Rubric for Grading a Mathematical Proof
A proof-grading rubric covering logic, rigour, structure and notation.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Open any free AI chat.
- 2. Paste the full prompt below.
- 3. Enter the theorem or statement and total marks.
- 4. Send and read the rubric.
- 5. Use it to mark every student's proof the same way.
🔧 If it is not right, reply with this: If it rewards the answer more than the reasoning, reply: "This is a proof, not a calculation. Shift more weight to logical justification and rigour, and reduce marks for merely stating the result."
THE PROMPT
ROLE: Act as a university-level mathematics professor and olympiad proof-grader.
CONTEXT: I teach Class [CLASS/GRADE] / [BOARD or EXAM e.g. JEE Advanced / Olympiad / ICSE]. I am grading students' written PROOFS, where correct reasoning matters more than the final line. I need a rubric that rewards rigour and logic, not lucky guesses.
YOUR TASK:
1. Restate the proof task cleanly.
2. Write a correct, rigorous model proof yourself.
3. Build a rubric out of [TOTAL MARKS] with criteria suited to proofs, such as: correct setup and assumptions, logical flow and justification of each step, completeness (no gaps or hand-waving), correct use of theorems with conditions checked, clarity of notation, and valid conclusion.
4. Define what counts as a fatal gap that caps the score, versus a minor slip.
5. State how to score a proof that is correct in idea but missing justification.
INPUT: Here is the statement to be proved: [PASTE THE STATEMENT OR THEOREM HERE]. Total marks: [TOTAL MARKS].
HOW TO WORK IT OUT: Construct the model proof internally first. VERIFY it by two independent checks (for example, test the conclusion on a specific case, and confirm every theorem used has its conditions satisfied). Never invent theorems or skip conditions. Keep all mathematics fully legible in clean LaTeX or clear plain text. Ensure the criterion marks add to exactly [TOTAL MARKS].
OUTPUT FORMAT, in this exact order:
1. STATEMENT TO PROVE (clean restatement).
2. MODEL PROOF (rigorous, step by step, with conditions checked).
3. PROOF RUBRIC TABLE: Criterion | What earns the marks | Marks, with a TOTAL row equal to [TOTAL MARKS].
4. FATAL-GAP LIST: errors that cap the maximum achievable score, and the cap.
5. PARTIAL-CREDIT GUIDE: how to score right-idea-but-incomplete proofs.
6. VERIFICATION NOTE: the two checks you used and that they agree.
RULES: Penalise hand-waving and unjustified jumps. Do not give full marks for a correct final statement with a flawed argument. If the statement is false or needs an added condition, say so clearly at the top before grading.
OUTPUT FILE FORMAT: present the complete result as a clean, ready-to-use document I can paste straight into Microsoft Word or Google Docs - a clear bold title, section headings, neatly numbered items, comfortable spacing, and simple tables only where helpful (avoid heavy formatting that breaks on paste). It must also print cleanly to PDF on A4 (File > Print > Save as PDF). Keep all mathematics fully readable (fractions as a/b, powers as x^2, roots as sqrt(x)).
FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes.
MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.
GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.
SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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Questions, feedback or appreciation are always welcome.
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