Abstract
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 language | English (US) |
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Pages (from-to) | 151-173 |
Number of pages | 23 |
Journal | Journal of Mathematical Behavior |
Volume | 52 |
DOIs | |
State | Published - Dec 2018 |
Keywords
- Fraction learning
- Guided reinvention
- Learning trajectory
- Mathematics learning
- Reflective abstraction
- Task design
ASJC Scopus subject areas
- Education
- Applied Psychology
- Applied Mathematics