
CMUCS02119
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS02119
Developing a Pedagogical Domain Theory of Early Algebra Problem Solving
Kenneth R. Koedinger, Benjamin A. MacLaren
March 2002
Also appears as HumanComputer Interaction Institute Technical Report
CMUHCII02100
CMUCS02119.ps
CMUCS02119.pdf
Keywords: Learning, cognitive modeling, cognitive architecture,
problem solving, mathematics education, modeldata fit
We describe a theory of quantitative representations and processes that
makes novel predictions about student problemsolving and learning
during the transition from arithmetic to algebraic competence or
"early algebra". Our Early Algebra Problem Solving (EAPS) theory comes
in the form of a cognitive model within the ACTR cognitive architecture.
As a "pedagogical domain theory", our EAPS theory can be used to make
sense of the pattern of difficulties and successes students experience
in early algebra problem solving and learning. In particular, the
theory provides an explanation for the surprising result that algebra
students perform better on certain word problems than on equivalent
equations (Koedinger & Nathan, 2000; Nathan & Koedinger, 2000). It also
makes explicit the knowledge and knowledge selection processes behind
student strategies and errors and provides a theoretical tool for
psychologists and mathematics educators to both productively generate
and accurately evaluate hypotheses about early algebra learning and
instruction. We have abstracted our development process into six
modelbuilding constraints that may be appropriate for creating cognitive
models of problem solving in other domains.
42 pages
