A Theoretical Framework for Describing Students’ Use of Mathematical Notations
Abstract: University mathematics coursework is replete with representations to which instructors ascribe distinct, interconnected meanings. Students, as apprentices within the field of mathematics, are expected to gain access to and fluently use these conventions in various ways to describe their thinking. In this presentation, I present the Expressions framework, a theoretical model I constructed from qualitative data to describe students’ construction of representations (i.e., expressions of thinking) to organize, record, or convey their thinking about mathematical ideas. I also present empirical data for three meanings students might attribute to their personally created algebraic notations in the context of infinite series convergence and logic of conditional statements. This framework is useful in contextualizing students’ development of meaning for notation, describing unique student symbolization, and providing a method for instructors to more explicitly describe the conventional ways mathematicians utilize and attribute meaning to representations.
This talk is appropriate for faculty, undergraduate students, and a more general audience.
Biography: Derek Eckman is an assistant professor of mathematics education at Idaho State University. He began his career as a high school mathematics instructor before earning his Ph.D. in mathematics education from Arizona State University. His current research interests involve undergraduate students’ construction and utilization of representations to convey their thinking, investigating how alternative grading methods impact student performance in current and future classes, and students’ construction of logic in proof contexts (e.g., quantification, conditional logic). He is also a member of Idaho State University’s NOYCE grant team and is working toward starting a mathematics education-oriented track in his department’s doctoral program.
Outside of school, Derek enjoys performing and creating music on the piano, organ, trumpet, and vocally. He also reads in a book club with his wife, cycles with his kids, and tries to cook meals that elicit as few groans as possible.
Contact: derekeckman@isu.edu