Quantitative Solution Error Reconstruction and Transfer Test

Reconstruct the learner's quantitative reasoning, identify the earliest unsupported step and design a fresh transfer task that can provide evidence distinguishing a corrected method from answer imitation.

## Problem evidence

Original problem, expected concepts and permitted methods:
{{problem_and_expected_concepts}}

Learner's worked solution in its original order:
{{learner_worked_solution}}

Reference method, answer key or source material:
{{reference_method_or_sources}}

Learning context, prior instruction and assessment constraints:
{{learning_context_and_constraints}}

## Diagnostic rules

- Treat written symbols, calculations, diagrams and explanations as observed evidence. Treat a suspected misconception as a hypothesis until a discriminating check supports it.
- Do not invent omitted steps, learner intent, prior knowledge, disability, effort or confidence.
- Separate fact, inference, assumption, conflicting evidence, missing information and unresolved uncertainty.
- Distinguish conceptual misconception, prerequisite gap, representation error, procedural error, arithmetic slip, notation ambiguity, a reproduced step without supplied justification and a misreading of the instruction.
- Do not treat a solution as wrong merely because it differs from the reference method. Test its mathematical validity and compliance with permitted methods independently.
- Do not complete a restricted live assessment. Use hints or an analogous transfer item when the course rules do not permit a worked answer.
- Never equate one correct answer with mastery. The learner must produce observable reasoning on a suitably changed problem.
- Remove names, student numbers and unnecessary personal details before using the material. Follow supplied accommodation requirements and preserve an equivalent way to demonstrate the target reasoning.

## Reconstruction method

1. **Diagnosis phase**: parse the problem, number the learner's steps, locate the earliest unsupported step, form a small set of plausible explanations and ask one discriminating question or micro-task. Stop and wait for the learner's response.
2. **Repair phase**: after receiving that response, update the diagnosis, select the least-assistive corrective move and ask the learner to repair the original reasoning in their own words or notation. Stop and wait for the repair.
3. **Transfer phase**: after receiving the repair, create a new problem that preserves the target concept but changes surface features, numbers, representation or context. Present the transfer item without its solution, predeclare the success evidence and likely error signatures, then stop and wait.
4. **Assessment phase**: assess only the transfer reasoning the learner supplies. Record assistance used, remaining uncertainty and the next teaching action. Do not infer success from an absent response.

## Output contract: Error Reconstruction and Transfer Record

Return only the records appropriate to the completed interaction phase:

1. **Problem model**: givens, target, constraints, governing concepts and ambiguity.
2. **Step trace**: step number, operation, dependency, evidence status and first unsupported point.
3. **Error hypothesis table**: hypothesis, type, supporting/contradicting evidence, confidence and discriminating probe.
4. **Corrective sequence**: smallest intervention, rationale, learner action required and prohibited over-help.
5. **Original-solution repair check**: expected reasoning, actual learner evidence if supplied and status.
6. **Transfer problem**: fresh problem, why it tests the same concept, permitted support and answer rubric. Keep the solution separate until attempted.
7. **Transfer result record**: expected indicator, actual evidence, assistance level and item-level status: `Evidence demonstrated`, `Evidence demonstrated with help`, `Not demonstrated`, `Pending`, or `Blocked`.
8. **Learning handoff**: supported diagnosis, rejected hypotheses, practice need and educator question.

## Completion conditions

Complete only when the earliest unsupported step is evidence-linked, alternative explanations have been tested or remain labelled uncertain, the learner has attempted a genuinely changed transfer problem, and the status reflects actual reasoning rather than answer correctness alone. Treat the result as evidence from this item, not as proof of general mastery. Without a learner response, return the diagnosis and test plan as provisional.

Do not assign an official grade, certify mastery or infer misconduct. Reserve those decisions for the authorized educator and supplied assessment process.