README.md

metadata

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

{
  "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.