Student Understanding In Signals And Systems: The Role Of Interval Matching In Student Reasoning

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.