Date of Final Oral Examination (Defense)
Type of Culminating Activity
Master of Arts in Education, Curriculum and Instruction
Curriculum, Instruction, and Foundational Studies
Jonathan Brendefur, Ph.D.
Michele Carney, Ph.D.
Philip P. Kelly, Ph.D.
Students’ misunderstandings of the equal sign have been well documented in children as young as kindergarten. Misconceptions of the symbol (=) hinder students’ relational thinking and impede access to algebraic contexts. Symbolic equations (e.g., 4+2=__+3) have been widely used to test students’ understanding and communication of equivalence. The purpose of this study was to explore how first grade students communicate their understanding of equivalence when instruction involved using a bar model versus symbolic equations. It used a two-case study approach to compare an atypical instruction design (the bar model) to a traditional design (symbolic equations). Distinct patterns in communication and changes in students’ understanding were found in both cases. In addition, the bar model group used specific, concrete methods of communicating their thinking earlier and more frequently, which suggests using the bar model along with symbolic representations may be an effective instructional design.
Van Vooren, Amber L., "First Graders’ Use of the Bar Model to Communicate Their Understanding of the Equal Sign" (2016). Boise State University Theses and Dissertations. 1147.