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

Teaching-learning interviews have been used in education to identify students’ conceptual weaknesses and to improve learning. This effort utilized teaching-learning interviews in a Spring 2010 linear systems course to (a) identify the conceptual difficulties that students face when studying Fourier series and (b) improve students’ understanding of this topic. These interviews attempted to focus more on higher-level Fourier series concepts (consistent with levels 4 through 6 in Bloom’s taxonomy) and less on the procedural calculations and plotting (levels 1 through 3 in Bloom’s taxonomy) in an effort to attempt to formalize assessment of this topic area relative to a well-established learning framework. Twenty eight students were interviewed for this study using a scripted protocol, where interview sessions lasted about one hour each. Conceptual struggles were identified in thematic areas such as (a) the definition of the mathematical integral and its connections to signal average/behavior, (b) properties of even/odd functions and their relationship to the trigonometric basis set, and (c) the links between time shifts/inversion and the resulting phases of the contributing coefficients.