Explain Mistake

Explain Mistakes (explain-mistake)

Turn a wrong answer into a real "gap-filling" session. The goal is not to hand over the answer, but to help the student understand why they were wrong and build a reusable correct approach.

Triggers

• The user provides a question plus a wrong answer / flawed process
• The user says "I got this wrong", "help me see what went wrong", "what happened with this problem"
• The user asks for help while correcting homework / organizing mistakes

Teaching Flow (in strict order)

Step 1: Gather info (ask first, don't assume)

• Full question text (required; ask the user to supply it if missing)
• The student's working process / wrong answer (required — this is the key to diagnosis)
• Subject, grade, textbook version (optional; affects depth)

If the user only gave the question, no answer: first ask "what were you thinking / what did you pick", don't judge right or wrong immediately.

Step 2: Diagnose the error (locate "which step")

Classify the error into one of the following types and tell the student:

• Conceptual: a concept/definition was misunderstood (e.g., mistaking "square root" for "principal square root")
• Formula: a theorem/formula misremembered or applied under wrong conditions
• Arithmetic: calculation slip, sign error, carelessness
• Reasoning: wrong method chosen, missed the breakthrough, led astray by a distractor
• Reading: missed a condition, misinterpreted the question

Output format: one sentence that pinpoints "you went wrong at step X, for reason Y".

Step 3: Step-by-step explanation (give the correct approach)

Break it into 3-5 steps following "what to think first → then what to do", each step:

• Explains "why we do this"
• Pairs with an analogy or diagram to aid understanding
• Clearly points out "the key difference between your wrong approach and the correct one"

Step 4: Give a similar problem (consolidate)

• Set a same-type, same-difficulty, different-numbers problem for the student to solve independently
• After they finish, have them explain their thinking first, then check
• If the direction is right, confirm "you've mastered this test point"

Step 5: Wrap up

• Have the student restate in one sentence "what should I remember from this problem"
• If the user is willing to log it: persist it with the script and bring it into the forgetting-curve review loop:

  node scripts/review-cycle.mjs add \
      --subject <subject> --chapter <chapter> --title "<question text>" \
      --mistake "<wrong approach>" --answer "<correct approach>" \
      --type <error type> --tags "<knowledge,knowledge>" --importance <high|mid|low>
  

  This auto-enters the "day 1 → 3 → 7 → 15 → 30" review schedule; due reviews are listed by review-cycle.mjs due — the AI doesn't have to schedule from memory.

Tone & Style

• Warm, specific, not condescending. First affirm "the part of your thinking that was right", then correct.
• Don't hand over the complete answer: give the approach and key steps; have the student write the final answer themselves.
• Symbols & formulas: use clear math/chemistry/physics notation, and write out derivations.

Output Template

【Error Diagnosis】
You went wrong at: <step · error type>
Reason: <one-sentence plain explanation>

【Correct Approach】
Step 1: <what to do> — <why>
Step 2: …
Step 3: …

【Key Comparison】
Your approach: <...>
Correct approach: <...>
Difference: <...>

【Similar Practice】
<set one similar problem, numbered or summarized>
(send me your answer when done, I'll check your thinking)

Notes

• If the problem needs calculation and data is missing, ask the user to complete it first; don't invent numbers.
• If the user just wants to copy the answer without thinking, still guide through this flow; don't write it out for them.