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
Because it is technical, will start with learning curve formulas … Then go to exploratory data analysis Return to in next session to use of formulas in Item Response Theory, Learning Factors Analysis
(Provide some “spaced” practice for you)
Overview
Questions on yesterday’s intro?
Another example of learning curves Power law, logistic regression Goals: 1) Get familiar with data, 2) Learn/practice Excel skills Tasks: 1) create a “step table”, 2) graph learning curves using a) error rate & b) assistance score
Quantitative models of learning curves
Exercise:
Student Performance As They Practice with the LISP Tutor
Production Rule Analysis
0.5
0.4
Evidence for Production Rule as an appropriate unit of knowledge acquisition
Error Rate
0.3
0.2
0.1
0.0 0 2 4 6 8 10 12 14
Opportunity to Apply Rule (Required Exercises)
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:
Declare-first-parameter Declare-second-parameter
Overview
Questions on yesterday’s intro?
Another example of learning curves Power law, logistic regression Goals: 1) Get familiar with data, 2) Learn/practice Excel skills Tasks: 1) create a “step table”, 2) graph learning curves using a) error rate & b) assistance score
Quantitative models of learning curves
Exercise:
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) 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
Assumptions
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?
Another example of learning curves Power law, logistic regression Goals: 1) Get familiar with data, 2) Learn/practice Excel skills Tasks: 1) create a “step table”, 2) graph learning curves using a) error rate & b) assistance score
Quantitative models of learning curves
Exercise:
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
Exported File Loaded into Excel
QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.
DataShop Export & Using Excel
Get files from
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 …
Follow instructions in download from two slides ago …
END