Datasets:

creativedatalab
/

math-v1-sample

---
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.

	---
	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.