Instructional module in Fourier spectral analysis, based on principles of "how people learn"

Journal of Engineering Education, Apr 2003 by Greenberg, Julie E, Smith, Natalie T, Newman, John H

ABSTRACT

This paper describes the design and evaluation of an instructional module for teaching/learning Fourier spectral analysis, with emphasis on biomedical applications. The module is based on the principles of "How People Learn" (HPL) as embodied in the Legacy cycle. This cycle is a particular instantiation of problem-based learning and includes components explicitly aimed at providing context and motivation, facilitating exploration, developing in-depth understanding, and incorporating opportunities for self-assessment. In the spectral analysis module, traditional teaching methods are augmented with small group discussions, peer-to-peer learning, a Web-based tutorial, and an interactive demonstration. Assessment included the development of rubrics for scoring student understanding of key concepts, revealing that students who used the module demonstrated better understanding relative to students who studied the material using traditional methods. Survey results and comments indicate that students generally liked the interactive tutorial and demonstration, as well as the structure provided by the HPL framework.

I. INTRODUCTION

A. Motivation

Fourier spectral analysis is an important concept relevant to many electrical and biomedical engineering applications, including speech analysis, speech processing, magnetic resonance imaging, and analysis of biomedical signals such as the electrocardiogram (ECG), electroencephalogram (EEG), and elcctromyogram (EMG). The motivation for developing this module comes from the first author's experiences teaching spectral analysis for six years in a graduate-level course entitled Biomedical Signal and Image Processing. Many students in this class had difficulty mastering the fundamentals of spectral analysis, appearing to be overwhelmed by the interaction of multiple variables. Results from lab reports indicated that even students who did master the fundamentals typically did not apply them, instead they managed to succeed in the lab exercises by fiddling with parameters. These experiences motivated the development of a module to assist students both in learning the fundamentals of Fourier spectral analysis and in applying those concepts to biomedical applications.

B. Pedagogical Framework

The instructional module described in this work is based on principles of "How People Learn" (HPL) [1], which specifies four qualities of effective learning environments:

1. Learner-centered environments consider students' previous experiences and prior knowledge as a basis for future learning.

2. Knowledge-centered environments present new material with the rationale for studying the topic and with relevant connections to other topics, in order to facilitate understanding, to develop accessible knowledge that can be applied appropriately, and to promote transfer of concepts to new situations.

3. Assessment-centered environments include opportunities for self-assessment, feedback, and revision.

4. Community-centered environments increase students' opportunities and motivation to interact with faculty and peers, receive feedback, and learn.

The Legacy cycle [2, 3] provides one possible approach for designing learning environments that incorporate the elements of HPL. It can be viewed as a particular instantiation of problem-based learning. The major steps of the Legacy cycle are:

1. The Challenge poses a complex goal to motivate students and to provide them with opportunities to explore new material by exercising problem solving and inquiry skills.

2. Generating Ideas allows students to explore their initial thoughts about the challenge, making explicit and documenting any naive preconceptions or misconceptions.

3. Multiple Perspectives provide expert insights, exposing students to advanced thinking on multiple aspects of the challenge, without providing a direct solution.

4. Research and Revise consists of resources and learning activities that help students develop expertise to effectively approach multiple aspects of the challenge.

5. Test your Mettle consists of opportunities for formative assessment, allowing students to reflect on what they have learned and to identify any weaknesses in their current understanding.

6. Go Public is the final, summative assessment of students' understanding of the material at the end of the module.

The Legacy cycle has proven quite versatile and has been applied to the design of instructional modules used in contexts ranging from elementary to post-graduate education, spanning time frames ranging from a few hours of class time to semester-long projects. The spectral analysis module described in Section II exemplifies how the HPL framework can be applied to material covered in a few hours of an advanced-undergraduate or graduate subject.

II. DESIGN OF THE INSTRUCTIONAL MODULE

The objective of the module as an educational innovation is to help students master the fundamentals of Fourier spectral analysis, ultimately increasing the number of students who obtain a working understanding of the topic. The design process began by specifying the learning objectives and key concepts for the module. The major learning objective is that students should be able to analyze the frequency content of an arbitrary signal and to interpret a given frequency representation. Key concepts underlying this objective include effect of window length, window shape, and discrete Fourier transform (DFT) length on both frequency resolution and amplitude resolution. These objectives and concepts subsequently guided the technical content authored for the module.