The role of balance scales in supporting productive thinking about equations among diverse learners

ABSTRACT

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks. Interview analyses revealed several categories of affordances of these tools for supporting students’ productive thinking about equations.

KEYWORDS:

• Early algebra
• elementary grades
• equal sign
• mathematical tools
• balance scales

Acknowledgments

The research reported here was supported in part by the National Science Foundation under Award # 1720129. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Notes

1. The population at this second school included 18% students of color and 17% who qualified for free or reduced-price lunch. We do not have data regarding the number of students in these classrooms with identified disabilities but can report that of the elementary schools in this district, this school is known for having a concentration of resources to support students with learning difficulties. Students struggling to meet grade-level expectations were identified by classroom teachers for participation in interviews.

2. Three different interview forms – two of which included equivalence tasks – were implemented in this study. As students had not yet encountered some of the early algebra content included in the intervention by the time of the mid-interview, more students were asked questions from interview forms that included equivalence tasks (i.e., content that had already been addressed in the intervention) at this time point.

Additional information

Notes on contributors

Ana Stephens

Ana Stephens is a Researcher at the Wisconsin Center for Education Research at the University of Wisconsin–Madison. Her research addresses the development of elementary students’ algebraic reasoning. She is particularly interested in students’ understanding of mathematical equivalence and the tasks that support the development of this understanding.

Yewon Sung is a doctoral student in Mathematics Education at the University of Wisconsin–Madison. She is interested in learners’ ways of thinking and feeling when learning early algebra in the elementary grades.

Susanne Strachota is the Faculty-in-Residence at the Patton College of Education at Ohio University. She studies how students develop algebraic reasoning.

Ranza Veltri Torres is a doctoral student in Mathematics Education at the University of Wisconsin–Madison. Her current research concerns mathematics identity, particularly in community college students who are enrolled in non-credit-bearing remedial math coursework.

Karisma Morton is an Assistant Professor in the Department of Teacher Education and Administration at the University of North Texas. Her research explores gender and racial/ethnic inequity in mathematics education with a particular interest in the impact of well-designed and reform-based mathematics curriculum and pedagogy that promotes mathematical literacy for all students.

Angela Murphy Gardiner is a senior research associate at TERC, Inc., in Cambridge, MA. Her primary research interests include students’ algebraic thinking and understanding of functions, methods for delivering effective teacher professional development, and understanding the relationship between characteristics of professional development and student outcomes.

Maria Blanton is a Senior Scientist at TERC, Inc., in Cambridge, MA. Her research focuses on the cognitive foundations of children’s algebraic thinking and the impacts of early algebra education on children’s algebra-readiness for middle grades.

Eric Knuth is a Professor and Director of the STEM Center at the University of Texas at Austin. His research concerns students’ engagement in mathematical practices, particularly practices related to algebraic reasoning and mathematical argumentation (justifying and proving).

Rena Stroud is an Assistant Professor in the Department of Education at Merrimack College. She is a quantitative methodologist with research interests in teaching and learning in early mathematics.