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Students’ Understanding of Sequence And Series as Applied in Electrical Engineering

Abstract

Across all engineering fields, upper-level engineering courses often build upon a strong mathematical foundation. As such, a critical component of understanding how students learn engineering concepts is studying how students apply their mathematical background to the engineering domain. Studying how students apply mathematical knowledge in engineering courses allows us to identify challenges, pitfalls, and common misconceptions. Through an NSF- funded study, we are addressing the broad goal of developing a better understanding of how students transfer mathematical knowledge to concepts in engineering. In this component of the study, we focus on electrical engineering students’ application of concepts in sequence and series to a junior-level signals and systems course. A strong understanding of sequence and series is fundamental to the study of discrete-time signals and systems. A discrete-time system response takes the form of a sequence, and the characteristics of this sequence and of the associated series dictate system properties such as causality, stability, memory, and finite vs. infinite impulse response. Additionally, sequence and series are the basis of discrete-time Fourier series and transforms, which provide the primary tool for frequency-domain signals and systems analysis. We have selected and analyzed five group problems based on their connection to significant concepts in sequence and series. The results of our analysis indicate that students encounter challenges in associating mathematical expressions with physical realities, providing logical justifications for their conclusions, and manipulating multiple representations of series. These results have direct application to instructional design, since the design of assessment items and problems can be informed by students' interpretations of items.

Background and Motivation

All facets of engineering require students to transfer mathematical knowledge from introductory mathematics courses into engineering courses. Electrical engineering is a mathematically intensive discipline, and the subfield of signals and systems has a particularly strong mathematical basis including applications for Fourier analysis, Laplace transforms and advanced calculus. In this work, we focus on students in an introductory discrete-time signals and systems course. As part of a larger NSF-funded study through which we aim to better understand how students transfer mathematical knowledge to concepts in engineering, we analyze student work in the discrete-time signals and systems course in an effort to characterize challenges students face in transferring knowledge of sequence and series to the study of discrete-time signals and systems. While the mathematics education community has studied students' understanding of limits and of the convergence and divergence of series, these studies have not addressed the link to engineering applications. In addition, there are few studies about students’ understanding of periodicity1 that is foundational to understanding signals and systems.

In our broader work, we aim to study the depth of both the procedural and conceptual elements of students' understanding as it applies to mathematics in electrical engineering. Procedural knowledge has been described as the understanding of rules and algorithms for mathematics

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Nelson, J., & Hjalmarson, M. (2009, June), Students’ Understanding Of Sequence And Series As Applied In Electrical Engineering Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5648