id string | split string | topic string | concept_id string | prereqs list | rung string | difficulty string | problem dict | ground_truth dict | attempts list | feedback list | solution dict | provenance dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
math-v1-A1-R3-133df093 | train | A | A1 | [] | R3 | medium | {
"template_id": "A1-R3-add-carry",
"params": {},
"text": "Compute 266 + 482.",
"options": null
} | {
"answer": 748,
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA01",
"text": "First, I added the ones: 6 + 2 = 8, and wrote down 8. Next, I added the tens: 6 + 8 = 14, and wrote down 4. Finally, I added the hundreds: 2 + 4 = 6, and wrote down 6. So, I got 648.",
"final_answer": 648
}
] | [
{
"for_attempt": 0,
"text": "When you added the tens, did you notice that the result was over 10? What do you think happens to the extra 10 when you're adding?"
}
] | {
"steps": [
"First, I added the ones: 6 + 2 = 8, and wrote down 8.",
"Next, I added the tens: 6 + 8 = 14, wrote down 4, and carried over 1.",
"Then, I added the hundreds: 2 + 4 + 1 = 7, and wrote down 7.",
"So, the answer is 748."
],
"final_answer": 748
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 1,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-A2-R3-87cfbe93 | train | A | A2 | [
"A1"
] | R3 | medium | {
"template_id": "A2-R3-subtract-borrow",
"params": {},
"text": "Compute 496 − 109.",
"options": null
} | {
"answer": 387,
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA02",
"text": "I subtracted the smaller digit from the larger in each column. Ones: 9 − 6 = 3. Tens: 9 − 0 = 9. Hundreds: 4 − 1 = 3. So, the answer is 393.",
"final_answer": 393
},
{
"misconception_id": "MA03",
"text": "I borrowed in the ones place and added 10, so 16... | [
{
"for_attempt": 0,
"text": "When subtracting, do we always subtract the smaller number from the larger one, or does the order of the numbers matter? Can you check with a simpler example like 12 − 9?"
},
{
"for_attempt": 1,
"text": "When you borrowed from the tens column, did you remember to red... | {
"steps": [
"Ones: borrow, 16 − 9 = 7",
"Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8",
"Hundreds: 4 − 1 = 3",
"So, 496 − 109 = 387"
],
"final_answer": 387
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 2,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-A3-R3-4b9b2ab3 | train | A | A3 | [
"A1"
] | R3 | medium | {
"template_id": "A3-R3-multiply-two-digit",
"params": {},
"text": "Compute 83 × 71.",
"options": null
} | {
"answer": 5893,
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA04",
"text": "I started by multiplying 83 by 1, which gives 83. Then, I multiplied 83 by 7, which gives 581. Finally, I added 83 and 581 to get 664.",
"final_answer": 664
}
] | [
{
"for_attempt": 0,
"text": "When you multiply by the tens digit, do you remember to shift the place value? How would that change your calculation?"
}
] | {
"steps": [
"First, I multiplied 83 by 1, which gives 83.",
"Then, I multiplied 83 by 70, which gives 5810.",
"Next, I added 83 and 5810, which gives 5893.",
"So, the final answer is 5893."
],
"final_answer": 5893
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 2,
"gen_attempt": 2,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-A4-R2-13473d44 | train | A | A4 | [
"A1",
"A3"
] | R2 | easy | {
"template_id": "A4-R2-which-first",
"params": {},
"text": "In the expression 25 − 6 × 7, which operation should be done first?",
"options": [
"A) 6 × 7, because multiplication comes before addition and subtraction.",
"B) 25 − 6, because we always work from left to right."
]
} | {
"answer": "A",
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA05",
"text": "I always do operations from left to right, so I'll start with 25 − 6 first. Then I'll move on to the rest. So I pick B.",
"final_answer": "B"
}
] | [
{
"for_attempt": 0,
"text": "What do the order of operations (PEMDAS) tell us about multiplication and subtraction?"
}
] | {
"steps": [
"First, handle multiplication before subtraction according to the order of operations.",
"Calculate 6 × 7 to get 42, then subtract this from 25.",
"The correct answer is A."
],
"final_answer": "A"
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 1,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-A5-R3-20854100 | train | A | A5 | [
"A2"
] | R3 | medium | {
"template_id": "A5-R3-add-negatives",
"params": {},
"text": "Compute (−10) + (−9).",
"options": null
} | {
"answer": -19,
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA06",
"text": "I think when you add two negative numbers, the negatives cancel out and you get a positive. So, (−10) + (−9) should be the same as 10 + 9, which gives me 19.",
"final_answer": 19
}
] | [
{
"for_attempt": 0,
"text": "Can you give an example where adding two negative numbers results in a positive number? How does that affect the idea that two negatives make a positive in addition?"
}
] | {
"steps": [
"Start with (−10) + (−9).",
"Adding two negative numbers means moving further to the left on the number line.",
"So, (−10) + (−9) = −19.",
"The final answer is −19."
],
"final_answer": -19
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 3,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-A6-R3-11517438 | train | A | A6 | [
"A3",
"A5"
] | R3 | medium | {
"template_id": "A6-R3-multiply-negatives",
"params": {},
"text": "Compute (−8) × (−2).",
"options": null
} | {
"answer": 16,
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA08",
"text": "I think when I multiply two negative numbers, the answer should be negative. So, (−8) × (−2) should be −16.",
"final_answer": -16
}
] | [
{
"for_attempt": 0,
"text": "Why do you think the product of two negative numbers should be negative? Can you think of a situation where multiplying two negatives would give you a positive?"
}
] | {
"steps": [
"To solve (−8) × (−2), remember that the product of two negative numbers is positive.",
"So, we can rewrite it as 8 × 2 = 16."
],
"final_answer": 16
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 2,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-B1-R3-2106807f | train | B | B1 | [
"A4"
] | R3 | medium | {
"template_id": "B1-R3-evaluate-coefficient",
"params": {},
"text": "Evaluate 7x + 1 when x = 5.",
"options": null
} | {
"answer": 36,
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA09",
"text": "I plugged x = 5 into 7x + 1. Since 7x means joining 7 and 5, I got 75 + 1, which equals 76.",
"final_answer": 76
}
] | [
{
"for_attempt": 0,
"text": "When you see 7x, what does it actually mean? Can you check by substituting x = 1? What do you get for 7x + 1?"
}
] | {
"steps": [
"Replace x with 5 in 7x + 1, we get 7 × 5 + 1.",
"First, compute 7 × 5, which equals 35.",
"Then, add 1 to 35, resulting in 36.",
"The final answer is 36."
],
"final_answer": 36
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 1,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
math-v1-B2-R2-4a7f3441 | train | B | B2 | [
"B1"
] | R2 | easy | {
"template_id": "B2-R2-can-combine",
"params": {},
"text": "Can 5x + 9 be simplified to a single term?",
"options": [
"A) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.",
"B) Yes, it simplifies to 14x."
]
} | {
"answer": "A",
"unit": null,
"tolerance_rel": 0
} | [
{
"misconception_id": "MA11",
"text": "I think 5x + 9 can be simplified to 14x because I add the number 9 to the coefficient 5 and then put the x at the end. So I pick B.",
"final_answer": "B"
}
] | [
{
"for_attempt": 0,
"text": "When you combine terms, do the variables have to be the same? Can you add a number without a variable to a term with a variable?"
}
] | {
"steps": [
"5x and 9 are unlike terms because one has a variable and the other does not.",
"Unlike terms cannot be combined into a single term.",
"Therefore, 5x + 9 cannot be simplified further.",
"The correct answer is A."
],
"final_answer": "A"
} | {
"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit",
"template_version": "0.1.0-spec",
"seed": 3,
"gen_attempt": 0,
"checks": {
"V2": "pass",
"V3": "pass",
"V4": "pass",
"V5": "pass",
"V6": "pass",
"V9": "pass",
"V10": "pass",
"V11": "pass",
"V7": "pass"
},
"human_... |
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 (US$149 per organization, instant access after purchase at creative-data-lab-production.up.railway.app).
Load it
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, evaluation use. The full dataset carries the same license for training and evaluation inside one organization.
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