Four (algorithms) in one (bag): an integrative framework of knowledge for teaching the standard algorithms of the basic arithmetic operations

Ira Raveh, Boris Koichu, Irit Peled, Orit Zaslavsky

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)43-60
Number of pages18
JournalResearch in Mathematics Education
Volume18
Issue number1
DOIs
StatePublished - 2 Jan 2016

Bibliographical note

Funding Information:
This research was conducted at the Technion ? Israel Institute of Technology. The Technion?s generous financial help is gratefully acknowledged.

Publisher Copyright:
© 2016 British Society for research into Learning Mathematics.

Keywords

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

ASJC Scopus subject areas

  • Education
  • Mathematics (all)

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