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  • © 2016

Teaching and Learning About Whole Numbers in Primary School

  • Presents a bird’s-eye view of research on teaching and learning about numbers
  • Discusses pivotal ideas that have occupied researchers in mathematics education over the last four decades
  • Draws lessons for further research
  • Includes supplementary material: sn.pub/extras

Part of the book series: ICME-13 Topical Surveys (ICME13TS)

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Table of contents (1 chapter)

  1. Front Matter

    Pages i-ix
  2. Teaching and Learning About Whole Numbers in Primary School

    • Terezinha Nunes, Beatriz Vargas Dorneles, Pi-Jen Lin, Elisabeth Rathgeb-Schnierer
    Pages 1-50Open Access

About this book

This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future.

The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.

Authors and Affiliations

  • Department of Education, University of Oxford Department of Education, Oxford, United Kingdom

    Terezinha Nunes

  • Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

    Beatriz Vargas Dorneles

  • Graduate Institute of Mathematics and Science Education, National Hsinchu University of Education, Hsinchu City, Taiwan

    Pi-Jen Lin

  • University of Education Weingarten , Weingarten, Germany

    Elisabeth Rathgeb-Schnierer

Bibliographic Information

  • Book Title: Teaching and Learning About Whole Numbers in Primary School

  • Authors: Terezinha Nunes, Beatriz Vargas Dorneles, Pi-Jen Lin, Elisabeth Rathgeb-Schnierer

  • Series Title: ICME-13 Topical Surveys

  • DOI: https://doi.org/10.1007/978-3-319-45113-8

  • Publisher: Springer Cham

  • eBook Packages: Education, Education (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2016

  • Softcover ISBN: 978-3-319-45112-1Published: 05 September 2016

  • eBook ISBN: 978-3-319-45113-8Published: 29 August 2016

  • Series ISSN: 2366-5947

  • Series E-ISSN: 2366-5955

  • Edition Number: 1

  • Number of Pages: IX, 50

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Mathematics Education, Learning & Instruction, Teaching and Teacher Education

Buy it now

Buying options

Softcover Book USD 19.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access