### Abstract

In line with continuing efforts to explain the demanding nature of multiplicative reasoning

among middle-school students, this study explores the fine-grained knowledge elements that

two pairs of 7th and 8th graders deployed in their attempt to coordinate the known and

unknown quantities in the gear-wheel problem. Failure to conceptualize the multiplicative

relation in reverse, mainly due to the numeric feature of the problem parameters and

inherent inverse proportional relationship, led the students to use more primitive fallback

strategies.

among middle-school students, this study explores the fine-grained knowledge elements that

two pairs of 7th and 8th graders deployed in their attempt to coordinate the known and

unknown quantities in the gear-wheel problem. Failure to conceptualize the multiplicative

relation in reverse, mainly due to the numeric feature of the problem parameters and

inherent inverse proportional relationship, led the students to use more primitive fallback

strategies.

Original language | English |
---|---|

Title of host publication | 35th Annual Conference of the Mathematics Education Research Group of Australasia |

Subtitle of host publication | Mathematics Education: Expanding Horizons |

Editors | J Dindyal, L.P Cheng, S.F Ng |

Place of Publication | Adelaide |

Publisher | Mathematics Education Research Group of Australasia |

Pages | 625-632 |

Number of pages | 8 |

ISBN (Print) | 9789810725273 |

Publication status | Published - 2012 |

Externally published | Yes |

Event | Annual Conference of the Mathematics Education Research Group of Australasia 2012: Mathematics Education: Expanding Horizons - Nanyang Technological University, Singapore, Singapore Duration: 2 Jul 2012 → 6 Jul 2012 https://merga.net.au/Public/Publications/Annual_Conference_Proceedings/2012_MERGA_CP.aspx |

### Conference

Conference | Annual Conference of the Mathematics Education Research Group of Australasia 2012 |
---|---|

Abbreviated title | MERGA 2012 |

Country | Singapore |

City | Singapore |

Period | 2/07/12 → 6/07/12 |

Internet address |

### Fingerprint

### Cite this

RAMFUL, A. (2012). Coordinating known and unknown quantities in a multiplicative context: Problem conceptualization affordances and constraints. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.),

*35th Annual Conference of the Mathematics Education Research Group of Australasia: Mathematics Education: Expanding Horizons*(pp. 625-632). Adelaide: Mathematics Education Research Group of Australasia.