Teaching Fourier series with tone experiments based on smartphone applications

Abstract

This study proposes a tone experiment using multiple smartphones or tablets to assist Fourier series teaching combined with a pedagogical strategy of the Visible Thinking framework. Fourier analysis is widely applied in many fields; therefore, it is an important subject in many professional courses of colleges, especially in engineering. While Fourier analysis is the core theoretical foundation of various experimental techniques, undergraduate courses often teach Fourier analysis from a mathematical perspective, leaving students with little intuition about how Fourier analysis works. The proposed tone experiment requires teamwork for students to manipulate smartphones to synthesize harmonic tones to simulate a periodic wave so that students can intuitively understand the physical meaning of the Fourier series formula. In addition, we conducted a pedagogical study on this course to evaluate the effects. The proposed method successfully improved the learning outcomes of beginner students and reduced the anxiety associated with learning Fourier analysis. Compared with the class that did not use the proposed tone experiment, the quiz scores improved by an average of 3.77 points. The students gave positive feedback and comments on the proposed experiments and teaching methods.

Digital visualization in graduate transport phenomena

“…Moreover, many seniors found the dual representation most helpful for the vapor absorption problem (Section 2.3). In addition to more quantitative graphs and color visualizations, other technology, such as smartphone apps, can aid in the study of Fourier series [46].…”