Date of Graduation
Master of Science in Education in Secondary Education in Mathematics
Why are students not making a smooth transition from arithmetic to algebra? The purpose of this study was to understand the nature of students’ algebraic reasoning through tasks involving generalizing. After students’ algebraic reasoning had been analyzed, the challenges they encountered while reasoning were analyzed. The data was collected through semi-structured interviews with six eighth grade students and analyzed by watching recorded interviews while tracking algebraic reasoning. Through data analysis of students’ algebraic reasoning, three themes emerged: 1) it was possible for students to reach stage two (informal abstraction) and have an abstract understanding of the mathematical pattern even if they were not transitioning to stage three (formal abstraction), 2) students relied heavily on visualizations of the tasks as reasoning tools to reach stage two (informal abstraction), and 3) using the context of the task to understand the mathematical patterns proved to be the most powerful way to reach stage two (informal abstraction). When analyzing challenges students faced reasoning algebraically one theme emerged: students often needed guidance transitioning from stage to stage of the generalization process. The findings of this study will provide teachers with evidence of the importance of algebraic reasoning tools and strategies to better equip students with algebraic tools.
algebraic challenges, generalization, algebraic reasoning, informal algebra, formal algebra
Algebra | Education | Mathematics | Secondary Education
© Andrea Lynn Martin
Martin, Andrea Lynn, "Transitioning from the Abstract to the Concrete: Reasoning Algebraically" (2020). MSU Graduate Theses. 3557.