Investigating Middle School Students' Reasoning with the Equal Sign

About This Grant

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 analyzed using structural equation modeling. In the second part, approximately 60 students will be interviewed and complete task-based interviews and surveys. Qualitative data from those interviews will be transcribed and qualitatively coded. One outcome from this project is better understanding relationships among equal sign conceptions, other foundational skills, and algebraic reasoning. Mathematical equivalence is a cornerstone 'big idea' of algebra and outcomes from this project have potential advance understanding of learners' conceptions of the equal sign and mathematical equivalence. This project is supported by NSF's EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.