# Investigating Middle School Students' Reasoning with the Equal Sign

> **NSF 04002526DB NSF STEM Education** · University of Wisconsin-Madison (WI) · $632,775

## Abstract

Algebra is a fundamental mathematics topic. A key part of algebra is understanding mathematical equations (e.g., 2+5=7). This project will explore how middle school learners make sense of mathematical expressions (e.g., 2+5) within an equation. More specifically, the project will explore how children think about the ways those expressions can be transformed into an alternate, but equivalent form (e.g., 7-2). This study has potential to inform mathematics teaching and learning as well as psychology about humans' developmental learning about the equal sign. A result from this study will be a deeper understanding of students' work with such mathematical transformations, which has capacity to support students' success in algebra. 

The equal sign takes on many different interpretations depending on how it is used in mathematical equations. A goal of this study of grade 6-8 students is to investigate relations among students' conceptions of the equal sign, the foundational understandings that support these conceptions, and students' algebraic reasoning. The project team seeks to answer the following research question during the three-year project:  How are students' conceptions of the equal sign related to their representational flexibility and algebraic reasoning? Over 210 grades 6-8 students will be recruited and asked to participate in task-based interviews to provide survey responses for the first part of this study. Quantitative data from those interviewed will be ana

## Key facts

- **NSF award ID:** 2500175
- **Awardee organization:** University of Wisconsin-Madison (WI)
- **SAM.gov UEI:** LCLSJAGTNZQ7
- **PI:** Ana C Stephens
- **Primary program:** 04002526DB NSF STEM Education
- **All programs:** STEM Learning & Learning Environments
- **Estimated total:** $632,775
- **Funds obligated:** $632,775
- **Transaction type:** Standard Grant
- **Period:** 07/15/2025 → 06/30/2029

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2500175

## Citation

> US National Science Foundation, Award 2500175, Investigating Middle School Students' Reasoning with the Equal Sign. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2500175. Licensed CC0.

---

*[NSF Awards dataset](/datasets/nsf-awards) · CC0 1.0*