---
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.