June 26, 2011
June 26, 2011
June 29, 2011
Electrical and Computer
22.1409.1 - 22.1409.16
Teaching-Learning Interviews to Understand and Remediate Student Difficulties with Fourier Series ConceptsAbstractLinear systems is a compulsory course in most electrical and computer engineering curricula. Itis widely perceived as useful but difficult, as it addresses subjects such as convolution, Fourierseries, and continuous/discrete Fourier transforms: higher-level concepts that rely on a well-developed understanding of lower-level mathematical constructs and procedures. Students withan inadequate mathematical foundation and a poor sense of the underlying systems theoryregularly struggle with such subjects, as they are typically able to perform sequences of theunderlying calculations but cannot piece together the higher conceptual relationships that drivethese procedures. As a result, many students are unable to address exam questions and analysisproblems that deviate from a solution recipe described in the textbook, and they often cannotexplain how slight changes in mathematical renderings will affect system or signal behavior.Teaching-learning interviews have been used in education to identify students’ conceptualweaknesses and to improve learning. This effort utilized teaching-learning interviews in a Spring2010 linear systems course to (a) identify the conceptual difficulties that students face whenstudying Fourier series and (b) improve students’ understanding of this topic. These interviewsattempted to focus more on higher-level Fourier series concepts (consistent with levels 4 through6 in Bloom’s taxonomy) and less on the procedural calculations and plotting (levels 1 through 3in Bloom’s taxonomy) in an effort to attempt to formalize assessment of this topic area relative toa well-established learning framework. Twenty eight students were interviewed for this studyusing a scripted protocol, where interview sessions lasted about one hour each. Conceptualstruggles were identified in thematic areas such as (a) the definition of the mathematical integraland its connections to signal average/behavior, (b) properties of even/odd functions and theirrelationship to the trigonometric basis set, and (c) the links between time shifts/inversion and theresulting phases of the contributing coefficients. The interview protocol, the sample questions,the conceptual misunderstandings related to Fourier series, and the learning assistance methodsutilized in the interviews are discussed in more detail in the paper.
Jia, C., & Bennett, A. G., & Nguyen, D., & Rebello, N. S., & Warren, S. (2011, June), Teaching-Learning Interviews to Understand and Remediate Student Difficulties with Fourier Series Concepts Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. https://peer.asee.org/18564
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