### Abstract

The purpose of this teaching experiment was to give fifth grade students activities using simple machines to see how they would use proportional reasoning to mathematize those activities. We chose a series of activities using two types of levers, because of their experiences with seesaws and because this combined mathematics with science. We hoped that they would develop models of the lever. We also hoped that they would recognize the inverse multiplicative relationship between distance and weight. The students did demonstrate evidence of preliminary models about the relationship between weights and distances on a lever. On the final day, the students, in a thought experiment, were able to discover the multiplicative relationship between distance and weight, but they did not realize the inverse nature of this relationship.

Original language | English (US) |
---|---|

Title of host publication | Modeling Students' Mathematical Modeling Competencies: ICTMA 13 |

Publisher | Springer US |

Pages | 301-312 |

Number of pages | 12 |

ISBN (Print) | 9781441905604 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### Keywords

- Inverse relationship
- Mental model cycle
- Scaffold
- Teaching experiments

### ASJC Scopus subject areas

- Social Sciences(all)
- Arts and Humanities(all)

### Cite this

*Modeling Students' Mathematical Modeling Competencies: ICTMA 13*(pp. 301-312). Springer US. https://doi.org/10.1007/978-1-4419-0561-1_26

**Two cases studies of fifth grade students reasoning about levers.** / Guerra, Paula; Hernández, Linda; Kim, Ahyoung; Menekse, Muhsin; Middleton, James.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Modeling Students' Mathematical Modeling Competencies: ICTMA 13.*Springer US, pp. 301-312. https://doi.org/10.1007/978-1-4419-0561-1_26

}

TY - CHAP

T1 - Two cases studies of fifth grade students reasoning about levers

AU - Guerra, Paula

AU - Hernández, Linda

AU - Kim, Ahyoung

AU - Menekse, Muhsin

AU - Middleton, James

PY - 2010

Y1 - 2010

N2 - The purpose of this teaching experiment was to give fifth grade students activities using simple machines to see how they would use proportional reasoning to mathematize those activities. We chose a series of activities using two types of levers, because of their experiences with seesaws and because this combined mathematics with science. We hoped that they would develop models of the lever. We also hoped that they would recognize the inverse multiplicative relationship between distance and weight. The students did demonstrate evidence of preliminary models about the relationship between weights and distances on a lever. On the final day, the students, in a thought experiment, were able to discover the multiplicative relationship between distance and weight, but they did not realize the inverse nature of this relationship.

AB - The purpose of this teaching experiment was to give fifth grade students activities using simple machines to see how they would use proportional reasoning to mathematize those activities. We chose a series of activities using two types of levers, because of their experiences with seesaws and because this combined mathematics with science. We hoped that they would develop models of the lever. We also hoped that they would recognize the inverse multiplicative relationship between distance and weight. The students did demonstrate evidence of preliminary models about the relationship between weights and distances on a lever. On the final day, the students, in a thought experiment, were able to discover the multiplicative relationship between distance and weight, but they did not realize the inverse nature of this relationship.

KW - Inverse relationship

KW - Mental model cycle

KW - Scaffold

KW - Teaching experiments

UR - http://www.scopus.com/inward/record.url?scp=84892347453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892347453&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-0561-1_26

DO - 10.1007/978-1-4419-0561-1_26

M3 - Chapter

AN - SCOPUS:84892347453

SN - 9781441905604

SP - 301

EP - 312

BT - Modeling Students' Mathematical Modeling Competencies: ICTMA 13

PB - Springer US

ER -