MathFish

This dataset is introduced by "Evaluating Language Model Math Reasoning via Grounding in Educational Curricula", and includes problems drawn from two open educational resources (OER): Illustrative Mathematics and Fishtank Learning. Problems are labeled with mathematical standards, which are K-12 skills and concepts that problems enable students to learn. These standards are defined and organized by Common Core State Standards.

Additional components of MathFish can be found at:

• allenai/achieve-the-core: Common Core mathematical standards and their descriptions
• allenai/mathfish_tasks: MathFish's dev set problems inserted into verification and tagging prompts for language models

Code to support Mathfish can be found in this Github repository.

Dataset Details

Dataset Description

Common Core State Standards (CCSS) offer fine-grained and comprehensive coverage of K-12 math skills/concepts. We scrape labeled problems from two reputable OER that span a wide range of grade levels and standards: Illustrative Mathematics and Fishtank Learning. Each problem is a segment of these materials demarcated by standards labels, and a problem may be labeled with multiple standards.

Number of problems: 4356 in dev.jsonl, 4355 in test.jsonl, 13065 in train.jsonl. In total, 21776 K-12 math problems.

Number of images: 1848 in fl_problem, 11736 in im_lesson, 27 in im_modelingprompt, 3497 in im_practice, 860 in im_task. In total, 17968 math images.

• Curated by: Lucy Li, Tal August, Rose E Wang, Luca Soldaini, Courtney Allison, Kyle Lo
• Funded by: The Gates Foundation
• Language(s) (NLP): English
• License: ODC-By 1.0

Uses

Direct Use

This dataset was originally created to evaluate models' abilities to identify math skills and concepts using publisher-labeled data pulled from curricular websites. This data may support investigations into the use of language models to support K-12 education.

Illustrative Mathematics is licensed as CC BY 4.0, while Fishtank Learning component is licensed under Creative Commons BY-NC-SA 4.0. Both sources are intended to be OER, which is defined as teaching, learning, and research materials that provides users free and perpetual permission to "retain, reuse, revise, remix, and redistribute" for educational purposes.

Out-of-Scope Use

Note that Fishtank Learning's original license prohibits commercial use.

Dataset Structure

Each *.jsonl file contains one problem or activity per line:

{
  id: '', # this is global
  text: ‘string representing activity or problem’,
  metadata: { source id, unit, lesson, other location data , url if possible, html version}, # this is source-specific
  acquisition_date: '', # YYYY-MM-DD
  elements: {identifier : name of image file or html of table}, # table, img, figure interweaved with text
  standards: [list of (relation, standard)], # relation could be addressing, alignment, building towards, etc
  source: '', 
}

Note: Among standard relation types, Addressing == Alignment, and we evaluate on these in our paper. Future work may investigate other types of relations between problems and math skills/concepts. Not all problems in each file contain standards.

Images are in the images folder, in zipped files named after image filenames' prefixes: fl_problem, im_lesson, im_modelingprompt, im_practice, im_task.

Dataset Creation

Curation Rationale

Math standards are informed by human learning progressions, and commonly used in real-world reviews of math content. In education, materials have focused alignment with a standard if they enable students to learn the full intent of concepts/skills described by that standard. Identifying alignment can thus inform educators whether a set of materials adequately targets core learning goals for students.

Data Collection and Processing

We pull problems from several parts of Illustrative Mathematics curriculum: tasks, centers, practice problems, lessons, and modeling prompts. For Fishtank learning, we pull problems from the lessons section of their website. What is considered a "lesson" and what is considered a "problem" or "task" is an artifact of the materials themselves. Some problems are hands-on group activities, while others are assessment-type problems.

Who are the source data producers?

Illustrative Mathematics and Fishtank Learning are nonprofit educational organizations in the United States.

Bias, Risks, and Limitations

Though these problems offer substantial coverage of a common K-12 curriculum in the United States, they may not directly translate to pedagogical standards or practices in other socio-cultural contexts.

Recommendations

Though language models have the potential to automate the task of identifying standards alignment in curriculum or improve educational instruction, their rule in education should be a supporting, rather than leading, one. To design such tools, we believe that it is best to co-create with teachers and curriculum specialists.

Citation

@misc{lucy2024evaluatinglanguagemodelmath,
      title={Evaluating Language Model Math Reasoning via Grounding in Educational Curricula}, 
      author={Li Lucy and Tal August and Rose E. Wang and Luca Soldaini and Courtney Allison and Kyle Lo},
      year={2024},
      eprint={2408.04226},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2408.04226}, 
}

Dataset Card Contact

kylel@allenai.org