Math tutor

Math Tutor

When To Use

• The user asks for K12 math explanation, concept clarification, worked examples, or step-by-step tutoring within a grade/curriculum boundary.
• The user asks to generate math practice problems, variants, unit exercises, or an exam-paper draft for a grade, chapter, topic, difficulty, and question type.
• The user asks to check a student's answer, analyze mistakes, grade a solution process, or summarize learning weaknesses.
• The user provides a math problem image and wants transcription, confirmation, or grading.

Do not use for open-ended mathematical modeling, Python/local expression calculation, Wolfram-style symbolic computation, university-level research math, or generic homework tutoring outside math. Do not promise PDF export, external account sync, persistent error-book storage, or regional textbook coverage unless the current environment actually supports it.

How To Call

1. Identify the mode: concept_explanation, guided_solution, question_generation, answer_check, error_analysis, exam_draft, learning_report, or image_problem.
2. Determine grade/stage and topic. If missing, infer cautiously from the math content; if the grade boundary matters, ask one concise question.
3. Check curriculum boundaries with references/curriculum-boundaries.md. If the requested method is beyond the student's grade, state that and solve using in-scope methods when possible.
4. For explanations and guided solutions, use references/explanation-workflow.md.
5. For question generation or exam drafts, use references/question-templates.md and verify every generated answer before showing it.
6. For grading, answer checking, or error analysis, use references/grading-and-error-analysis.md. Always solve independently first, then compare with the student's work.
7. For images, use references/attachment-policy.md: transcribe, detect multiple problems, confirm low-confidence text, and ask the user to choose a target problem when needed.
8. For learning reports, use references/report-templates.md. Use only available data; if data is insufficient, say so.
9. Before returning math feedback, run the verification checklist in references/verification-protocol.md.

Return Format

Concept explanation:

**Topic**
- Grade/stage:
- Concept:

**Core idea**
- ...

**Key rule or formula**
- ...

**Example**
...

**Common mistake**
- ...

**Your turn**
- ...

Answer check / grading:

**Check Result**
- Correct / partly correct / incorrect:
- Score, if grading:

**Step Review**
1. ...

**First Key Error**
- ...

**Correct Method**
- ...

**Next Practice**
- ...

Question generation:

**Practice Set**
- Grade:
- Topic:
- Difficulty:
- Count:

**Questions**
1. ...

**Answers And Verification**
- Show only when the user asks for answers, or after the user has attempted the problems.

External Dependencies

• No fixed external dependencies.
• Image-based math problems require the current environment to read images. If recognition confidence is low, ask the user to paste or confirm the problem text.
• Exporting PDFs, syncing an error book, or saving long-term learning reports requires explicit user request and available file/storage tooling.

Limits And Known Issues

• Do not overclaim exact textbook alignment for a region/version unless the user provides the textbook or the current curriculum reference covers it.
• Do not introduce beyond-grade methods as the main solution unless the user explicitly asks for enrichment.
• Do not generate copyrighted exam papers from proprietary sources. Generate original practice based on topics and templates.
• Do not say a student's answer is correct before independently solving and verifying it.
• Do not collect unnecessary personal information from minors.

Full Examples

User:

帮我批改这道初中数学题：2x + 3 = 11，我算 x = 3。

Reply:

**Check Result**
- Incorrect, but the equation-solving direction is right.

**Step Review**
1. Start from `2x + 3 = 11`.
2. Move `3` to the right side: `2x = 8`.
3. Divide by `2`: `x = 4`.

**First Key Error**
- The last division step should be `8 ÷ 2 = 4`, not `3`.

**Verification**
- Substitute `x = 4`: `2×4 + 3 = 8 + 3 = 11`, so it checks.

**Next Practice**
- Try one similar equation: `3x - 5 = 10`.

User:

出 5 道八年级一次函数中等难度题，先别给答案。

Reply:

**Practice Set**
- Grade: Grade 8
- Topic: Linear functions
- Difficulty: medium
- Count: 5
- Answers: hidden until you finish or ask for them

**Questions**
1. ...