### 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) |
---|---|

Journal | Journal of Mathematical Behavior |

DOIs | |

State | Accepted/In press - Jan 1 2018 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Education
- Applied Psychology
- Applied Mathematics

### Cite this

*Journal of Mathematical Behavior*. https://doi.org/10.1016/j.jmathb.2018.03.002

**Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication : A study of the learning through activity research program.** / Simon, Martin; Kara, Melike; Norton, Anderson; Placa, Nicora.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication

T2 - A study of the learning through activity research program

AU - Simon, Martin

AU - Kara, Melike

AU - Norton, Anderson

AU - Placa, Nicora

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Fraction learning

KW - Guided reinvention

KW - Learning trajectory

KW - Mathematics learning

KW - Reflective abstraction

KW - Task design

UR - http://www.scopus.com/inward/record.url?scp=85045423555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045423555&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2018.03.002

DO - 10.1016/j.jmathb.2018.03.002

M3 - Article

AN - SCOPUS:85045423555

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

ER -