Using Interactive Web Applications to Help Teach Math

and Science Concepts:An Example from Signal

Processing

Julie Greenberg

January 20, 2005

Background

Biomedical Signal and Image Processing (HST582J/6.555J/16.456J) 25-35 students once/year (Spring term) Graduate level subject

mostly seniors and first-year grad students Diverse backgrounds

HST, EECS, MechE, NucE, Aero/Astro 90-minute lecture twice weekly 4-hour software lab once per week

Initial Problem

Motivated by my frustration in teaching Fourier spectral analysis Observed that students couldn’t apply lecture

material in lab Experience shared by my colleagues Many students seemed to be overwhelmed by

interaction of variables Difficulty preparing examples for lecture

Initial solution

Developed a simulation/interactive demonstration to permit hands-on exploration of key variables in spectral analysis: Select signal sources (sum of cosines, ECG,

speech) Select parameters (window length, window shape,

DFT length) Options to save and compare parameter sets http://web.mit.edu/6.555/www/matweb/demo.html

Simulation: Input Screen

Simulation: Output Screen

New Problem/Concerns

We have the simulation. What do we do next? What are advantages/disadvantages of this type of

educational technology? How do we make effective use of this educational

technology in the context of the course?

Used alone, the simulation would likely have led to “fiddling” without much learning.

Overview of approach

Defined learning objectives and key concepts Great value to having these stated explicitly

Implemented Legacy cycle Reused/modified existing

educational activities Added new elements

Small group discussions Interactive tutorial to guide

students as they use the

simulation to develop

understanding of key concepts

Identified Learning Objectives

Student can analyze and interpret frequency content of biomedical signals

After completing this module, students should be able to: analyze the effects of multiple variables on a

frequency-domain representation select parameters to perform frequency analysis of

a signal, given desired specifications interpret a given frequency-domain representation,

given the parameters used make inferences as to the parameter used,

given a frequency-domain representation

Identified Key Concepts

Major Concept: Fourier spectral analysis

Supporting concepts: factors affecting amplitude resolution factors affecting frequency resolution effect of changing window length effect of changing window shape effect of changing DFT length effect of changing multiple parameters

simultaneously

Legacy Cycle: 1 of 4

Initial Challenge Design an electrocardiogram (ECG) monitor to

detect life-threatening ventricular arrhythmias 90-minute guest lecture on cardiac function 15 minute introduction in lab

Legacy Cycle: 2 of 4

Generate Ideas Students brainstorm in groups of two 30-40 minutes in lab

Multiple Perspectives Class reconvenes in lab Each group presents their ideas Other students and instructor comment Moderated discussion follows 30-40 minutes in lab

Legacy Cycle: 3 of 4

Research and Revise Interactive tutorial on Web

Learning objectives and key concepts guided our generation of tutorial content

Series of questions that explore key concepts with immediate feedback

Guidance for using simulation General text summaries of key concepts Glossary, tables, figures Optional hints and tips

Spectral analysis lecture – chalk and simulation

Legacy Cycle: 4 of 4

Test your Mettle students work in pairs to solve the ventricular

arrhythmia challenge (entire four hour lab session during following week)

homework problem

Go Public individual lab reports quiz

Results

Students liked it Survey data indicates strong positive reaction

Student learning improved Study shows that students using the module

demonstrated better understanding of key concepts than students not using module (JEE April 2003)

Instructor and TAs liked it Extremely rewarding

Take Home Messages

Provide framework (e.g. web-based tutorial) to support students in making effective use of educational technologies

Identify learning objectives and key concepts Strategic planning for teaching

Use HPL/Legacy cycle to deliver on learning objectives. Provides overall structure so that elements (e.g.

tutorial and simulation) are used in a pedagogically-informed context

Credits

Julie Greenberg, project leader Dinh-Yen Tran, simulation software Jeffrey Steinheider, simulation software Natalie Smith, tutorial implementation Tomas Lozano-Perez, tutorial software Leonardo Cedolin, teaching assistant Minnan Xu, teaching assistant Sean Brophy, learning sciences consultant Mark D’Avila, learning sciences consultant Lori Breslow, learning sciences consultant John Newman, assessment and evaluation

consultant