Interpreting freeform equation solving

Anna N. Rafferty, Thomas L. Griffiths

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


Learners’ step-by-step solutions can offer insight into their misunderstandings. Because of the difficulty of automatically interpreting freeform solutions, educational technologies often structure problem solving into particular patterns. Hypothesizing that structured interfaces may frustrate some learners, we conducted an experiment comparing two interfaces for solving equations: one requires users to enter steps in an efficient sequence and insists each step be mathematically correct before the user can continue, and the other allows users to enter any steps they would like. We find that practicing equation solving in either interface was associated with improved scores on a multiple choice assessment, but that users who had the freedom to make mistakes were more satisfied with the interface. In order to make inferences from these more freeform data, we develop a Bayesian inverse planning algorithm for diagnosing algebra understanding that interprets individual equation solving steps and places no restrictions on the ordering or correctness of steps. This algorithms draws inferences and exhibits similar confidence based on data from either interface. Our work shows that inverse planning can interpret freeform problem solving, and suggests the need to further investigate how structured interfaces affect learners’ motivation and engagement.

Original languageEnglish (US)
Title of host publicationArtificial Intelligence in Education - 17th International Conference, AIED 2015, Proceedings
EditorsCristina Conati, Neil Heffernan, Antonija Mitrovic, M. Felisa Verdejo
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783319197722
StatePublished - 2015
Externally publishedYes
Event17th International Conference on Artificial Intelligence in Education, AIED 2015 - Madrid, Spain
Duration: Jun 22 2015Jun 26 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other17th International Conference on Artificial Intelligence in Education, AIED 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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