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Understanding Naïve Reasonings in Signals and Systems: A Foundation for Designing Effective Instructional Material

Student naïve reasonings in an undergraduate engineering course, signals and systems, were investigated in order to provide the groundwork for designing effective instructional material. Students majoring in aerospace engineering at the Massachusetts Institute of Technology were interviewed to probe their reasoning about different signals and systems topics, particularly in their analysis of continuous-time, linear, time-invariant systems using the fundamental properties of LTI systems and linear systems tools. In this paper, we present central naïve reasonings that were identified related to the concepts of linearity, time-invariance, and convolution. We then discuss how these findings support instructors in designing effective instructional materials for signals and systems, such as concept questions for use in interactive lectures, guides for recitation sessions targeted to address student conceptual problems, and exam questions that accurately diagnose student conceptual problems.