### Abstract

ABSTRACT: In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic operations with rational numbers. In order to evaluate the potential applicability of the framework to task design, it was used for the design of mathematical learning tasks for teachers. The article includes examples of the tasks, their theoretical analysis, and empirical evidence of the sensitivity of the tasks to variations in teachers’ knowledge of the subject. This evidence is based on a study of 46 primary school teachers. The article concludes with remarks on the applicability of the framework to research and practice, highlighting its potential to encourage teaching the four algorithms with an emphasis on conceptual understanding.

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

Pages (from-to) | 43-60 |

Number of pages | 18 |

Journal | Research in Mathematics Education |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2 2016 |

### Fingerprint

### Keywords

- mathematical knowledge for teaching
- Standard algorithms of the four basic arithmetic operations
- task design

### ASJC Scopus subject areas

- Education
- Mathematics(all)

### Cite this

*Research in Mathematics Education*,

*18*(1), 43-60. https://doi.org/10.1080/14794802.2016.1141313

**Four (algorithms) in one (bag) : an integrative framework of knowledge for teaching the standard algorithms of the basic arithmetic operations.** / Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit.

Research output: Contribution to journal › Article

*Research in Mathematics Education*, vol. 18, no. 1, pp. 43-60. https://doi.org/10.1080/14794802.2016.1141313

}

TY - JOUR

T1 - Four (algorithms) in one (bag)

T2 - an integrative framework of knowledge for teaching the standard algorithms of the basic arithmetic operations

AU - Raveh, Ira

AU - Koichu, Boris

AU - Peled, Irit

AU - Zaslavsky, Orit

PY - 2016/1/2

Y1 - 2016/1/2

N2 - ABSTRACT: In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic operations with rational numbers. In order to evaluate the potential applicability of the framework to task design, it was used for the design of mathematical learning tasks for teachers. The article includes examples of the tasks, their theoretical analysis, and empirical evidence of the sensitivity of the tasks to variations in teachers’ knowledge of the subject. This evidence is based on a study of 46 primary school teachers. The article concludes with remarks on the applicability of the framework to research and practice, highlighting its potential to encourage teaching the four algorithms with an emphasis on conceptual understanding.

AB - ABSTRACT: In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic operations with rational numbers. In order to evaluate the potential applicability of the framework to task design, it was used for the design of mathematical learning tasks for teachers. The article includes examples of the tasks, their theoretical analysis, and empirical evidence of the sensitivity of the tasks to variations in teachers’ knowledge of the subject. This evidence is based on a study of 46 primary school teachers. The article concludes with remarks on the applicability of the framework to research and practice, highlighting its potential to encourage teaching the four algorithms with an emphasis on conceptual understanding.

KW - mathematical knowledge for teaching

KW - Standard algorithms of the four basic arithmetic operations

KW - task design

UR - http://www.scopus.com/inward/record.url?scp=84959332795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959332795&partnerID=8YFLogxK

U2 - 10.1080/14794802.2016.1141313

DO - 10.1080/14794802.2016.1141313

M3 - Article

VL - 18

SP - 43

EP - 60

JO - Research in Mathematics Education

JF - Research in Mathematics Education

SN - 1479-4802

IS - 1

ER -