Comparing student understanding of signals and systems using a concept inventory, a traditional exam and interviews

Concept inventories play a growing role in assessing student understanding in engineering curricula. A common application of concept inventories is a pre/post- test assessment in a course. For this reason, it is important to confirm the validity of any new concept inventory, i.e., to verify that the inventory measures what it is designed to assess. The signals and systems concept inventory (SSCI) is a 25-question multiple-choice exam assessing core concepts in undergraduate signals and systems courses. This paper presents two analyses supporting the validity of the SSCI. The first analysis compares the responses of 40 students to final exam questions with their responses to related SSCI questions. This analysis finds statistically-significant correlations between the SSCI and the final exam for questions on convolution and Fourier transform properties. The second analysis examines the interview responses of 18 students to SSCI questions on frequency-selective filtering and convolution. The interviews suggest students have a strong understanding of high and low frequency, have some understanding of the relationship between time and frequency domains, but struggle to interpret frequency responses. The interviews also suggest that many students retain some conceptual understanding of convolution after their memory of the convolution integral has faded.