A Step-Based Tutoring System to Teach Underachieving Students How to Construct Algebraic Models

Kurt VanLehn, Fabio Milner, Chandrani Banerjee, Jon Wetzel

Research output: Contribution to journalArticlepeer-review


An algebraic model uses a set of algebraic equations to describe a situation. Constructing such models is a fundamental skill, but many students still lack the skill, even after taking several algebra courses in high school and college. For such students, we developed instruction that taught students to decompose the to-be-modelled situation into schema applications, where a schema represents a simple relationship such as distance-rate-time or part-whole. However, when a model consists of multiple schema applications, it needs some connection among them, usually represented by letting the same variable appear in the slots of two or more schemas. Students in our studies seemed to have more trouble identifying connections among schema applications than identifying the schema applications themselves. We developed several tutoring systems and evaluated them in university classes. One of them, a step-based tutoring system called OMRaaT (One Mathematical Relationship at a Time), was both reliably superior (p = 0.02, d = 0.67) to baseline and markedly superior (p < 0.001, d = 0.84) to an answer-based tutoring system using only commercially available software (MATLAB Grader).

Original languageEnglish (US)
Pages (from-to)224-246
Number of pages23
JournalInternational Journal of Artificial Intelligence in Education
Issue number2
StatePublished - Jun 2024


  • Algebra story problem solving
  • Algebra word problem solving
  • Algebraic model construction
  • Intelligent tutoring system

ASJC Scopus subject areas

  • Education
  • Computational Theory and Mathematics


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