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Student Understanding in Signals and Systems: The Role of Interval Matching in Student Reasoning

Abstract

This study was designed to investigate student understanding in signals and systems, particularly the study of continuous-time linear, time-invariant systems. In this paper, we report on a principal finding of this investigation, namely, the importance of the interval matching reasoning resource in accounting for the faulty reasonings that students invoke in reasoning about central topics in signals and systems. The qualitative method of clinical interviewing was employed for probing into student understanding. Fifty-one undergraduate students majoring in aerospace engineering at the Massachusetts Institute of Technology volunteered to participate in this study. Data was analyzed with the aim of identifying the faulty reasonings that participants invoked in their response to different signals and systems problems, and the cognitive structures of reasoning resources that describe and explain the origin of these faulty reasonings. Results indicate that there is a consistency across student faulty reasonings related to three different signals and systems topics — superposition, convolution, and the Laplace transform. This consistency is ascribed to the systematicity in student invocation of the reasoning resource of the interval matching readout strategy.

Introduction

This study was designed to investigate student understanding in the undergraduate engineering course, signals and systems. Signals and systems is a core discipline in Electrical Engineering departments, and in other engineering departments, such as aerospace. Signals and systems is the study of signals and how they interact with systems, particularly linear, time-invariant (LTI) systems. Generally, the breadth and context of presentation of topics in signals and systems varies among institutions. The main variations are whether the course covers both continuous- and discrete-time systems, or only continuous-time, and whether the context of application is electric circuitry. Despite these variations, a central theme that cuts across introductory signals and systems courses is the study of continuous-time LTI systems, which constitutes the focus of this research.

It has been maintained in the science education literature that learners frequently express conceptions that are in discord with expert understanding.1 Such conceptions could hinder student learning if not appropriately addressed and refined through instructional approaches. Research has shown that traditional modes of instruction which do not take into account students’ initial knowledge state result in small gains in student understanding2, 3 In fact, an effective means for improving student understanding is through the implementation of active learning methods.4 Such methods are most effective when designed based on an understanding of the nature of student understanding and the difficulties they encounter in their study of a particular discipline.

There have been few studies on student conceptual understandings in signals and systems with the notable exception of the research conducted by Wage, Buck, Welch and Wright5–7 who developed the Signals and Systems Concept Inventory (SSCI) to measure student understanding of core concepts in the study of linear, time-invariant systems. Despite these efforts, there is a dearth of

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Nasr, R., & Hall, S., & Garik, P. (2007, June), Student Understanding In Signals And Systems: The Role Of Interval Matching In Student Reasoning Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2543