Elijah Cooley
Research Mentor: Vilma Mesa
Mentor Department: School of Education, Education
Author(s): Elijah Cooley, Vilma Mesa, Ayla Carvalho
Session: Session 2 (10:00 AM – 10:50 AM)
Presentation Type: Poster 17
Abstract
The PreTeXt-Runestone: Open Textbooks Engaging Undergraduates in STEM (PROTEUS) project examines how students, instructors, textbook authors, and researchers can work together to create better interactive calculus and linear algebra textbooks that promote student engagement, and how these questions ultimately function within real classroom settings. As a part of the PROTEUS project, this study aims to examine how pivot concepts in undergraduate linear algebra classes are implemented through an open source digital textbook, and how students’ responses to interactive questions reveal their mathematical conceptions. Prior research has documented patterns in student responses to questions in undergraduate mathematics, but less is known about how these patterns arise for specific linear algebra concepts, such as pivots, and how this information ultimately can be used to refine textbook content. This study focuses on Section 1.4: Pivots and Their Influence on Solution Spaces of the Understanding Linear Algebra textbook (ULA), addressing two research questions: 1) what conceptions about pivot are revealed in the ULA textbook and in the student responses for open question? and 2) how does knowing those conceptions inform the teaching of those topics? Using Balacheff’s cK¢ model, we identified problems, operators, representations, and control structures in the textbook explanations, and then analyzed students’ short answer responses to pivot related questions, identifying recurring conceptions and patterns of reasoning associated with pivot concepts. By examining the relationship between textbook design and student conceptions, this work contributes to the efforts within the PROTEUS project to develop effective design principles for open source interactive textbooks and to support informed pedagogical decision making at the undergraduate level.
