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使用关联规则来指导搜索最佳拟合.doc
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Using Association Rules to Guide a Search for Best Fitting
Transfer Models of Student Learning
Jonathan Freyberger, Neil T. Heffernan, and Carolina Ruiz
Department of Computer Science
Worcester Polytechnic Institute
Worcester, MA 01609
frey@wpi.edu, nth@wpi.edu, and ruiz@wpi.edu
Abstract: We say a transfer model is a mapping between the questions in an intelligent tutoring system and the
knowledge components (i.e., skills, strategies, declarative knowledge, etc) needed to answer a question
correctly. [JKT00] showed how you could take advantage of 1) the Power Law Of Learning, 2) an existing
transfer model, and 3) set of tutorial log files, to learn a function (using logistic regression) that will predict
when a student will get a question correct. In the main conference proceeding [CHK2004] give an example of
using this technique for transfer model selection. Koedinger and Junker [KJ99] also conceptualized a search
space where each state is a new transfer model. The operators in this search space split, add or merge
knowledge components based upon factors that are tagged to questions. Koedinger and Junker called this
method learning factors analysis emphasizing that this method can be used to study learning. Unfortunately, the
search space is huge and searching for good fitting transfer models is exponential. The main goal of this paper
is show a technique that will make searching for transfer models more efficient. Our procedure implements a
search method using association rules as a means of guiding the search. The association rules are mined from a
dataset derived from student-tutor interaction logs. The association rules found in the mining process determine
what operations to perform on the current transfer model. We report on the speed up achieved. Being able to
find good transfer models quicker will help intelligent tutor system builders as well as cognitive science
researchers better assess what makes certain problems hard and other problems easy for students.
Keywords: transfer models, logistic regression, association rules, prediction, search, learning factors analysis
Introduction
Intelligent tutoring systems are able to provide instruction to students and to model their current knowledge by
knowing what skill(s) (we use the term skill and knowledge component interchangeable) a student needs to solve
a given problem. However, creating an accurate model of a student's knowledge can be quite difficult
[KLEG92]. Problems usually have more than one skill associated with them. Transfer of knowledge is the
process by which practice on one type of problems makes a student more likely to do well on a different type of
problem. We assume that transfer only happens between problems types if the two problem types share
knowledge components that are required to solve both types of problems. Transfer models reify assumptions of
when knowledge component are shared between problem types. Creating and comparing transfer models can
make it easier to assess what skills are required for a given problem. A transfer model is a mapping between
different types of problems and the skills needed to solve them. If two different problem types have one or more
skills in common then this suggests that transfer between these two different problems exists. Thus, students
practicing with one type of problem might cause them to perform better on the other type of problem. We
further make a large simplifying assumption that if the model predicts transfer then it should happen, as we do
not model students not realizing that transfer is possible.
For instance, a hypothetical transfer model is shown below for two question types. Suppose you gave students
both 1) problems that involved calculating the area of a circle, given the radius, as well as 2) problems where
Freyberger, J., Heffernan, N., & Ruiz, C. (2004) Using Association Rules to Guide a Search for Best Fitting Transfer
Models of Student Learning Workshop on “Analyzing Student-Tutor Interaction Logs to Improve Educational Outcomes”
at the Proceedings of 7
th
Annual Intelligent Tutoring Systems Conference, Maceio, Brazil.
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