June 22, 2008
June 22, 2008
June 25, 2008
13.284.1 - 13.284.9
Challenges and Innovations in Teaching Linear Algebra
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.
The topics and techniques of linear algebra are especially important for engineering majors, mathematics majors, chemistry majors, and computer science majors. Engineering, chemistry, and computer science majors have an inherent need for an understanding of the practical applications of the theory in a particular discipline. In fact, many of the ABET program criteria speciﬁcally list the knowledge and application of linear algebra as a necessary skill.1 In addition to applications, the theory and mathematical reasoning skills developed in an introductory linear algebra course will be invaluable to math majors as they progress to more proof oriented content courses.
At Georgia College & State University, there are approximately 110 mathematics majors. Roughly half of these majors are enrolled in the pre-engineering program. This program is a transfer program offered in conjunction with The Georgia Institute of Technology. The pre-engineering majors complete ﬁrst and second year math courses at Georgia College & State University (GCSU). The linear algebra course at GCSU is taught at the sophomore level, and it is a required course for the pre-engineering, mathematics, and computer science majors. Occasionally, majors in other disciplines such chemistry, economics, and middle grades education
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