---
language:
- en
tags:
- math
- education
license: odc-by
pretty_name: mathfish
---

# MathFish

<!-- Provide a quick summary of the dataset. -->

This dataset is introduced by "Evaluating Language Model Math Reasoning via Grounding in Educational Curricula" (link TBD), 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](https://huggingface.co/datasets/allenai/achieve-the-core): Common Core mathematical standards and their descriptions
- [allenai/mathfish_tasks](https://huggingface.co/datasets/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](https://github.com/allenai/mathfish/tree/main).

## Dataset Details

### Dataset Description

<!-- Provide a longer summary of what this dataset is. -->

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](https://illustrativemathematics.org/) and [Fishtank Learning](https://fishtanklearning.org/). Each problem is a segment of these materials demarcated by standards labels, and a problem may be labeled with multiple standards. 

- **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

<!-- Address questions around how the dataset is intended to be used. -->

### Direct Use

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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](https://creativecommons.org/licenses/by/4.0/), while Fishtank Learning component is licensed under Creative Commons [BY-NC-SA 4.0](https://creativecommons.org/licenses/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

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

## Dataset Structure

<!-- This section provides a description of the dataset fields, and additional information about the dataset structure such as criteria used to create the splits, relationships between data points, etc. -->

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 : path to image files or html of element}, # html elements, e.g. 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.

Images are in the `images` folder, and filenames should match values of problems' `elements` dicts. 

## Dataset Creation

### Curation Rationale

<!-- Motivation for the creation of this dataset. -->

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

<!-- This section describes the data collection and processing process such as data selection criteria, filtering and normalization methods, tools and libraries used, etc. -->

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?

<!-- This section describes the people or systems who originally created the data. It should also include self-reported demographic or identity information for the source data creators if this information is available. -->

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

## Bias, Risks, and Limitations

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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

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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 

<!-- If there is a paper or blog post introducing the dataset, the APA and Bibtex information for that should go in this section. -->

BibTeX TBD

## Dataset Card Contact

kylel@allenai.org