Advanced mathematical thinking in tasks involving linear transformations

Abstract

This article presents the results of research that aimed to identify and discuss the evidence and characteristics of the processes of the Advanced Mathematical Thinking students in a mathematics course expressed when dealing with tasks related to the content of linear transformations. For this, we designed a study using some theories of Advanced Mathematical Thinking, which served as the foundation for analyzing students' written records. We conclude that some participants of the research expressed characteristics of the processes of representation and abstraction of Advanced Mathematical Thinking, and only two showed evidence of processes involved in abstraction. These students' written records present difficulties with notation for the concepts in question, as with the manipulation of these notations. Thus, there is a need for professors to create moments of reflection in relation to the development of Advanced Mathematical Thinking.

Keywords:
Mathematics education; Advanced mathematical thinking; Linear algebra; Higher education