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```Educational data mining overview
& Introduction to Exploratory
Data Analysis
Ken Koedinger
CMU Director of PSLC
Professor of Human-Computer Interaction &
Psychology
Carnegie Mellon University
Plan



curve formulas …
Then go to exploratory data analysis
in Item Response Theory, Learning Factors
Analysis

(Provide some “spaced” practice for you)
Overview

Questions on yesterday’s intro?


Quantitative models of learning curves


Another example of learning curves
Power law, logistic regression
Exercise:


Goals:
1) Get familiar with data,
2) Learn/practice Excel skills
1) create a “step table”,
2) graph learning curves using a) error rate & b)
assistance score
Student Performance As They
Practice with the LISP Tutor
Error Rate
Production Rule Analysis
0.5
Evidence for Production Rule as an
appropriate unit of knowledge acquisition
0.4
0.3
0.2
0.1
0.0
0
2
4
6
8
10
Opportunity to Apply Rule (Required Exercises)
12
14
Using learning curves to
evaluate a cognitive model


Lisp Tutor Model
 Learning curves used to validate cognitive model
 Fit better when organized by knowledge components
(productions) rather than surface forms (programming language
terms)
But, curves not smooth for some production rules
 “Blips” in leaning curves indicate the knowledge
representation may not be right
 Corbett, Anderson, O’Brien (1995)
 Let me illustrate …
Curve for “Declare
Parameter” production rule
What’s happening
on the 6th & 10th
opportunities?


How are steps with blips different from others?
What’s the unique feature or factor explaining these
blips?
Can modify cognitive model using unique
factor present at “blips”


Blips occur when to-be-written program has 2 parameters
Split Declare-Parameter by parameter-number factor:
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
Declare-first-parameter
Declare-second-parameter
Overview

Questions on yesterday’s intro?


Quantitative models of learning curves


Another example of learning curves
Power law, logistic regression
Exercise:


Goals:
1) Get familiar with data,
2) Learn/practice Excel skills
1) create a “step table”,
2) graph learning curves using a) error rate & b)
assistance score
Learning curve analysis

The Power Law of Learning
(Newell & Rosenbloom, 1993)
Y = a Xb
Y – error rate
X – opportunities to
practice a skill
a – error rate on 1st opportunity
b – learning rate
After the log transformation
“a” is the “intercept” or starting point of the learning curve
“b” is the “slope” or steepness of the learning curve
More sophisticated learning
curve model

Generalized Power Law to fit learning curves


Logistic regression (Draney, Wilson, Pirolli, 1995)
Assumptions
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
Different students may initially know more or less
=> use an intercept parameter for each student
Students learn at the same rate
=> no slope parameters for each student

Some productions may be more known than others
=> use an intercept parameter for each production

Some productions are easier to learn than others
=> use a slope parameter for each production

These assumptions are reflected in detailed math model …
More sophisticated learning curve model
 
ln p  i Xi   j Yj   j YjTj
p
1 p
Probability of getting a step correct (p) is proportional to:
- if student i performed this step = Xi,
add overall “smarts” of that student = i
-
if skill j is needed for this step = Yj,
add easiness of that skill = j
add product of number of opportunities to learn = Tj
& amount gained for each opportunity = j
Use logistic regression because response is discrete (correct or not)
Probability (p) is transformed by “log odds”
“stretched out” with “s curve” to not bump up against 0 or 1
(Related to “Item Response Theory”, behind standardized tests …)
Overview

Questions on yesterday’s intro?


Quantitative models of learning curves


Another example of learning curves
Power law, logistic regression
Exercise:


Goals:
1) Get familiar with data,
2) Learn/practice Excel skills
1) create a “step table”,
2) graph learning curves using a) error rate & b)
assistance score
TWO_CIRCLES_IN_SQUARE problem:
Initial screen
TWO_CIRCLES_IN_SQUARE problem:
An error a few steps later
TWO_CIRCLES_IN_SQUARE problem:
Student follows hint & completes prob
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
DataShop Export & Using Excel

Get files from
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Go to Learnlab.org
Click on “Enabling Technologies”
Click on “Meetings”
Click on “Documents”
Don’t do yet …
Demo …
Demo: Export Step Roll
Up from Data Shop …
Now try it yourself …
