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Teaching-Learning Interviews to Understand and Remediate Student Difficulties with Fourier Series Concepts

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Conference

2011 ASEE Annual Conference & Exposition

Location

Vancouver, BC

Publication Date

June 26, 2011

Start Date

June 26, 2011

End Date

June 29, 2011

ISSN

2153-5965

Conference Session

Innovative Instructional Strategies and Curricula in ECE I

Tagged Division

Electrical and Computer

Page Count

16

Page Numbers

22.1409.1 - 22.1409.16

Permanent URL

https://peer.asee.org/18564

Download Count

14

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Paper Authors

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Chen Jia Kansas State University

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Andrew G. Bennett Kansas State University

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Andrew Bennett received his Ph.D. in Mathematics from Princeton University in 1985. Since 1988, he has been at Kansas State University, where he is currently Director of the Center for Quantitative Education.

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Dong-Hai Nguyen Kansas State University

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Department of Physics

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N. Sanjay Rebello Kansas State University

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Associate Professor of Physics, has over 10 years experience in physics education research, particularly in the area of transfer of learning. His current research focuses on problem solving and transfer of these skills from mathematics to physics to engineering.

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Steve Warren Kansas State University

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Steve Warren received a B.S. and M.S. in Electrical Engineering from Kansas State University in 1989 and 1991, respectively, followed by a Ph.D. in Electrical Engineering from The University of Texas at Austin in 1994. Dr. Warren is an Associate Professor in the Department of Electrical & Computer Engineering at Kansas State University. Prior to joining KSU in August 1999, Dr. Warren was a Principal Member of the Technical Staff at Sandia National Laboratories in Albuquerque, NM. He directs the KSU Medical Component Design Laboratory, a facility partially funded by the National Science Foundation that provides resources for the research and development of distributed medical monitoring technologies and learning tools that support biomedical contexts. His research focuses on 1.) plug-and-play, point-of-care medical monitoring systems that utilize interoperability standards, 2.) wearable sensors and signal processing techniques for the determination of human and animal physiological status, and 3.) educational tools and techniques that maximize learning and student interest. Dr. Warren is a member of the American Society for Engineering Education and the Institute of Electrical and Electronics Engineers.

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Abstract

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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