PSLE Mathematics errors need different repairs. A wrong answer may come from a missing concept, a misread diagram, an unsuitable method, a procedural mistake, inaccurate arithmetic, a lost unit, misunderstood language or difficulty completing the work. Calling every error a careless mistake hides the decision that needs attention. A useful error analysis asks where the student’s working first stops matching the question.
This taxonomy of PSLE Mathematics errors gives parents, teachers and students a practical way to classify mistakes and choose the next teaching step. It separates nine useful categories, explains their overlaps, and supplies worked examples, follow-up questions and a reusable error log. The aim is not to attach a label to a child. It is to make the next piece of mathematics easier to teach accurately.
For Primary 6 mathematics revision, problem-solving practice and examination preparation, the central rule is simple: repair the earliest unsupported step, then check that the repair works on a changed question without the original help. A student who chose the right model but divided incorrectly needs a different response from a student who calculated perfectly using the wrong quantity. Both deserve an explanation more precise than “be careful”.
The 50-second route
Start with one wrong answer and keep the original working. Ask the learner to explain what each number represents. Find the first step that the question or mathematics does not justify. Choose a provisional category from the nine below, ask a small follow-up question that could challenge your diagnosis, and teach the identified gap. Finish with a new problem, not merely a copied correction.
For a quick correction: read the nine categories and the matching case. For a recurring pattern: use the error log and the two fictional learner profiles. For a lesson: use the teaching guide at the end. This is an eduKate teaching framework, not an official SEAB marking scheme, a standardised assessment or a diagnosis of a learning condition.
Open the contents
Evidence before labels · The nine categories · Worked diagnostic casebook · Overlapping errors · A useful error log · Two fictional learner profiles · Retesting and transfer · Questions parents ask · Sources and related learning · Teaching guide
1. Keep the evidence before choosing the label
A final answer tells you whether the response matches the expected result. It does not necessarily tell you how the student arrived there. The same wrong number can follow from several routes, while a correct number can occasionally come from a guess or two compensating mistakes. Begin with the question, the student’s actual working and the student’s explanation. Do not replace missing evidence with a confident story about what the child must have been thinking.
Ask a neutral question such as, “What were you trying to find in this line?” A leading question such as, “You forgot to find the remainder, didn’t you?” supplies the diagnosis before the learner has explained. The child may then agree without recognising the original issue. Neutral questions allow a surprising but valid method to emerge and make it easier to distinguish a misunderstanding from a copying slip.
Separate an observation from an interpretation. “The student used 500 as the base after 20% had left” is an observation. “The student does not understand percentages” is a much broader interpretation. A follow-up might show that percentages are understood but the word remainder was overlooked. Record the observation first; keep the interpretation provisional until a discriminating question supports it.
Assessment that informs teaching should identify what a learner knows and what needs further attention, not merely produce a total. The Education Endowment Foundation’s discussion of assessment in mathematics recommends combining tests with questioning, observation and other low-stakes evidence. Its guidance concerns mathematics teaching in England; the nine-category framework and examples here are eduKate’s teaching tools, not a framework validated by that source.
2. The nine categories at a glance
C — Concept: the underlying mathematical meaning is mistaken or missing. R — Representation: the learner misreads or builds a diagram, table, fraction, bar model or other mathematical form. M — Method: the selected relationship does not answer the question. P — Procedure: an appropriate method is carried out through an invalid step.
A — Arithmetic: a local calculation is wrong within an otherwise suitable method. U — Unit or quantity identity: the number loses its unit, referent or stage in the problem. L — Language: a relationship expressed in the wording is misunderstood. K — Checking: an available independent check is missing or ineffective. T — Timed execution: performance changes when pacing, completion and time constraints are added.
These are working categories, not mutually exclusive boxes. A representation error can begin with a concept error. An arithmetic slip can survive because checking was absent. Timed execution is often a condition surrounding another error rather than a separate mathematical cause. Use a primary code for the earliest supported break and, when helpful, a secondary code for what allowed it to pass unnoticed. The codes organise evidence; they do not replace it.
Concept errors: the meaning needs rebuilding
A concept error appears when the student’s rule conflicts with the mathematical relationship itself. Examples include treating 2:3 as two thirds of the combined total, believing that a longer decimal must be larger, or claiming that multiplication by a positive number always increases the starting quantity. These are not merely forgotten steps. The student’s explanation gives the wrong job to the notation or operation.
Ask for meaning before supplying a rule. Two parts to three parts make five equal parts altogether; the first quantity is therefore two fifths of the total. Multiplying eight by one half produces four because the operation takes half of eight. A picture, counters or a short number example can expose the contradiction. After rebuilding the meaning, remove the representation gradually and test whether the student can explain a different example.
Representation errors: the same relationship changes appearance
A learner may understand a relationship when it is spoken but lose it in a table or diagram. The bars in a ratio model might be unequal even though every unit should stand for the same amount. A graph interval might represent five items while the child counts each interval as one. A triangle’s sloping side might be used as its height without checking whether it is perpendicular to the selected base.
Move between two forms while keeping the meaning visible. Ask the learner to point to the quantity named by a sentence, then show that quantity in the diagram. If a bar stands for the total, identify the whole bar before labelling a fraction of it. The repair is not simply to copy a neater drawing. It is to explain what each part represents and why the relationship survives the change of form.
Method-selection errors: a correct operation answers the wrong question
Sometimes every calculation is accurate, but the chosen calculation finds something other than the requested quantity. A learner may subtract two lengths when asked how many times as long one is, calculate a perimeter when asked for area, or take a percentage of the original amount after the question has moved to the remainder. More arithmetic practice alone does not directly address this selection problem.
Pause before calculation. Ask, “What would this operation find?” Then compare it with the quantity requested. For a rectangle, adding the side lengths once each does not find the surface covered; it combines two different lengths. Ask the learner to predict the type of answer and its unit. A method should earn its place by matching the relationship, not because a familiar keyword or diagram triggered it.
Procedure errors: the route is suitable but a step is invalid
A procedure error occurs when the learner has selected an appropriate method but does not preserve the mathematical rules while carrying it out. In subtraction, a regrouping step may change one place without changing the adjacent place. In adding fractions, a denominator may be changed without the numerator being scaled. The student may know what is being sought but not yet control the transformations used to find it.
Make the vulnerable step visible and explain what must remain unchanged. Renaming one whole as ten tenths must preserve the number. Rewriting one half as three sixths must preserve the fraction’s value. Use a small worked example, then a partially completed example, then an independent one. When the learner explains why the step is valid, speed can develop from a reliable procedure rather than conceal a fragile one.
Arithmetic errors: a local calculation fails
Arithmetic errors include evaluating 64 divided by 8 as 7 or writing 7 multiplied by 8 as 54. However, classify cautiously. A wrong fact once is not proof that the learner lacks every related number fact. A copied digit, a skipped line and an incorrect calculation may look similar in the final answer. Ask the student to reconstruct the particular calculation before deciding what practice is needed.
A suitable repair might be a fact relationship, a written calculation, an estimate or an inverse check. Since eight groups of eight make sixty-four, 64 divided by 8 must be 8. If the result is 7, multiplying back rejects it. Practise the relationship that failed, then place it inside another problem. There is little value in restarting a correctly understood ratio model simply because a division within it was inaccurate.
Unit and quantity-identity errors: the number loses its meaning
A number needs a name. It might be the original number of students, the number remaining, the amount spent, the distance travelled or the area of one part. Writing “400 students remaining” gives the next step more protection than writing an isolated 400. A student can calculate successfully and still answer with the number who left when the question asks how many stayed.
Units also have mathematical jobs. Centimetres measure length, square centimetres measure area, and cubic centimetres measure volume. Adding 2 m and 35 cm requires compatible units: 200 cm plus 35 cm gives 235 cm, or 2.35 m. A repair should connect the unit to the quantity, not merely teach the learner to decorate the final answer with whichever symbol appeared in the question.
Language errors: the wording changes the relationship
Words such as remaining, altogether, more than, fewer than and each do not operate as automatic calculation buttons. “Ali has 18 more stickers than Ben” tells us a relationship. Whether we add or subtract depends on whose quantity is known and whose is required. A learner who circles more and always adds may know addition well while reading the relationship incorrectly.
Ask the student to restate the sentence, identify the larger quantity and show the comparison with a small example. Separate reading the problem from solving it. A spoken explanation or a simpler sentence can help reveal whether the obstacle is linguistic or mathematical. Do not lower the mathematical demand merely because the sentence needs unpacking; instead, make the relationship accessible and then return to the original wording.
Checking failures: an error survives its chance of detection
Checking is a second layer of protection. It does not explain every original mistake, but it can explain why an implausible answer was accepted. Repeating the same calculation with the same assumption may reproduce the same result. An independent check asks a different question: Does the answer fit the total? Does it satisfy the original comparison? Is the unit appropriate? Is the magnitude possible?
Choose a check that could actually expose the suspected error. Multiplying a division answer back tests the calculation. Substituting both quantities into the original total tests a ratio allocation. Comparing an area with the enclosing rectangle tests a geometry result. “Check everything again” is vague; “your two shares must add to sixty-four” gives the learner a specific condition the answer must satisfy.
Timed-execution errors: establish the comparison before naming the cause
A blank answer under time pressure does not establish that the student knew how to solve it. Equally, a solved example immediately after being shown a method does not establish independent readiness. To investigate timed execution, compare similar fresh questions under clearly described conditions, including whether prompts, a calculator or extra working time were available.
If a method is accurate independently but consistently slow, practise its vulnerable component and a sensible return-to-question routine. If the same relationship fails without a timer, teach it before increasing time pressure. Avoid interpreting one tired session as the child’s normal capacity. The purpose of a timed comparison is to identify a workable next step, not to assign a fixed identity such as “slow learner”.
3. Worked diagnostic casebook
All the examples below are constructed teaching examples, not reported student records or reproduced examination questions. Each case shows a proposed interpretation, a question that can test that interpretation and a complete mathematical correction. The follow-up questions are deliberately short so that a teacher can inspect one relationship without making the child complete another whole paper.
Case 1: the longer decimal
Student’s answer: 0.125 is larger than 0.8 because 125 is larger than 8. The explanation suggests a concept error: the digits after the point are being treated as an independent whole-number string. It is not enough to point at the correct answer. Ask the learner to describe both quantities in the same unit.
Correction: 0.8 is eight tenths, which is 800 thousandths. The other number is 125 thousandths. Therefore 0.800 is greater than 0.125. The added zeros do not make the number larger; they display an equivalent representation. A number line provides a second check because 0.8 lies much closer to one whole.
Discriminating follow-up: compare 0.41 and 0.405. The correct comparison is 0.410 greater than 0.405. Ask why, rather than accepting a lucky choice. If the learner says the longer decimal is smaller in every case, the repair has merely replaced one unreliable shortcut with another. Compare 0.41 and 0.415 next to expose that new shortcut.
Case 2: a ratio share mistaken for a fraction of the whole
Student’s answer: red counters and blue counters are in the ratio 2:3, so red counters are two thirds of all the counters. Ask the learner to build a small example with two red and three blue counters. There are five counters altogether, not three. This identifies what the denominator must count when the question concerns the whole collection.
Correction: the red share is 2 divided by 5, or two fifths of the total. If there are 30 counters altogether, five ratio units represent 30 counters. One unit is 6 counters, and red counters number 12. Check that the remaining 18 blue counters preserve 12:18 = 2:3 and that the two groups sum to 30.
Discriminating follow-up: in the same example, red is what fraction of blue? Now two thirds is correct because the denominator refers to the blue quantity, not the total. The two questions use the same numbers but different reference quantities. That contrast tests understanding more sharply than another total-sharing calculation with larger numbers.
Case 3: correct arithmetic applied to the wrong remainder
Problem: there are 500 participants. Twenty per cent leave. Twenty-five per cent of those remaining join an activity. Student’s working: 25% of 500 = 125. The multiplication is correct, but it answers a different question. The next investigation is whether the student missed the language or lost track of the changing population.
Correction: 20% of 500 is 100, so 400 remain. The activity takes 25% of 400, which is 100. Label each stage: original 500; left 100; remaining 400; activity 100. An independent check is that the activity takes one quarter of the remaining group, and four groups of 100 make 400.
Discriminating follow-up: ask for the final calculation after supplying “400 participants remain”. If the learner now finds 100 correctly, investigate reading or quantity tracking before reteaching percentage calculation. If the learner still cannot find a quarter of 400, the underlying proportion calculation also needs attention. The same original response can therefore lead to different lesson choices.
Case 4: a right ratio model with a wrong division
Problem: A:B = 3:5 and the total is 64. Student’s working: eight units equal 64; one unit equals 7; B equals 35. The total-unit model is appropriate. The first visible invalid step is 64 divided by 8 equals 7. A provisional arithmetic code is more precise than deciding that the whole topic of ratio is missing.
Correction: one unit equals 8. A is 3 multiplied by 8, or 24. B is 5 multiplied by 8, or 40. Check the total: 24 plus 40 equals 64. Check the ratio: 24:40 simplifies to 3:5. These two checks inspect different parts of the answer and together give better protection than repeating only the multiplication for B.
Discriminating follow-up: change the total to 72 while keeping 3:5. The correct shares are 27 and 45. Ask the learner to explain why there are still eight units before dividing. A correct division without the unit explanation would not, by itself, establish that the representation remained secure.
Case 5: a fraction procedure that changes the quantities
Student’s working: one half plus one third equals two fifths. Ask the learner to draw or describe half of one whole and a third of the same-sized whole. Their sum must exceed a half because a positive quantity is being added. Two fifths is less than one half, so the proposed answer fails a magnitude check before any algorithm is discussed.
Correction: use equal-sized sixths. One half equals three sixths; one third equals two sixths. Their sum is five sixths. The denominator names the unit being counted, while the numerator tells how many such units there are. Adding the numerators works only after the fractions have been expressed using the same unit.
Discriminating follow-up: ask for one half plus one sixth. The answer is four sixths, or two thirds. Ask what stayed unchanged when one half became three sixths. If the learner can execute the common-denominator procedure but cannot explain equivalence, record both the procedural success and the conceptual support still required.
Case 6: metres and centimetres added as bare numbers
Student’s working: 2 m plus 35 cm equals 37 cm. This combines the printed numbers without preserving their units. Ask how many centimetres are in the two-metre length. A correct response of 200 cm suggests that the conversion is known but was not activated. An incorrect response calls for work on the unit relationship itself.
Correction: 2 m = 200 cm, so the combined length is 235 cm. In metres, 35 cm = 0.35 m and the sum is 2.35 m. Both forms describe the same length. A simple reasonableness check rejects 37 cm because adding a positive length to 2 m cannot produce a total shorter than 2 m.
Discriminating follow-up: compare 1.4 m with 135 cm. Expressing both in centimetres gives 140 cm and 135 cm, so 1.4 m is longer by 5 cm. This checks whether the conversion can support a comparison as well as an addition. Keep the unit attached to the difference, too.
Case 7: “more than” used as an automatic addition instruction
Problem: Ali has 18 more stickers than Ben. Ali has 50 stickers. How many does Ben have? Student’s answer: 50 + 18 = 68. Ask who has more. If the learner says Ben, the relationship has been reversed in reading. If the learner says Ali but still gives Ben 68, ask whether the proposed numbers satisfy the sentence.
Correction: Ben has 50 − 18 = 32 stickers. Substituting back gives Ali’s 50 as 18 more than Ben’s 32. The check reads the original sentence rather than trusting a keyword rule. This is especially useful because the arithmetic in the wrong answer was not the source of the difficulty.
Discriminating follow-up: keep the sentence but say that Ben has 50 stickers and ask for Ali’s number. Now 68 is correct. The change in the known quantity changes the operation without changing “more than”. Ask the learner to explain this contrast in words before giving a third problem.
Case 8: a triangle calculation with two errors
Problem: a triangle has base 12 cm and perpendicular height 5 cm. Student’s answer: 12 × 5 = 60 cm. Two visible issues are present: the area calculation omits the factor one half, and the final unit describes length rather than area. Ask the learner to explain how two congruent copies of the triangle relate to a parallelogram.
Correction: the area is one half multiplied by 12 multiplied by 5, or 30 cm². The parallel-sided comparison shape with the same base and perpendicular height has area 60 cm²; one of the two triangles occupies half that area. Correcting only the unit to cm² would leave the numerical result wrong.
Discriminating follow-up: use base 10 cm and perpendicular height 7 cm. The answer is 35 cm². Then change the orientation of the triangle without changing its dimensions. The student should identify the corresponding perpendicular height rather than choose whichever side happens to look upright on the page.
Case 9: a remainder that answers a different practical question
Problem: 38 children travel in vehicles that each hold at most 6 children. How many vehicles are needed? Student’s working: 38 ÷ 6 = 6 remainder 2; answer 6 vehicles. The division is suitable and the calculation is accurate. The break happens when the mathematical result is interpreted for the practical requirement that every child needs a place.
Correction: six vehicles carry at most 36 children. Two children still require space, so seven vehicles are needed. The extra vehicle need not be full. A useful check is to test the proposed capacity: 6 × 6 = 36 is insufficient, while 7 × 6 = 42 provides enough places.
Discriminating follow-up: ask how many complete groups of six can be made from 38 children, leaving any others ungrouped. Now six complete groups is correct. The same division supports a different final answer because the requested quantity has changed. This is an interpretation problem, not evidence that division itself must be retaught.
Case 10: an apparently difficult question that was never reached
Observation: a final multi-step question is blank. There is no evidence yet that the method was unknown, known or forgotten. Ask whether the learner reached the question and inspect the pacing record, if one exists. An answer such as “I could have done it” should be tested gently with a comparable fresh task rather than accepted or dismissed automatically.
Diagnostic comparison: first offer a fresh problem of similar structure without a tight time limit and without teaching the method. Record the working and any help given. On another occasion, use a comparable problem in a short timed set. These are not perfectly controlled experiments: the questions and the student’s condition may differ. They provide clues, not a numerical measure of intelligence.
Repair decision: if the underlying method fails in both conditions, teach it. If it works independently but the set remains unfinished, investigate lengthy working, repeated checking, delayed starts or poor decisions about returning to resistant questions. Choose one observable behaviour to practise. More time pressure is not a substitute for finding out what used the time.
4. When several categories fit, do not force a false choice
A student can misunderstand the word remainder and then use the wrong percentage base. Language and quantity tracking are both plausible descriptions. The useful question is which small intervention changes the performance. If a neutral paraphrase resolves the difficulty, language may be the most productive initial teaching target. If the learner still applies the percentage to the wrong group after explaining the sentence correctly, the quantity-state representation needs attention.
The categories are not a competition. It is acceptable to record “L/U — needs another probe” rather than pretend to know more than the work reveals. Teachers should also consider alternative valid methods. A line can look unusual because the learner has combined two steps mentally. Ask for the missing reasoning before marking the line as an error. Diagnosis requires understanding the student’s route, not forcing every solution into the teacher’s preferred layout.
Checking generally belongs after the initiating error in the record. A wrong ratio division might be recorded as “A, then K: inverse check absent”. This preserves the distinction between the mistake and the missed chance to detect it. It also prevents an unfair conclusion that every error exists because the student did not check hard enough. The first teaching task remains the mathematical relationship that failed.
5. Build an error log that changes the next lesson
A useful log can fit on one page. Record the date and task, the original incorrect step, the provisional category, the evidence supporting it, the follow-up question, the correction and the result of a later independent attempt. Add the support level: no help, general prompt, specific prompt or worked example. A correct response after a worked example is useful progress, but it should not be recorded as independent performance.
For the ratio case, a completed record might read: “3:5 total 64; wrote one unit = 7; provisional arithmetic error; explained eight total units correctly; follow-up 72 ÷ 8 correct; practised multiplying back; next independent sharing problem correct.” This entry says much more than “ratio mistake corrected”. It specifies what went wrong, what stayed secure and what evidence supports moving on.
Keep the log small enough to use. Do not transcribe an entire paper into a database that nobody revisits. Select recurring mechanisms, prerequisite gaps and errors that substantially alter the solution. The purpose is to choose teaching, not accumulate labels. A one-line entry followed by a meaningful retest is more useful than a colourful chart that records twenty mistakes but never changes the next question.
Do not double-count a chain of consequences as several independent weaknesses. If the wrong remaining total feeds three later calculations, record the initiating quantity-state error and note its downstream effects. The later arithmetic may be entirely sound given the mistaken starting value. The marking scheme may allocate marks across those steps, but your teaching diagnosis should not confuse the number of affected lines with the number of separate concepts requiring repair.
6. Two fictional profiles: similar marks, different next lessons
Profile A: a learner loses marks on a ratio question, a percentage question and a measurement question. The initial impression is broad topic weakness. Looking at the working reveals appropriate models in all three, but one incorrect division, one transposed number and one missing unit. Short follow-ups show that the relationships are understood. The next lesson can target the calculation and recording steps without repeating every chapter from the beginning.
For this learner, use a few carefully selected calculations inside short problems. Require intermediate quantity labels and one relevant independent check. Observe whether the learner actually uses the check rather than merely writes a reminder at the top of the page. A successful practice session would show accurate independent working across changed questions, not simply a promise to be more careful next time.
Profile B: another learner receives a similar total but calculates accurately throughout. The ratio is interpreted as a fraction of the wrong whole, the percentage uses the original quantity rather than the remainder, and the measurement answer finds the amount removed rather than the amount left. Arithmetic fluency practice would miss the shared problem: the quantities and reference relationships are not being kept stable.
For this learner, temporarily reduce the arithmetic burden. Use small numbers, spoken restatements, labelled bars and questions asking only for the next justified operation. Then rebuild full solutions. The aim is not to make the work permanently easier. It is to reveal and repair the relationship-selection problem before calculation distracts from it. These fictional profiles illustrate instructional choices; they do not establish how common either pattern is.
7. A correction is not yet evidence of transfer
Copying a correct solution demonstrates that the learner can reproduce what is visible. Solving the same question immediately after a demonstration shows more, but the route may still be held in short-term memory or supplied by the surrounding context. A stronger check changes something meaningful: the numbers, wording, representation, requested quantity or position of the unknown.
Change one feature at first so that an error remains interpretable. In the sticker comparison, swap which person’s amount is known while retaining the same relationship. In the ratio example, ask about a fraction of the other group rather than a fraction of the total. Later, combine variations in a short mixed set. Removing the chapter heading tests whether the student can choose the method without being told which topic to use.
A later check also matters, but there is no universal interval that proves mastery for every child and every skill. Choose a later lesson or a suitable independent practice opportunity, record the conditions, and inspect the result. If the error returns, reduce support thoughtfully and revisit the missing relationship. Do not treat one successful retest as a permanent guarantee, or one later slip as proof that no learning occurred.
8. Questions parents and students ask
Should we stop using the phrase careless mistake?
You do not need to police every phrase. The problem is using careless as the end of the explanation. Translate it into something observable: a digit was copied wrongly, a unit was omitted, the question’s final instruction was not answered, or a regrouping step was skipped. An observable description points towards a check or teaching action. A personality label does not.
How many errors should we repair in one session?
Use the learner’s available attention and the complexity of the repair, rather than a fixed quota. One foundational misunderstanding can deserve a whole short session. Several isolated transcription slips may be addressed together through a recording routine. End with a task the learner attempts independently so that the session supplies evidence, not just explanations delivered by the adult.
Does a correct multiple-choice answer prove understanding?
Not by itself. The learner might understand, guess, eliminate options partially or make two mistakes that happen to cancel. Ask for the relationship and then change a relevant feature of the question. Equally, a wrong selected option does not reveal a unique misconception. Treat the option as a clue that helps choose a follow-up, not as a complete account of the child’s thinking.
What should we do when the child cannot explain the original working?
Do not manufacture a diagnosis. Record that the route is unknown and use a small fresh problem to observe the thinking directly. Some learners explain more clearly through a drawing, objects or a demonstration than through an immediate verbal account. Keep the mathematical demand visible while allowing an accessible way to show the relationship. Ask the class teacher for support when a difficulty persists across teaching and contexts.
9. Official references and related learning
For examination requirements, use SEAB’s PSLE formats examined in 2026 and choose the relevant Standard or Foundation Mathematics document. This guide does not replace those documents or prescribe official mark allocation. Its examples are teaching examples, and practice should be matched to the learner’s course and school teaching sequence.
For the distinction between a mistake and a persistent misconception, the EEF’s discussion of learning from mathematical mistakes provides further professional reading. Its mathematics guidance for Key Stages 2 and 3 supplies broader teaching context. These references support careful assessment and teaching; they do not certify this particular taxonomy or promise a specific examination gain.
Within eduKateSG, continue with Decimal Place Value to Thousandths Without Digit-Position Errors for decimal meaning, Building a Reliable Checking Routine for PSLE Mathematics for independent checks, and Primary 6 Mixed-Topic Transfer Diagnostic for choosing a method without a chapter cue. Those pages teach the next steps; this page helps identify which next step is needed.
Teaching guide: from one wrong answer to one justified next step
Choose a recent piece of work that the learner is willing to discuss. Begin with a correct part of the reasoning so that the conversation distinguishes what is secure from what needs repair. Then examine one unsupported step. Ask for its intended quantity, listen to the explanation and choose a provisional category. Avoid turning the exercise into a rapid interrogation about every lost mark.
Prepare two follow-up questions before teaching. The first should help distinguish your leading explanation from another plausible one. The second should test the repaired relationship with a changed feature. For a remainder-percentage error, you might first supply the correct remaining total to check percentage calculation, then present a new story requiring the learner to identify that total independently.
Teach only what the evidence currently supports. Demonstrate the missing relationship, ask the learner to complete part of a related example, then remove the support for the independent check. Record whether the final task was completed without hints. A correct answer after a specific reminder is not a failure, but the reminder is part of the evidence and should remain visible in the record.
Close with a sentence the learner can use: “My first wrong step was ____. It did not fit the question because ____. Next time I will check ____.” Revisit the relationship in a later suitable task. The outcome to seek is not a page with every correction copied neatly. It is a student who can recognise the relevant quantities, choose a justified method, carry it out and notice when the result does not fit.