### Abstract

In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context, for example graphically as slope, verbally as rate of change, or kinesthetically as velocity. We will illustrate three main cases of metonymy using data from student reasoning with derivative-paradigmatic metonymy, individual metonymy and part-part metonymy. Metonymies may function both in powerful and problematic ways for students as they come to understand and work with a complicated concept such as the derivative. It is the goal of this paper to illuminate and clarify how metonymy may function in student reasoning in the hopes of providing insights to teachers and researchers.

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

Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Journal of Mathematical Behavior |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - 2006 |

### Fingerprint

### Keywords

- Calculus
- Derivative
- Metaphor
- Metonymy
- Rate
- Slope

### ASJC Scopus subject areas

- Applied Mathematics
- Applied Psychology
- Education

### Cite this

**Exploring the role of metonymy in mathematical understanding and reasoning : The concept of derivative as an example.** / Zandieh, Michelle; Knapp, Jessica.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Exploring the role of metonymy in mathematical understanding and reasoning

T2 - The concept of derivative as an example

AU - Zandieh, Michelle

AU - Knapp, Jessica

PY - 2006

Y1 - 2006

N2 - In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context, for example graphically as slope, verbally as rate of change, or kinesthetically as velocity. We will illustrate three main cases of metonymy using data from student reasoning with derivative-paradigmatic metonymy, individual metonymy and part-part metonymy. Metonymies may function both in powerful and problematic ways for students as they come to understand and work with a complicated concept such as the derivative. It is the goal of this paper to illuminate and clarify how metonymy may function in student reasoning in the hopes of providing insights to teachers and researchers.

AB - In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context, for example graphically as slope, verbally as rate of change, or kinesthetically as velocity. We will illustrate three main cases of metonymy using data from student reasoning with derivative-paradigmatic metonymy, individual metonymy and part-part metonymy. Metonymies may function both in powerful and problematic ways for students as they come to understand and work with a complicated concept such as the derivative. It is the goal of this paper to illuminate and clarify how metonymy may function in student reasoning in the hopes of providing insights to teachers and researchers.

KW - Calculus

KW - Derivative

KW - Metaphor

KW - Metonymy

KW - Rate

KW - Slope

UR - http://www.scopus.com/inward/record.url?scp=32044452243&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32044452243&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2005.11.002

DO - 10.1016/j.jmathb.2005.11.002

M3 - Article

AN - SCOPUS:32044452243

VL - 25

SP - 1

EP - 17

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

IS - 1

ER -