| --- |
| pretty_name: Math-HQ-20k |
| language: |
| - en |
| license: mit |
| size_categories: |
| - 10K<n<100K |
| task_categories: |
| - text-generation |
| - question-answering |
| tags: |
| - math |
| - reasoning |
| - synthetic |
| - instruction-tuning |
| - algebra |
| - combinatorics |
| - geometry |
| - number-theory |
| - discrete-math |
| - verification |
| --- |
| |
| # Math-HQ-20k |
|
|
| A curated synthetic dataset of 20,000 English-language math reasoning examples designed for supervised fine-tuning, reasoning evaluation, and error-analysis workflows. |
|
|
| Each record contains a problem statement, one or more solution paths, a consistency reconciliation, a catalogue of plausible mistakes, and a short conceptual takeaway. |
|
|
| ## Dataset summary |
|
|
| - **Records:** 20,000 |
| - **Topics:** 120 |
| - **Difficulty levels:** 1–10 |
| - **Format:** JSONL |
| - **Language:** English |
| - **License:** MIT |
| - **File size:** ~72.2 MB |
|
|
| ## What is inside |
|
|
| Each example includes: |
|
|
| - `id` — unique row identifier |
| - `topic` — topic label |
| - `difficulty` — integer difficulty rating from 1 to 10 |
| - `problem_statement` — the task prompt |
| - `solution_paths` — multiple worked solution methods |
| - `reconciliation` — cross-check and robustness notes |
| - `error_catalogue` — plausible mistakes and why they are wrong |
| - `conceptual_takeaway` — short summary of the key idea |
|
|
| ## Technical specifications |
|
|
| | Metric | Value | |
| |---|---:| |
| | Total examples | 20,000 | |
| | Unique topics | 120 | |
| | Difficulty range | 1 to 10 | |
| | Difficulty distribution | 2,000 examples per level | |
| | JSONL validity | 100% parse success | |
| | Top-level field completeness | 100% | |
| | Exact prompt duplicates | 0 | |
| | Average problem length | 63.1 words | |
| | Median problem length | 62 words | |
| | Average solution content | 88.5 words | |
| | Average reconciliation content | 68.1 words | |
| | Average solution paths per item | 2.04 | |
| | Items with 2 solution paths | 19,298 | |
| | Items with 3 solution paths | 702 | |
| | Average error entries per item | 2.88 | |
|
|
| ## Schema |
|
|
| ```json |
| { |
| "id": "math-000001", |
| "topic": "Elementary Algebra: Linear Equations — Inverse Operations", |
| "difficulty": 1, |
| "problem_statement": "...", |
| "solution_paths": [ |
| { |
| "method_name": "Inverse Operations", |
| "approach": "...", |
| "steps": ["...", "..."], |
| "final_answer": "..." |
| } |
| ], |
| "reconciliation": { |
| "consistency_check": "...", |
| "robustness_analysis": "..." |
| }, |
| "error_catalogue": [ |
| { |
| "error_description": "...", |
| "why_plausible": "...", |
| "why_wrong": "...", |
| "which_method_catches_it": "..." |
| } |
| ], |
| "conceptual_takeaway": "..." |
| } |
| ``` |
|
|
| ## Intended use |
|
|
| This dataset is suitable for: |
|
|
| - supervised fine-tuning on step-by-step mathematical reasoning |
| - multi-solution reasoning behavior |
| - answer verification and self-check training |
| - error detection and correction tasks |
| - curriculum-style difficulty experiments |
|
|
| ## Notes |
|
|
| The dataset is synthetic and intentionally structured for reasoning quality. |
|
|
| Most examples contain more than one solution path to support comparison and verification. |
|
|
| The error catalogue is designed to model common student and model mistakes. |
|
|
| The prompts are intentionally consistent in style to make reasoning supervision easier. |
|
|
| ## Limitations |
|
|
| The dataset is not a collection of real-world student work. |
|
|
| The writing style is intentionally template-like, which may reduce natural-language diversity. |
|
|
| The dataset focuses on mathematical reasoning and does not aim to cover general open-domain QA. |
|
|
| ## Citation |
|
|
| If you use this dataset, please cite it as: |
|
|
| Math-HQ-20k. Synthetic JSONL dataset for supervised mathematical reasoning and verification. |
