Blame for README.md

---
pretty_name: Learning Paths in Arithmetic and Early Algebra (sample)
license: other
license_name: creative-data-lab-dataset-license
license_link: https://creative-data-lab-production.up.railway.app/terms.html
language:
- en
task_categories:
- question-answering
- text-generation
tags:
- education
- tutoring
- synthetic
- misconceptions
- creative-data-lab
- math
- arithmetic
- algebra
size_categories:
- n<1K
configs:
- config_name: master
  data_files:
  - split: train
    path: master/records.jsonl
  default: true
- config_name: sft
  data_files:
  - split: train
    path: exports/sft.jsonl
- config_name: tutor
  data_files:
  - split: train
    path: exports/tutor.jsonl
- config_name: preference
  data_files:
  - split: train
    path: exports/preference.jsonl
- config_name: step_labels
  data_files:
  - split: train
    path: exports/step_labels.jsonl
---

# Learning Paths in Arithmetic and Early Algebra: free sample

*Creative Data Lab · 8 of 60 records from batch-001*

Learning paths through multi-digit arithmetic, integers and early algebra. Each record is a problem, one or two realistic wrong attempts tagged with a documented misconception, Socratic tutor feedback, and a correct worked solution.

This is a **free sample** so you can check the schema and quality. The full dataset is
[creativedatalab/math-v1](https://huggingface.co/datasets/creativedatalab/math-v1) (US$149 per organization, instant access after purchase at
[creative-data-lab-production.up.railway.app](https://creative-data-lab-production.up.railway.app/#datasets)).

## Load it

```python
from datasets import load_dataset

records    = load_dataset("creativedatalab/math-v1-sample", "master")       # full records (default)
sft        = load_dataset("creativedatalab/math-v1-sample", "sft")          # problem -> worked solution
tutor      = load_dataset("creativedatalab/math-v1-sample", "tutor")        # problem + wrong attempt -> guiding question
preference = load_dataset("creativedatalab/math-v1-sample", "preference")   # chosen / rejected pairs
steps      = load_dataset("creativedatalab/math-v1-sample", "step_labels")  # per-step labels, first error marked
```

## Files

| File | Sample rows | Full dataset |
|---|---:|---:|
| `master/records.jsonl` | 8 | 60 |
| `exports/sft.jsonl` | 8 | 60 |
| `exports/tutor.jsonl` | 9 | 64 |
| `exports/preference.jsonl` | 9 | 64 |
| `exports/step_labels.jsonl` | 16 | 120 |

## How it was made

- **Ground truth is computed by code.** Every problem comes from a parameterised template; the correct answer
  and each misconception's wrong answer are computed with sympy, never by a language model.
- **Text is written by an open-weight model**: `mlx-community/Qwen2.5-32B-Instruct-4bit` (Apache 2.0), which writes problem wording,
  student attempts, feedback and solution steps around the computed values.
- **Every record passed automated checks**: answer matches truth within 1%; each wrong attempt lands exactly on its
  misconception's predicted answer; feedback does not leak the answer; all arithmetic in the text recomputes;
  no LaTeX or formatting debris; no duplicate problems.
- **Human review**: 0 of 72 records reviewed so far.

Batch yield: 72 of 72 problems kept (66 on the first try).

## Coverage

| Topic | Records |
|---|---:|
| A Arithmetic and integers | 28 |
| B Early algebra | 32 |

| Rung | Records |
|---|---:|
| R2 Definition | 8 |
| R3 One step | 40 |
| R4 Multi step | 8 |
| R5 Transfer | 4 |

| Concept | Records |
|---|---:|
| A1 Addition with carrying | 4 |
| A2 Subtraction with borrowing | 4 |
| A3 Multi-digit multiplication | 4 |
| A4 Order of operations | 8 |
| A5 Adding and subtracting integers | 4 |
| A6 Multiplying integers | 4 |
| B1 Evaluating expressions | 4 |
| B2 Combining like terms | 8 |
| B3 Distributive property | 4 |
| B4 One-step equations | 4 |
| B5 Two-step equations | 4 |
| B6 Variables on both sides | 4 |
| B7 Word problems to equations | 4 |

| Misconception | Records |
|---|---:|
| MA01 Forgets to carry | 4 |
| MA02 Subtracts smaller digit from larger | 4 |
| MA03 Borrows without reducing the next column | 4 |
| MA04 Forgets the place-value shift | 4 |
| MA05 Works strictly left to right | 8 |
| MA06 Two negatives make a positive (in addition) | 4 |
| MA08 Negative times negative is negative | 4 |
| MA09 Coefficient next to variable means joining digits | 4 |
| MA11 Combines unlike terms | 8 |
| MA12 Distributes to the first term only | 4 |
| MA14 Moves a term without changing its sign | 4 |
| MA15 Undoes operations in the wrong order | 4 |
| MA16 Keeps the sign when moving a variable term | 4 |
| MA17 Translates 'less than' in reading order | 4 |

## Record schema (master)

`id`, `split`, `topic`, `concept_id`, `prereqs`, `rung` (R1 intuition → R5 transfer), `difficulty`,
`problem` (template, params, text, options), `ground_truth` (answer, unit, tolerance), `attempts`
(misconception_id, text, final_answer), `feedback`, `solution` (steps, final_answer), `provenance`
(generator, template version, seed, check results, human review).

## Step labels: how to read them

Correct solutions are labelled +1 at every step. For misconception attempts, the first step that reaches the
misconception's wrong answer, and every step after it, are labelled -1. Earlier steps are `null`: they are not
verified either way.

## Limitations

- Sample batch: 13 of 13 planned concepts, 60 training records.
- Multiple-choice stems are template-written, so wording repeats across records of the same template.
- Physics is checked by code; pedagogy (realism of attempts, quality of feedback) relies on human review.

## License

Problems are original, generated from in-house templates. Dataset license: per client agreement.

## License

Sample: [Creative Data Lab Dataset License](https://creative-data-lab-production.up.railway.app/terms.html), evaluation use. The full dataset
carries the same license for training and evaluation inside one organization.