Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the Learning Through Activity research program

Martin A. Simon, Melike Kara, Anderson Norton, Nicora Placa

Research output: Contribution to journalArticle


We report on a teaching experiment intended to foster a concept of multiplication that would both subsume students’ multiple-groups concept of whole number multiplication and provide a conceptual basis for understanding multiplication of fractions. The teaching experiment, which used a rigorous single-subject methodology, began with an attempt to build on students’ multiple-groups concept by promoting generalizing assimilation. This was not totally successful and led to a redesign aimed at promoting reflective abstraction. Analysis of this latter phase led to several significant conclusions, which in turn led to a revised hypothetical learning trajectory. The revised trajectory aims to foster a concept of multiplication as a change in units.

Original languageEnglish (US)
Pages (from-to)151-173
Number of pages23
JournalJournal of Mathematical Behavior
StatePublished - Dec 2018



  • Fraction learning
  • Guided reinvention
  • Learning trajectory
  • Mathematics learning
  • Reflective abstraction
  • Task design

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

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