Keywords

Linear Algebra; Linearity; Linear Transformations; APOS

Abstract

The intent of this thesis is to investigate student approaches to linearity within a linear algebra context, focusing on definitional, computational, and theoretical skills. Linear algebra’s abstract nature constitutes a major challenge for a significant sector of STEM students, with the course often serving as undergraduates’ first encounter with mathematical proofs and extrapolations. The current student struggle is reflected through the prominent gap in knowledge derived from a lack of a concrete understanding of rudimentary concepts (like linearity), pivotal to student success. As such, this investigation aimed to bridge this gap by considering students’ modes of thinking regarding the elementary notion of linearity to improve the current course delivery and curriculum. Students were given three assessment questions targeting different skills integral to the mastery of linearity. Their responses were categorized using Action, Process, Object, Schema (APOS) and analyzed through Sierpinska’s (2000) proposed modes of thinking. About 26% of the participants responded correctly to question 1, 77% to question 2, and 59% to question 3. The analytic mode proved pivotal, specifically when considering definition application and computational abilities. The synthetic-geometric mode, however, was integral to the practical application of the concept. Further discussion and suggestions regarding the results and their implications on the current structure of linear algebra instruction are provided.

Thesis Completion Year

2024

Thesis Completion Semester

Spring

Thesis Chair

Teixeira, Katiuscia

College

College of Sciences

Department

Mathematics

Thesis Discipline

Mathematics

Language

English

Access Status

Open Access

Length of Campus Access

None

Campus Location

Orlando (Main) Campus

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Rights Statement

In Copyright