Challenges And Innovations In Teaching Linear Algebra

Abstract

A solid grounding in linear algebra is essential in many fields of engineering. As a result, at our institution, linear algebra is a required course for our pre-engineering majors and is taught at the sophomore level. The students enrolled in this course have not usually had a proof methods course; however, the course focuses not only on computation but also on reasoning and theory. The content in this course presents a specific challenge in that it is difficult to cover the required material in one semester while at the same time devoting a sufficient amount of class time for homework questions and in-depth problem solving. In addition, it is difficult to develop test questions that can be completed within one class period while adequately assessing the students' skills in problem solving. Further, homework collection and grading can become burdensome very quickly. Collectively, these challenges can reduce the course's effectiveness in teaching students to properly apply linear algebra in solving real-world problems and can make it difficult for the instructor to evaluate student progress and provide timely feedback.In this paper, we describe some of the challenges particular to teaching linear algebra as well as specific methods and techniques that we have used to help meet these challenges. We will describe some of the pedagogical innovations that we have employed in teaching linear algebra. These innovations include writing assignments in the form of student journals and class activities geared toward team-formation and enhancing student participation and learning. We will also discuss techniques, including using rubrics and brief writing assignments, used to evaluate students' understanding of linear algebra concepts. We will conclude with a discussion of the benefits, drawbacks and effectiveness of each of these methods in meeting the challenges associated with teaching linear algebra.