Updated 23 September 2026. How to improve IP Mathematics with Bukit Timah tuition begins by recognising that there is no single universal IP Mathematics syllabus. Different Integrated Programme schools can differ in sequencing, depth, assessments and enrichment, so effective tuition must align to the student’s actual school programme while strengthening the mathematical capabilities that transfer across schools.
The legacy title mentions distinction results, but a responsible programme should not promise a specific outcome. The controllable job is excellence teaching: deep conceptual understanding, algebraic fluency, proof and justification, functions and graphs, problem solving, transfer, retrieval, independent learning and preparation for the student’s actual next stage—JC, IB or another school-specific route.
The central proposition is: IP Mathematics improves when tuition follows the student’s real school programme but teaches the deeper mathematical structures that remain useful when the school’s surface, pacing or assessment changes. This page owns the IP improvement system: school-specific alignment plus transferable advanced mathematical capability, while neighbouring Bukit Timah pages continue to handle generic tutor selection, stage-specific quality standards and examination-specific guides.
Where current Singapore pathway facts matter, use official MOE and SEAB guidance. Where a school runs its own IP sequence, the actual school curriculum, assessment pattern and progression expectations take priority over generic assumptions.
50-second router
| What you see | Likely mechanism | Useful next step |
|---|---|---|
| School pace is fast but understanding is shallow | Coverage-depth mismatch | Repair concepts and representations |
| Strong marks, weak unfamiliar problems | Transfer ceiling | Use proof, generalisation and non-routine tasks |
| Algebra errors contaminate advanced topics | Carrier weakness | Repair algebra upstream |
| Student relies on tuition preview | Acquisition dependence | Reduce preview and test school learning |
| Different school syllabus from tutor materials | Alignment problem | Follow actual school sequence and assessments |
What this page owns: improving IP Mathematics without inventing one generic IP syllabus
This owner should be school-programme-aware but not school-specific in claims it cannot verify. It explains what strong IP tuition should do across varying sequences: diagnose carriers, deepen reasoning, support proofs and functions, and protect independent acquisition.
- Actual school sequence
- Algebraic fluency
- Functions and graphs
- Proof and justification
- Trigonometric reasoning where relevant
- Calculus readiness or calculus where relevant
- Non-routine problem solving
- Retrieval
- Transfer
- JC/IB readiness
Improvement operating loop
1. Read
Use authentic first attempts, current school work and recent assessment evidence. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
2. Diagnose
Locate the earliest repeated weakness, not only the final wrong answer. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
3. Prioritise
Choose the weakness with the highest downstream cost. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
4. Repair
Teach the missing relationship, representation or execution routine directly. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
5. Practise
Use enough focused work to stabilise the mechanism without creating rote dependence. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
6. Connect
Reintroduce the skill into mixed Mathematics and related topics. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
7. Perform
Test under novelty, timing and school-assessment conditions when useful. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
8. Review
Use delayed transfer and reduced prompting to decide whether the target can close. In IP Mathematics, the loop should produce a visible change in independent mathematical control rather than simply a larger completed workload.
Capability atlas
1. algebraic fluency
Improvement in algebraic fluency should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
2. functions
Improvement in functions should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
3. graphs
Improvement in graphs should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
4. proof and justification
Improvement in proof and justification should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
5. logical argument
Improvement in logical argument should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
6. trigonometric reasoning
Improvement in trigonometric reasoning should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
7. calculus readiness
Improvement in calculus readiness should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
8. calculus interpretation where relevant
Improvement in calculus interpretation where relevant should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
9. coordinate geometry
Improvement in coordinate geometry should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
10. non-routine problem solving
Improvement in non-routine problem solving should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
11. generalisation
Improvement in generalisation should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
12. inverse reasoning
Improvement in inverse reasoning should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
13. modelling
Improvement in modelling should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
14. retrieval
Improvement in retrieval should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
15. independent learning
Improvement in independent learning should be separated into knowledge, recognition, representation, execution, retrieval and transfer. The tutor should show how this capability appears in the student’s actual school Mathematics, which prerequisites carry it and where the first recurring failure occurs.
The quality test is portability: the repaired capability should survive a changed surface, a delay and reduced prompting. If it works only on the original tuition worksheet or only after the tutor identifies the method, the improvement is not yet durable.
Diagnostic laboratory
Diagnostic 1: school-sequence audit
Use a compact discriminating task around school-sequence audit. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 2: algebra carrier check
Use a compact discriminating task around algebra carrier check. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 3: function meaning
Use a compact discriminating task around function meaning. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 4: graph interpretation
Use a compact discriminating task around graph interpretation. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 5: proof-chain audit
Use a compact discriminating task around proof-chain audit. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 6: counterexample task
Use a compact discriminating task around counterexample task. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 7: generalisation task
Use a compact discriminating task around generalisation task. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 8: trig structure check
Use a compact discriminating task around trig structure check. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 9: calculus-readiness test
Use a compact discriminating task around calculus-readiness test. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 10: representation switching
Use a compact discriminating task around representation switching. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 11: unfamiliar transfer
Use a compact discriminating task around unfamiliar transfer. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 12: delayed retrieval
Use a compact discriminating task around delayed retrieval. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 13: mixed recognition
Use a compact discriminating task around mixed recognition. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 14: prompt audit
Use a compact discriminating task around prompt audit. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Diagnostic 15: school-acquisition test
Use a compact discriminating task around school-acquisition test. Preserve the first attempt, identify the student’s representation and method choice, and locate the earliest invalid or missing step. The purpose is to distinguish the mathematical mechanism before prescribing practice.
After the repair, vary the question and return later. If the student can initiate, execute and check without the same prompt, the target can move down the priority list. If not, the mechanism remains active.
Failure-mode map
1. Generic IP curriculum assumption
What it looks like: Tutor materials do not match the student’s school. Repair: Start from the actual school sequence and assessment evidence. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
2. Acceleration without depth
What it looks like: Student has seen advanced topics but cannot transfer. Repair: Use proof, generalisation and representation switching. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
3. Algebra carrier fragility
What it looks like: Advanced questions fail because manipulation is unstable. Repair: Repair algebra across contexts. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
4. Proof is treated as model-answer memorisation
What it looks like: Student reproduces wording but cannot build argument. Repair: Use statement-reason chains, counterexamples and reconstruction. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
5. Functions are notation-only
What it looks like: Input-output and graph meaning are weak. Repair: Connect representations. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
6. Non-routine questions trigger panic
What it looks like: Student depends on familiar school surfaces. Repair: Increase controlled novelty and structure-search. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
7. Preview dependence
What it looks like: School lessons become repetition. Repair: Reduce preview and preserve school acquisition. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
8. Retrieval gaps
What it looks like: Earlier advanced content disappears between terms. Repair: Use spaced mixed return. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
9. Working is elegant-looking but opaque
What it looks like: Steps are over-compressed. Repair: Expose high-risk transformations. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
10. Distinction language becomes a promise
What it looks like: Outcome claims replace process evidence. Repair: Report capability receipts instead of guarantees. The repair should be tested in a different context so the student learns the relationship rather than the surface form.
Parent casebook
Case 1: keeps up with pace but lacks depth during school-specific IP lessons
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether keeps up with pace but lacks depth reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 2: scores highly but struggles with novelty during advanced algebra
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to advanced algebra, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 3: has fragile algebra during functions/graphs
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 4: memorises proofs during proof tasks
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in proof tasks becomes more independent and more reliable.
Case 5: functions feel abstract during trigonometry
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether functions feel abstract reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 6: panics at non-routine questions during calculus or calculus readiness
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to calculus or calculus readiness, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 7: needs tuition preview during school assessments
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 8: forgets earlier advanced topics during non-routine problems
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in non-routine problems becomes more independent and more reliable.
Case 9: over-compresses working during holiday enrichment
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether over-compresses working reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 10: is bored by routine school work during JC/IB transition planning
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to JC/IB transition planning, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 11: keeps up with pace but lacks depth during school-specific IP lessons
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 12: scores highly but struggles with novelty during advanced algebra
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in advanced algebra becomes more independent and more reliable.
Case 13: has fragile algebra during functions/graphs
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether has fragile algebra reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 14: memorises proofs during proof tasks
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to proof tasks, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 15: functions feel abstract during trigonometry
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 16: panics at non-routine questions during calculus or calculus readiness
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in calculus or calculus readiness becomes more independent and more reliable.
Case 17: needs tuition preview during school assessments
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether needs tuition preview reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 18: forgets earlier advanced topics during non-routine problems
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to non-routine problems, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 19: over-compresses working during holiday enrichment
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 20: is bored by routine school work during JC/IB transition planning
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in JC/IB transition planning becomes more independent and more reliable.
Case 21: keeps up with pace but lacks depth during school-specific IP lessons
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether keeps up with pace but lacks depth reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 22: scores highly but struggles with novelty during advanced algebra
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to advanced algebra, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 23: has fragile algebra during functions/graphs
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 24: memorises proofs during proof tasks
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in proof tasks becomes more independent and more reliable.
Case 25: functions feel abstract during trigonometry
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether functions feel abstract reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 26: panics at non-routine questions during calculus or calculus readiness
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to calculus or calculus readiness, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 27: needs tuition preview during school assessments
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 28: forgets earlier advanced topics during non-routine problems
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in non-routine problems becomes more independent and more reliable.
Case 29: over-compresses working during holiday enrichment
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether over-compresses working reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 30: is bored by routine school work during JC/IB transition planning
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to JC/IB transition planning, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 31: keeps up with pace but lacks depth during school-specific IP lessons
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 32: scores highly but struggles with novelty during advanced algebra
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in advanced algebra becomes more independent and more reliable.
Case 33: has fragile algebra during functions/graphs
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether has fragile algebra reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 34: memorises proofs during proof tasks
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to proof tasks, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 35: functions feel abstract during trigonometry
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 36: panics at non-routine questions during calculus or calculus readiness
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in calculus or calculus readiness becomes more independent and more reliable.
Case 37: needs tuition preview during school assessments
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether needs tuition preview reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 38: forgets earlier advanced topics during non-routine problems
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to non-routine problems, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 39: over-compresses working during holiday enrichment
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 40: is bored by routine school work during JC/IB transition planning
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in JC/IB transition planning becomes more independent and more reliable.
Case 41: keeps up with pace but lacks depth during school-specific IP lessons
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether keeps up with pace but lacks depth reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 42: scores highly but struggles with novelty during advanced algebra
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to advanced algebra, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Case 43: has fragile algebra during functions/graphs
A strong small-group lesson makes reasoning visible. Let the student attempt first, compare a valid route with a plausible wrong route, and remove the tutor cue on the next task. The improvement should be visible in independent initiation and checking.
Case 44: memorises proofs during proof tasks
This case should end with a decision: focused repair, mixed transfer, timed integration, reduced scaffolding or closure. The intervention is valuable only if the student’s future behaviour in proof tasks becomes more independent and more reliable.
Case 45: functions feel abstract during trigonometry
Begin by distinguishing the visible symptom from the mathematical mechanism. Compare the first attempt and corrected work and decide whether functions feel abstract reflects missing knowledge, method recognition, representation, execution, retrieval or pressure. Use one focused test before adding volume.
Case 46: panics at non-routine questions during calculus or calculus readiness
Look for a shared carrier. If the same error appears in several topics, repair it once at the carrier level. If the problem is local to calculus or calculus readiness, keep the repair local. In both cases, use a changed question and delayed retest before declaring the issue solved.
Repair protocols
1. school-alignment reset
For school-alignment reset, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
2. algebra carrier repair
For algebra carrier repair, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
3. function representation
For function representation, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
4. graph interpretation
For graph interpretation, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
5. proof reconstruction
For proof reconstruction, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
6. counterexample training
For counterexample training, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
7. generalisation
For generalisation, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
8. trig target structure
For trig target structure, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
9. calculus readiness
For calculus readiness, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
10. calculus interpretation
For calculus interpretation, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
11. unfamiliar transfer
For unfamiliar transfer, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
12. spaced retrieval
For spaced retrieval, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
13. prompt fading
For prompt fading, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
14. school-acquisition protection
For school-acquisition protection, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
15. next-stage handover
For next-stage handover, isolate the mechanism from unrelated difficulty, rebuild the relationship or condition, use contrastive correct/incorrect examples and a short focused set, then reconnect the skill to ordinary IP Mathematics work. Transfer and delayed retrieval are part of the repair, not optional extras.
3-pax small-group standard
1. Independent first attempts before discussion
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
2. Working inspected, not just answers
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
3. Different valid methods compared
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
4. Plausible wrong methods analysed constructively
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
5. Individual prompts matched to individual weak links
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
6. Shared mathematical object keeps group coherence
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
7. Wait time protects productive search
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
8. Answer changes require mathematical evidence
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
9. Task depth can differ without splitting the lesson
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
10. The fastest student does not become the answer source
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
11. Foundation repair carries no stigma
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
12. High-readiness students receive reasoning depth
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
13. Homework reflects real mechanisms
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
14. Prompt fading is planned
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
15. Independent transfer closes the learning cycle
For IP Mathematics, this matters because small groups should increase observation resolution. Parents should see the benefit in specific feedback and in the student’s ability to start, select, check and recover with less tutor involvement.
Retrieval and transfer system
1. Immediate variation
Change numbers, wording or representation after repair. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
2. Delayed retrieval
Return after days or weeks. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
3. Mixed recognition
Place the method among unrelated familiar topics. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
4. Non-example discrimination
Use a similar-looking problem where the method is invalid. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
5. Representation switching
Move among words, diagrams, tables, graphs and equations. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
6. Teach-back
Explain the relationship using a fresh example. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
7. School transfer
Look for the capability in normal school work. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
8. Timed transfer
Add time only after untimed accuracy stabilises. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
9. Error-log retest
Return to repeated mechanisms, not random questions. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
10. Tool-independent reconstruction
After notes, calculator or AI support, solve a fresh problem independently. The aim is to prove that the student owns the mathematical decision rather than merely recognising the tuition setting.
Performance system
1. unfamiliar-problem reading
Train unfamiliar-problem reading as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
2. proof communication
Train proof communication as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
3. method selection
Train method selection as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
4. representation choice
Train representation choice as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
5. step granularity
Train step granularity as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
6. checking
Train checking as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
7. time protection
Train time protection as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
8. recovery
Train recovery as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
9. school-assessment post-mortem
Train school-assessment post-mortem as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
10. independent review
Train independent review as a visible routine. Establish a baseline, practise in a controlled mini-set, then verify under realistic IP Mathematics conditions. If the problem appears only under time or novelty, target performance rather than re-teaching the whole topic.
Parent questions
1. What is my child’s actual IP Mathematics sequence?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
2. How does tuition align without duplicating school?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
3. Which algebra carrier is limiting advanced work?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
4. How are proofs taught beyond memorisation?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
5. How are functions connected to graphs?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
6. How are non-routine problems trained?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
7. How is preview dependence avoided?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
8. How is old advanced content retrieved?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
9. How is JC/IB readiness considered?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
10. What would justify reducing tuition?
A strong answer should point to actual first attempts, recurring error families, school/pathway context, prompt depth, transfer and the next independent test. The programme should also say what evidence would justify reducing support.
Red flags
1. One generic IP syllabus is assumed
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
2. The tutor teaches a different sequence without reason
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
3. Advanced-looking content replaces depth
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
4. Proofs are memorised
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
5. Algebra gaps are ignored
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
6. School acquisition is replaced by preview
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
7. Novelty appears only in exams
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
8. Retrieval is not spaced
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
9. Distinction results are implied as guaranteed
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
10. There is no exit logic
This should trigger a specific audit: what mathematical decision is being trained, how do we know it is weak, why is this activity the right intervention and what changed question will prove the learning transfers?
Green flags
1. First attempts are preserved
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
2. Error families are named precisely
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
3. Focused practice is purposeful
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
4. Mixed practice follows stabilisation
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
5. Representations change deliberately
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
6. Method conditions are explicit
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
7. Retrieval is spaced
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
8. Checking is mathematical
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
9. Prompt depth falls
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
10. School learning becomes more independent
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
11. Parents receive transfer evidence
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
12. Strong students get reasoning depth
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
13. Foundations are repaired directly
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
14. Group fit is reviewed
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
15. Support can reduce when independence is stable
This is meaningful only when it appears in the student’s work. The capability should eventually survive a changed problem, a delay and reduced prompting.
Twelve-week improvement architecture
1. Weeks 1–2
Baseline and high-value weak-link map. The sequence remains adaptive: if a prerequisite is still unstable, repair it before increasing complexity or examination volume.
2. Weeks 3–4
Focused repair of the main shared carrier. The sequence remains adaptive: if a prerequisite is still unstable, repair it before increasing complexity or examination volume.
3. Weeks 5–6
Reconnect to current school Mathematics and spaced retrieval. The sequence remains adaptive: if a prerequisite is still unstable, repair it before increasing complexity or examination volume.
4. Weeks 7–8
Mixed recognition and representation variation. The sequence remains adaptive: if a prerequisite is still unstable, repair it before increasing complexity or examination volume.
5. Weeks 9–10
Timing, checking and recovery where appropriate. The sequence remains adaptive: if a prerequisite is still unstable, repair it before increasing complexity or examination volume.
6. Weeks 11–12
Delayed mixed transfer, prompt reduction and exit review. The sequence remains adaptive: if a prerequisite is still unstable, repair it before increasing complexity or examination volume.
Frequently asked questions
1. Is there one IP Mathematics syllabus?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
2. How should tuition follow a school-specific programme?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
3. How much acceleration is useful?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
4. How should proof be taught?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
5. How should functions and graphs be deepened?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
6. When is calculus readiness appropriate?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
7. How should non-routine questions be trained?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
8. How is JC or IB readiness handled?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
9. Can strong IP students still need tuition?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
10. What proves IP improvement?
There is no useful universal answer without evidence from the learner. The decision should consider the actual mathematical bottleneck, school programme, workload, transfer and independence. A strong tutor should turn the question into an observable test and a reviewable next step.
Stop rules
1. Stop adding worksheets when the error mechanism is unknown
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
2. Stop teaching ahead when current foundations destabilise
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
3. Stop repeating papers when the same carrier error persists
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
4. Stop prompting when the student can proceed
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
5. Stop one representation when another makes the structure clearer
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
6. Stop a failing route when progress has stalled
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
7. Stop changing answers without evidence
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
8. Stop escalating difficulty when independence collapses
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
9. Stop duplicate homework that adds no new learning evidence
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
10. Stop high-intensity tuition when ordinary learning is sufficient again
A stop rule protects time and independence. The tutor should be able to explain what evidence triggered the stop and what higher-value task replaced it.
Exit criteria
- The original weak link is stable across changed questions.
- Important learning survives a delay.
- Mixed method recognition is reliable enough for the current stage.
- Working is clear and checkable.
- The student uses mathematical verification independently.
- One hard problem no longer destabilises later work.
- Prompt depth has fallen substantially.
- School learning is increasingly independent.
- Remaining needs are narrow enough for lighter support.
Internal eduKate routes
How to Improve Secondary 3 Mathematics with Bukit Timah Tuition
Bukit Timah IP Math Tutors | Integrated Advanced & Higher Mathematics from Year 1–4
Secondary Mathematics Tutor in Bukit Timah | Guiding Students to O-Level & IP Excellence
Final conclusion
IP Mathematics tuition improves when it respects the actual school programme while building mathematical depth that survives beyond it: algebraic fluency, representation, proof, non-routine transfer, retrieval and independent learning. Excellence teaching should make the student more portable, not more dependent.
The best improvement is visible when the student becomes more capable of running the Mathematics without the tutor supplying the route.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: retrieval
For retrieval, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: preview dependence
Audit preview dependence with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: JC/IB readiness
Treat JC/IB readiness as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: independent acquisition
For independent acquisition, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: retrieval
For retrieval, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: preview dependence
Audit preview dependence with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: JC/IB readiness
Treat JC/IB readiness as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: independent acquisition
For independent acquisition, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: retrieval
For retrieval, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: preview dependence
Audit preview dependence with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: JC/IB readiness
Treat JC/IB readiness as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: independent acquisition
For independent acquisition, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: retrieval
For retrieval, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: preview dependence
Audit preview dependence with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: JC/IB readiness
Treat JC/IB readiness as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: independent acquisition
For independent acquisition, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: retrieval
For retrieval, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: preview dependence
Audit preview dependence with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: JC/IB readiness
Treat JC/IB readiness as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: independent acquisition
For independent acquisition, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: retrieval
For retrieval, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: preview dependence
Audit preview dependence with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: JC/IB readiness
Treat JC/IB readiness as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: independent acquisition
For independent acquisition, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: school alignment
Audit school alignment with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: algebra
Treat algebra as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: functions/graphs
For functions/graphs, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: proof
Audit proof with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: generalisation
Treat generalisation as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: non-routine transfer
For non-routine transfer, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: retrieval
Audit retrieval with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: preview dependence
Treat preview dependence as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: JC/IB readiness
For JC/IB readiness, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: independent acquisition
Audit independent acquisition with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: school alignment
Treat school alignment as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: algebra
For algebra, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: functions/graphs
Audit functions/graphs with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: proof
Treat proof as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: generalisation
For generalisation, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: non-routine transfer
Audit non-routine transfer with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: retrieval
Treat retrieval as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: preview dependence
For preview dependence, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: JC/IB readiness
Audit JC/IB readiness with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: independent acquisition
Treat independent acquisition as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: school alignment
For school alignment, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: algebra
Audit algebra with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: functions/graphs
Treat functions/graphs as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.
Extended improvement audit: proof
For proof, evidence should lead directly to action. Parents should see why the issue deserves time, why the chosen intervention is better than generic practice and what transfer task will prove portability. This prevents endless drilling of already-stable skills.
Extended improvement audit: generalisation
Audit generalisation with one authentic first attempt. Identify the decision point, competing explanations for the error and the smallest task that can distinguish them. Repair only after the mechanism is clearer, then schedule a changed-question retest. The target is complete when the student can carry the decision with less prompting.
Extended improvement audit: non-routine transfer
Treat non-routine transfer as an observable system. Define what success looks like before instruction, after focused repair, after delay and under mixed conditions. If the student can now initiate, execute and verify independently, close the target and move lesson time to the next higher-value need.