Date of Final Oral Examination (Defense)
Type of Culminating Activity
Doctor of Education in Curriculum and Instruction
Curriculum, Instruction, and Foundational Studies
Michele Carney, Ph.D.
Joe Champion, Ph.D.
Julianne A. Wenner, Ph.D.
Tatia Totorica, Ed.D.
Proportional reasoning is an integral component of adolescent mathematical cognitive development and a foundational concept for students to understand in order to be successful in higher level mathematics and science courses. Yet research indicates students struggle to proportionally reason. Task features of proportional reasoning problems are known to influence student cognition and success in problem solving, including familiarity with problem context, problem type, numerical content, and mode of task representation. The purpose of this study was to examine the influence of two iconic representations (tape diagrams and bar models) and three ratio relationships (6:3, 8:2, and 5:2) on student cognition in proportional reasoning via individual cognitive interviews. Data was analyzed through a combination of protocol analysis and verbal analysis. Results suggest there is some evidence to support the claim the bar model provides more scaffolding than the tape diagram in terms of helping students visualize the multiplicative comparison relationship.
Paulding, Katie, "The Influence of Tape Diagrams and Bar Models on Middle School Students' Proportional Reasoning" (2019). Boise State University Theses and Dissertations. 1584.