PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Linear algebra thinking in the embodied, symbolic and formal worlds: Students’ reasoning behind preferring certain worlds
Page: 555
To understand linear algebra concepts, one needs to be familiar in many different modes of thinking. Mathematicians often move between these modes of thinking fluently and expect that students will pick up the main ideas along the way. Yet, a majority of students do not have the cognitive framework to perform the move that is so natural to mathematicians. Employing Tall’s (2013) three-world model, in this research a set of linear algebra tasks were given to students in order to encourage them to move between Tall’s embodied, symbolic and formal worlds of mathematical thinking. Our working hypothesize is that by creating opportunities to move between the worlds, students may be exposed to multiple modes of thinking which results in richer conceptual understanding. The results of a survey revealed that a majority of students preferred the symbolic world. Their reasoning for their choices will be discussed.