math-v1 batch-001

README.md

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+---
+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.

exports/preference.jsonl

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+{"id": "math-v1-A1-R3-133df093-a0", "prompt": "Compute 266 + 482.", "chosen": "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.", "rejected": "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.", "rejected_misconception_id": "MA01"}
+{"id": "math-v1-A2-R3-87cfbe93-a0", "prompt": "Compute 496 − 109.", "chosen": "Ones: borrow, 16 − 9 = 7. Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8. Hundreds: 4 − 1 = 3. So, 496 − 109 = 387.", "rejected": "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.", "rejected_misconception_id": "MA02"}
+{"id": "math-v1-A2-R3-87cfbe93-a1", "prompt": "Compute 496 − 109.", "chosen": "Ones: borrow, 16 − 9 = 7. Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8. Hundreds: 4 − 1 = 3. So, 496 − 109 = 387.", "rejected": "I borrowed in the ones place and added 10, so 16 − 9 = 7. In the tens, 9 − 0 = 9. In the hundreds, 4 − 1 = 3. So, the answer is 397.", "rejected_misconception_id": "MA03"}
+{"id": "math-v1-A3-R3-4b9b2ab3-a0", "prompt": "Compute 83 × 71.", "chosen": "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.", "rejected": "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.", "rejected_misconception_id": "MA04"}
+{"id": "math-v1-A4-R2-13473d44-a0", "prompt": "In the expression 25 − 6 × 7, which operation should be done first?\nA) 6 × 7, because multiplication comes before addition and subtraction.\nB) 25 − 6, because we always work from left to right.", "chosen": "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.", "rejected": "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.", "rejected_misconception_id": "MA05"}
+{"id": "math-v1-A5-R3-20854100-a0", "prompt": "Compute (−10) + (−9).", "chosen": "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.", "rejected": "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.", "rejected_misconception_id": "MA06"}
+{"id": "math-v1-A6-R3-11517438-a0", "prompt": "Compute (−8) × (−2).", "chosen": "To solve (−8) × (−2), remember that the product of two negative numbers is positive. So, we can rewrite it as 8 × 2 = 16.", "rejected": "I think when I multiply two negative numbers, the answer should be negative. So, (−8) × (−2) should be −16.", "rejected_misconception_id": "MA08"}
+{"id": "math-v1-B1-R3-2106807f-a0", "prompt": "Evaluate 7x + 1 when x = 5.", "chosen": "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.", "rejected": "I plugged x = 5 into 7x + 1. Since 7x means joining 7 and 5, I got 75 + 1, which equals 76.", "rejected_misconception_id": "MA09"}
+{"id": "math-v1-B2-R2-4a7f3441-a0", "prompt": "Can 5x + 9 be simplified to a single term?\nA) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.\nB) Yes, it simplifies to 14x.", "chosen": "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.", "rejected": "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.", "rejected_misconception_id": "MA11"}

exports/sft.jsonl

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+{"id": "math-v1-A1-R3-133df093", "messages": [{"role": "user", "content": "Compute 266 + 482."}, {"role": "assistant", "content": "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."}]}
+{"id": "math-v1-A2-R3-87cfbe93", "messages": [{"role": "user", "content": "Compute 496 − 109."}, {"role": "assistant", "content": "Ones: borrow, 16 − 9 = 7. Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8. Hundreds: 4 − 1 = 3. So, 496 − 109 = 387."}]}
+{"id": "math-v1-A3-R3-4b9b2ab3", "messages": [{"role": "user", "content": "Compute 83 × 71."}, {"role": "assistant", "content": "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."}]}
+{"id": "math-v1-A4-R2-13473d44", "messages": [{"role": "user", "content": "In the expression 25 − 6 × 7, which operation should be done first?\nA) 6 × 7, because multiplication comes before addition and subtraction.\nB) 25 − 6, because we always work from left to right."}, {"role": "assistant", "content": "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."}]}
+{"id": "math-v1-A5-R3-20854100", "messages": [{"role": "user", "content": "Compute (−10) + (−9)."}, {"role": "assistant", "content": "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."}]}
+{"id": "math-v1-A6-R3-11517438", "messages": [{"role": "user", "content": "Compute (−8) × (−2)."}, {"role": "assistant", "content": "To solve (−8) × (−2), remember that the product of two negative numbers is positive. So, we can rewrite it as 8 × 2 = 16."}]}
+{"id": "math-v1-B1-R3-2106807f", "messages": [{"role": "user", "content": "Evaluate 7x + 1 when x = 5."}, {"role": "assistant", "content": "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."}]}
+{"id": "math-v1-B2-R2-4a7f3441", "messages": [{"role": "user", "content": "Can 5x + 9 be simplified to a single term?\nA) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.\nB) Yes, it simplifies to 14x."}, {"role": "assistant", "content": "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."}]}

exports/step_labels.jsonl

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+{"id": "math-v1-A1-R3-133df093-sol", "prompt": "Compute 266 + 482.", "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."], "labels": [1, 1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-A1-R3-133df093-a0", "prompt": "Compute 266 + 482.", "steps": ["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."], "labels": [null, null, null, -1], "first_error_step": 3, "outcome": "incorrect", "misconception_id": "MA01"}
+{"id": "math-v1-A2-R3-87cfbe93-sol", "prompt": "Compute 496 − 109.", "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"], "labels": [1, 1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-A2-R3-87cfbe93-a0", "prompt": "Compute 496 − 109.", "steps": ["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."], "labels": [null, null, null, null, -1], "first_error_step": 4, "outcome": "incorrect", "misconception_id": "MA02"}
+{"id": "math-v1-A2-R3-87cfbe93-a1", "prompt": "Compute 496 − 109.", "steps": ["I borrowed in the ones place and added 10, so 16 − 9 = 7.", "In the tens, 9 − 0 = 9.", "In the hundreds, 4 − 1 = 3.", "So, the answer is 397."], "labels": [null, null, null, -1], "first_error_step": 3, "outcome": "incorrect", "misconception_id": "MA03"}
+{"id": "math-v1-A3-R3-4b9b2ab3-sol", "prompt": "Compute 83 × 71.", "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."], "labels": [1, 1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-A3-R3-4b9b2ab3-a0", "prompt": "Compute 83 × 71.", "steps": ["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."], "labels": [null, null, -1], "first_error_step": 2, "outcome": "incorrect", "misconception_id": "MA04"}
+{"id": "math-v1-A4-R2-13473d44-sol", "prompt": "In the expression 25 − 6 × 7, which operation should be done first?\nA) 6 × 7, because multiplication comes before addition and subtraction.\nB) 25 − 6, because we always work from left to right.", "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."], "labels": [1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-A4-R2-13473d44-a0", "prompt": "In the expression 25 − 6 × 7, which operation should be done first?\nA) 6 × 7, because multiplication comes before addition and subtraction.\nB) 25 − 6, because we always work from left to right.", "steps": ["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."], "labels": [null, null, -1], "first_error_step": 2, "outcome": "incorrect", "misconception_id": "MA05"}
+{"id": "math-v1-A5-R3-20854100-sol", "prompt": "Compute (−10) + (−9).", "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."], "labels": [1, 1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-A5-R3-20854100-a0", "prompt": "Compute (−10) + (−9).", "steps": ["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."], "labels": [null, -1], "first_error_step": 1, "outcome": "incorrect", "misconception_id": "MA06"}
+{"id": "math-v1-A6-R3-11517438-sol", "prompt": "Compute (−8) × (−2).", "steps": ["To solve (−8) × (−2), remember that the product of two negative numbers is positive.", "So, we can rewrite it as 8 × 2 = 16."], "labels": [1, 1], "outcome": "correct"}
+{"id": "math-v1-B1-R3-2106807f-sol", "prompt": "Evaluate 7x + 1 when x = 5.", "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."], "labels": [1, 1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-B1-R3-2106807f-a0", "prompt": "Evaluate 7x + 1 when x = 5.", "steps": ["I plugged x = 5 into 7x + 1.", "Since 7x means joining 7 and 5, I got 75 + 1, which equals 76."], "labels": [null, -1], "first_error_step": 1, "outcome": "incorrect", "misconception_id": "MA09"}
+{"id": "math-v1-B2-R2-4a7f3441-sol", "prompt": "Can 5x + 9 be simplified to a single term?\nA) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.\nB) Yes, it simplifies to 14x.", "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."], "labels": [1, 1, 1, 1], "outcome": "correct"}
+{"id": "math-v1-B2-R2-4a7f3441-a0", "prompt": "Can 5x + 9 be simplified to a single term?\nA) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.\nB) Yes, it simplifies to 14x.", "steps": ["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."], "labels": [null, -1], "first_error_step": 1, "outcome": "incorrect", "misconception_id": "MA11"}

exports/tutor.jsonl

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+{"id": "math-v1-A1-R3-133df093-a0", "misconception_id": "MA01", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Compute 266 + 482.\n\nMy attempt: 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."}, {"role": "assistant", "content": "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?"}]}
+{"id": "math-v1-A2-R3-87cfbe93-a0", "misconception_id": "MA02", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Compute 496 − 109.\n\nMy attempt: 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."}, {"role": "assistant", "content": "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?"}]}
+{"id": "math-v1-A2-R3-87cfbe93-a1", "misconception_id": "MA03", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Compute 496 − 109.\n\nMy attempt: I borrowed in the ones place and added 10, so 16 − 9 = 7. In the tens, 9 − 0 = 9. In the hundreds, 4 − 1 = 3. So, the answer is 397."}, {"role": "assistant", "content": "When you borrowed from the tens column, did you remember to reduce the tens digit by 1? How does borrowing affect the digits in each column?"}]}
+{"id": "math-v1-A3-R3-4b9b2ab3-a0", "misconception_id": "MA04", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Compute 83 × 71.\n\nMy attempt: 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."}, {"role": "assistant", "content": "When you multiply by the tens digit, do you remember to shift the place value? How would that change your calculation?"}]}
+{"id": "math-v1-A4-R2-13473d44-a0", "misconception_id": "MA05", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "In the expression 25 − 6 × 7, which operation should be done first?\nA) 6 × 7, because multiplication comes before addition and subtraction.\nB) 25 − 6, because we always work from left to right.\n\nMy attempt: 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."}, {"role": "assistant", "content": "What do the order of operations (PEMDAS) tell us about multiplication and subtraction?"}]}
+{"id": "math-v1-A5-R3-20854100-a0", "misconception_id": "MA06", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Compute (−10) + (−9).\n\nMy attempt: 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."}, {"role": "assistant", "content": "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?"}]}
+{"id": "math-v1-A6-R3-11517438-a0", "misconception_id": "MA08", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Compute (−8) × (−2).\n\nMy attempt: I think when I multiply two negative numbers, the answer should be negative. So, (−8) × (−2) should be −16."}, {"role": "assistant", "content": "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?"}]}
+{"id": "math-v1-B1-R3-2106807f-a0", "misconception_id": "MA09", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Evaluate 7x + 1 when x = 5.\n\nMy attempt: I plugged x = 5 into 7x + 1. Since 7x means joining 7 and 5, I got 75 + 1, which equals 76."}, {"role": "assistant", "content": "When you see 7x, what does it actually mean? Can you check by substituting x = 1? What do you get for 7x + 1?"}]}
+{"id": "math-v1-B2-R2-4a7f3441-a0", "misconception_id": "MA11", "messages": [{"role": "system", "content": "You are a patient tutor. When a student shares a wrong attempt, ask a short guiding question that exposes the flawed idea. Never give the answer."}, {"role": "user", "content": "Can 5x + 9 be simplified to a single term?\nA) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.\nB) Yes, it simplifies to 14x.\n\nMy attempt: 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."}, {"role": "assistant", "content": "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?"}]}

master/records.jsonl

@@ -0,0 +1,8 @@
+{"id": "math-v1-A1-R3-133df093", "split": "train", "topic": "A", "concept_id": "A1", "prereqs": [], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A1-R3-add-carry", "params": {}, "text": "Compute 266 + 482.", "options": null}, "ground_truth": {"answer": 748, "unit": null, "tolerance_rel": 0}, "attempts": [{"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}], "feedback": [{"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?"}], "solution": {"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}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-A2-R3-87cfbe93", "split": "train", "topic": "A", "concept_id": "A2", "prereqs": ["A1"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A2-R3-subtract-borrow", "params": {}, "text": "Compute 496 − 109.", "options": null}, "ground_truth": {"answer": 387, "unit": null, "tolerance_rel": 0}, "attempts": [{"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 − 9 = 7. In the tens, 9 − 0 = 9. In the hundreds, 4 − 1 = 3. So, the answer is 397.", "final_answer": 397}], "feedback": [{"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 reduce the tens digit by 1? How does borrowing affect the digits in each column?"}], "solution": {"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}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-A3-R3-4b9b2ab3", "split": "train", "topic": "A", "concept_id": "A3", "prereqs": ["A1"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A3-R3-multiply-two-digit", "params": {}, "text": "Compute 83 × 71.", "options": null}, "ground_truth": {"answer": 5893, "unit": null, "tolerance_rel": 0}, "attempts": [{"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}], "feedback": [{"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?"}], "solution": {"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}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-A4-R2-13473d44", "split": "train", "topic": "A", "concept_id": "A4", "prereqs": ["A1", "A3"], "rung": "R2", "difficulty": "easy", "problem": {"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."]}, "ground_truth": {"answer": "A", "unit": null, "tolerance_rel": 0}, "attempts": [{"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"}], "feedback": [{"for_attempt": 0, "text": "What do the order of operations (PEMDAS) tell us about multiplication and subtraction?"}], "solution": {"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"}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-A5-R3-20854100", "split": "train", "topic": "A", "concept_id": "A5", "prereqs": ["A2"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A5-R3-add-negatives", "params": {}, "text": "Compute (−10) + (−9).", "options": null}, "ground_truth": {"answer": -19, "unit": null, "tolerance_rel": 0}, "attempts": [{"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}], "feedback": [{"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?"}], "solution": {"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}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-A6-R3-11517438", "split": "train", "topic": "A", "concept_id": "A6", "prereqs": ["A3", "A5"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A6-R3-multiply-negatives", "params": {}, "text": "Compute (−8) × (−2).", "options": null}, "ground_truth": {"answer": 16, "unit": null, "tolerance_rel": 0}, "attempts": [{"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}], "feedback": [{"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?"}], "solution": {"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}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-B1-R3-2106807f", "split": "train", "topic": "B", "concept_id": "B1", "prereqs": ["A4"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "B1-R3-evaluate-coefficient", "params": {}, "text": "Evaluate 7x + 1 when x = 5.", "options": null}, "ground_truth": {"answer": 36, "unit": null, "tolerance_rel": 0}, "attempts": [{"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}], "feedback": [{"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?"}], "solution": {"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}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}
+{"id": "math-v1-B2-R2-4a7f3441", "split": "train", "topic": "B", "concept_id": "B2", "prereqs": ["B1"], "rung": "R2", "difficulty": "easy", "problem": {"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."]}, "ground_truth": {"answer": "A", "unit": null, "tolerance_rel": 0}, "attempts": [{"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"}], "feedback": [{"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?"}], "solution": {"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"}, "provenance": {"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_review": {"reviewed": false, "verdict": null}}}