missing, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
164. Delay criterion missing
When the failure is delay criterion missing, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
165. Support not faded
When the failure is support not faded, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
166. Hint dependency
When the failure is hint dependency, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
167. Calculator dependency
When the failure is calculator dependency, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
168. Formula-sheet dependency
When the failure is formula-sheet dependency, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
169. Chapter-label dependency
When the failure is chapter-label dependency, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
170. Context dependency
When the failure is context dependency, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
171. Surface-feature dependency
When the failure is surface-feature dependency, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
172. Final integration failure
When the failure is final integration failure, do not begin by rewriting the whole solution. Trace the response backward and identify the last state that still satisfies the question. The next transition is the repair boundary unless earlier hidden assumptions also fail.
Classification drill. Decide whether this is primarily knowledge, selection, representation, execution, tool use, checking, interpretation, pacing or feedback failure. If two categories are involved, identify which occurred first. The earliest causal failure usually deserves priority.
Minimum repair. Design the smallest exercise that forces the missing behaviour while preserving everything already correct. Contrast methods for selection failures; isolate arithmetic for fluency failures; reconstruct theorem conditions for geometry; use fresh interpretation prompts for scope failures.
Retest. Use an unseen question after the correction is no longer visually available. Change surface details while preserving the underlying relationship. If the learner succeeds only on the corrected item, the repair has not generalised.
Regression check. Inspect downstream skills that could have been disturbed by the repair. Faster work must remain accurate; more visible working must remain efficient; a new formula routine must preserve units and restrictions. Improvement is a system change, not a single corrected line.
Part III. Fifty original error-repair laboratories
Laboratory 1. reverse percentage
Observed error. Student writes72×1.2 for price after20% discount.
Earliest failure. First failure: reference whole/model.
Repair. Repair0.8P=72; fresh reverse-change contrasts.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 2. ratio remainder
Observed error. Student takes1/3 of original total after1/4 used.
Earliest failure. First failure: state/reference update.
Repair. Mark remainder before second fraction; fresh remainder problems.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 3. average speed
Observed error. Student averages30 and60.
Earliest failure. First failure: definition/method selection.
Repair. Rebuild total distance/total time.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 4. algebra sign
Observed error. −3 copied as+3.
Earliest failure. First failure: transcription.
Repair. Bracket/sign checkpoint; preserve correct method.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 5. cancellation
Observed error. Cancels x across x+3.
Earliest failure. First failure: structural algebra rule.
Repair. Factor/cancel contrasts showing cancellation only of factors.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 6. quadratic roots
Observed error. Only x=2 reported from roots2,3.
Earliest failure. First failure: completeness.
Repair. Fresh multi-root equations plus target scan.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 7. square equation
Observed error. Extraneous root accepted.
Earliest failure. First failure: non-reversible transformation not checked.
Repair. Original-equation substitution.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 8. inequality
Observed error. Divides by−2 without reversing.
Earliest failure. First failure: order rule.
Repair. Number-line demonstration then mixed signs.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 9. bounds
Observed error. 8.2 treated exact.
Earliest failure. First failure: measurement model.
Repair. Reverse-rounding interval practice.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 10. capacity
Observed error. 11.375 rounded to11.
Earliest failure. First failure: contextual constraint.
Repair. Neighbour feasibility test.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 11. Pythagoras
Observed error. Applied without right angle.
Earliest failure. First failure: theorem condition.
Repair. Right/non-right diagram contrast.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 12. similarity
Observed error. Correct factor on wrong side pair.
Earliest failure. First failure: correspondence.
Repair. Mark matching vertices first.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 13. trig
Observed error. Opposite/adjacent swapped.
Earliest failure. First failure: representation relative to target angle.
Repair. Relabel same triangle for different angles.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 14. bearing
Observed error. Measures from east.
Earliest failure. First failure: reference direction.
Repair. Draw north line at origin point.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 15. circle
Observed error. Uses tangent theorem on ordinary chord.
Earliest failure. First failure: configuration recognition.
Repair. Tangent/chord contrast set.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 16. probability
Observed error. Second draw denominator unchanged without replacement.
Earliest failure. First failure: state update.
Repair. Branch-state annotation.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 17. independence
Observed error. Multiplies probabilities without justification.
Earliest failure. First failure: relationship assumption.
Repair. Independent/dependent contrast questions.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 18. double count
Observed error. Adds overlapping sets without subtracting intersection.
Earliest failure. First failure: event representation.
Repair. Venn reconstruction.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 19. combined mean
Observed error. Averages group means.
Earliest failure. First failure: weighting.
Repair. Recover totals with mean×count.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 20. histogram
Observed error. Reads height as frequency.
Earliest failure. First failure: representation definition.
Repair. Density×width reconstruction.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 21. statistics
Observed error. Sample result claimed for everyone.
Earliest failure. First failure: scope.
Repair. Rewrite conclusion at sample level.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 22. proof
Observed error. Tests five examples for universal claim.
Earliest failure. First failure: evidence type.
Repair. General variable proof.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 23. converse
Observed error. Uses B⇒A from A⇒B.
Earliest failure. First failure: implication direction.
Repair. Write arrows and counterexample.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 24. calculator
Observed error. Trig answer wrong from radian mode.
Earliest failure. First failure: tool state.
Repair. Pre-trig mode check.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 25. rounding
Observed error. Intermediate values rounded heavily.
Earliest failure. First failure: precision workflow.
Repair. Keep stored/full precision until final.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 26. formula
Observed error. Diameter entered as radius.
Earliest failure. First failure: variable mapping.
Repair. Label symbols before substitution.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 27. graph
Observed error. Scale read as1 per square instead of5.
Earliest failure. First failure: extraction.
Repair. Write one-small-interval value before reading.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 28. word problem
Observed error. Correct remainder found but stops before per-person answer.
Earliest failure. First failure: completion/target.
Repair. Target noun check after calculation.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 29. calculus
Observed error. f’=0 labelled maximum automatically.
Earliest failure. First failure: classification.
Repair. Second derivative/sign/endpoints as appropriate.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 30. integral
Observed error. Forgets+C.
Earliest failure. First failure: answer form/concept.
Repair. Differentiate family of antiderivatives.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 31. optimisation
Observed error. Negative length accepted.
Earliest failure. First failure: feasibility.
Repair. Domain/constraint check.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 32. modelling
Observed error. Linear model for constant percentage growth.
Earliest failure. First failure: mechanism selection.
Repair. Fixed-addition versus fixed-proportion contrasts.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 33. pacing
Observed error. Eight minutes repeat same stalled route.
Earliest failure. First failure: move-on decision.
Repair. Progress trigger and restart note.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 34. checking
Observed error. Recalculates same wrong equation.
Earliest failure. First failure: check independence.
Repair. Use reverse/substitution/unit check.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 35. confidence
Observed error. Correct answer changed because unusual.
Earliest failure. First failure: evidence hierarchy.
Repair. Require objective failed check.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 36. mark scheme
Observed error. Student assumes every line gets one mark.
Earliest failure. First failure: marking-model misconception.
Repair. Calibrate against actual official schemes.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 37. solution copy
Observed error. Can reproduce model immediately.
Earliest failure. First failure: recognition mistaken for learning.
Repair. Close model, delay, reconstruct.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 38. repeat paper
Observed error. Score jumps on third identical attempt.
Earliest failure. First failure: evidence contamination.
Repair. Fresh isomorphic retest.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 39. feedback
Observed error. Teacher writes ‘careless’.
Earliest failure. First failure: feedback specificity.
Repair. Translate to observable error action.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 40. repair
Observed error. Whole chapter relearned for one sign-copy error.
Earliest failure. First failure: repair granularity.
Repair. Preserve correct blocks; target transcription.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 41. retest
Observed error. Same corrected question repeated immediately.
Earliest failure. First failure: independence of evidence.
Repair. Delay and change surface features.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 42. regression
Observed error. More working added, paper now unfinished.
Earliest failure. First failure: repair side effect.
Repair. Compress to high-information lines; timed regression test.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 43. error log
Observed error. Fifty historical errors all active.
Earliest failure. First failure: queue management.
Repair. Retire mechanisms that survive repeated transfer.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 44. priority
Observed error. Frequent tiny arithmetic error chosen over rare model error that destroys long questions.
Earliest failure. First failure: risk weighting.
Repair. Rank by frequency×downstream cost.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 45. prerequisite
Observed error. Quadratic errors caused by weak integer factor pairs.
Earliest failure. First failure: earlier skill.
Repair. Repair factor fluency before quadratic speed.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 46. selection
Observed error. Can solve each topic separately but not mixed.
Earliest failure. First failure: retrieval discrimination.
Repair. Interleave near-neighbour methods.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 47. language
Observed error. Misreads ‘at least’ as ‘more than’.
Earliest failure. First failure: command/quantifier.
Repair. Boundary-value contrast.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 48. notation
Observed error. Treats f(x) as multiplication.
Earliest failure. First failure: notation meaning.
Repair. Mapping/substitution drills.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Laboratory 49. final integration
Observed error. Targeted repairs pass, full paper still weak.
Earliest failure. First failure now may be pacing/retrieval integration.
Repair. Return to timed mixed/full paper and re-diagnose.
Preserve. Mark every earlier line or skill that was already correct. The repair should not erase successful knowledge merely because the final answer failed.
Retest protocol. Close the correction, delay, use a fresh structurally related question, then mix it with neighbouring methods. Record whether the learner selected and executed the repair without a topic label or hint.
Part IV. A 20-day error-repair programme
Day 1. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 2. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 3. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 4. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 5. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 6. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 7. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 8. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 9. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 10. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 11. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 12. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 13. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 14. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 15. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 16. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 17. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 18. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 19. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Day 20. Repair one mechanism, preserve the rest
Choose three wrong or uncertain responses from recent work. For each, trace backward to the last valid state and circle the first invalid transition. Write a specific mechanism label such as “wrong reference whole,” “copied negative sign,” “missing theorem condition” or “stayed stalled too long.”
Design a short repair set for only the earliest mechanism. Keep already-correct skills out of the repair unless they are necessary context. After correction, close all solutions and complete a fresh question without hints. If the same mechanism fails again, reduce the task until the missing behaviour becomes observable.
Finish with one mixed transfer question and one regression check. Confirm that the repair did not damage speed, notation, units, checking or another previously stable skill. Update the active error queue only from this evidence.
Part V. Frequently asked questions
What is the best way to correct maths mistakes?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
Should I rewrite the whole solution?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
What does first error mean?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
Is ‘careless mistake’ a useful diagnosis?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How do I make an error log?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
What categories should a maths error log use?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How many errors should I work on at once?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How do I decide which error to fix first?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
What if I understand the correction immediately?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How long should I wait before retesting?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
Should I repeat the same question?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How do I know a correction has stuck?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
What is transfer in maths practice?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
What is regression testing after a correction?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
Can fixing one problem create another?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How do I use teacher feedback?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
How do I use mark-scheme feedback?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
When should I retire an error from my log?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
Why do the same mistakes keep returning?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
When should I return to full past papers?
Start with the first invalid transition, not the emotional label attached to the final result. Preserve everything before that point that is mathematically sound. Then choose a repair matched to the mechanism and demand fresh delayed evidence before declaring the problem fixed.
For practice, compare two wrong solutions that end with the same incorrect answer but fail for different reasons. Design a different repair for each. This prevents error analysis from collapsing into answer correction.
A creative-writing lens: revise the broken hinge
If a story’s ending fails because the character’s decision has no motive, rewriting every sentence may polish the prose without repairing the causal gap. Mathematics is more formal, but the editing principle is similar: locate the first broken hinge, preserve what still works and test the revision against the whole structure.
Use the eduKate ecosystem as a route
Use How Mistakes Improve Learning | Error Repair Workbook for the broader learning mechanism, Additional Mathematics Repair Sequencing for advanced multi-error correction, How to Check Maths Answers for live verification and How to Use Maths Past Papers for the paper-level repair loop.
Scope note and final answer
Official marking decisions belong to the relevant examination authority and mark scheme. This article uses original teaching examples and does not assign official marks. Adrian, Jo, Ben, Aisha, Ryan, Mira, Clara and Ethan are fictional teaching characters.
The central habit is: do not repair the wrong answer; repair the first mechanism that made the answer wrong. Preserve correct blocks, retest with fresh evidence and return the repaired skill to mixed mathematics before closing the case.
Route: use the Examinations & Assessment Hub for exam-performance strategy, the Mathematics Learning Hub for subject progression and repair, or the Deep Reading Index for the complete mathematics long tail.