Determining the dimensions of variables in physics algebraic equations

C. W. Liew, Joel A. Shapiro, D. E. Smith

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper describes work on methods that evaluate algebraic solutions to word problems in physics. Many current tutoring systems rely on substantial scaffolding and consequently require students to completely describe every variable used in the solution. A heuristic, based on constraint propagation, capable of inferring the description of variables (i.e., the possible dimensions and physics concepts) is shown to be highly reliable on three real world data sets, one covering a few problems with a small number of student answers and two others covering a large class of problems (∼100) with a large number of student answers (~11,000). The heuristic uniquely determines the dimensions of all the variables in 91-92% of the equation sets. By asking the student for dimension information about one variable, an additional 3% of the sets can be determined. An ITS tutoring system can use this heuristic to reason about a student's answers even when the scaffolding and context are removed.

Original languageEnglish (US)
Pages (from-to)25-41
Number of pages17
JournalInternational Journal on Artificial Intelligence Tools
Issue number1-2
StatePublished - Feb 2005

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence


  • Constraint propagation
  • Intelligent tutoring systems
  • Units

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