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Katie Paulding

June 4 @ 10:30 am - 12:30 pm MDT

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Dissertation Information

Title: Influence of Models and Ratio Relationships on Middle School Students’ Cognition in Proportional Reasoning

Program: Doctor of Education in Curriculum and Instruction

Advisor: Dr. Michelle Carney, Curriculum, Instruction, and Foundational Studies

Committee Members: Dr. Joe Champion, Mathematics, Dr. Tatia Totorica, College of Education, and Dr. Julianne A. Wenner, Curriculum, Instruction, and Foundational Studies


Proportional reasoning is an integral component of adolescent cognitive development and a foundational concept for students to understand for success 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. This study examines 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 is analyzed through a combination of protocol analysis and verbal analysis.