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)  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 

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