Using Interactive Web
Applications to Help Teach Math
and Science Concepts:
An Example from Signal
Processing
Julie Greenberg
January 20, 2005
Background
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Biomedical Signal and Image Processing
(HST582J/6.555J/16.456J)
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25-35 students once/year (Spring term)
Graduate level subject
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Diverse backgrounds
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mostly seniors and first-year grad students
HST, EECS, MechE, NucE, Aero/Astro
90-minute lecture twice weekly
4-hour software lab once per week
Initial Problem
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Motivated by my frustration in teaching Fourier
spectral analysis
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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
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Developed a simulation/interactive
demonstration to permit hands-on exploration
of key variables in spectral analysis:
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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
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We have the simulation. What do we do next?
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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
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Defined learning objectives and key concepts
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Great value to having these stated explicitly
Implemented Legacy cycle
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Reused/modified existing
educational activities
Added new elements
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Small group discussions
Interactive tutorial to guide
students as they use the
simulation to develop
understanding of key concepts
Identified Learning Objectives
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Student can analyze and interpret frequency
content of biomedical signals
After completing this module, students should
be able to:
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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
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Major Concept:
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Fourier spectral analysis
Supporting concepts:
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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
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Initial Challenge
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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
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Generate Ideas
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Students brainstorm in groups of two
30-40 minutes in lab
Multiple Perspectives
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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
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Research and Revise
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Interactive tutorial on Web
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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
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Test your Mettle
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students work in pairs to solve the ventricular
arrhythmia challenge (entire four hour lab session
during following week)
homework problem
Go Public
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individual lab reports
quiz
Results
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Students liked it
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Student learning improved
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Survey data indicates strong positive reaction
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
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Extremely rewarding
Take Home Messages
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Provide framework (e.g. web-based tutorial) to
support students in making effective use of
educational technologies
Identify learning objectives and key concepts
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Strategic planning for teaching
Use HPL/Legacy cycle to deliver on learning
objectives.
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Provides overall structure so that elements (e.g.
tutorial and simulation) are used in a pedagogicallyinformed context
Credits
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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