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The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes
Sun,Xu Hua1; Chambris,Christine2; Sayers,Judy3; Siu,Man Keung4; Cooper,Jason5; Dorier,Jean Luc6; de Lora Sued,Sarah Inés González7; Thanheiser,Eva8; Azrou,Nadia9; McGarvey,Lynn10; Houdement,Catherine11; Ejersbo,Lisser Rye12
2018-03
Source PublicationBuilding the Foundation: Whole Numbers in the Primary Grades - The 23rd ICMI Study
PublisherSpringer, Cham
Pages91-124
Abstract

Increasing globalization encourages assumptions of universalism in teaching and learning, in which cultural and contextual factors are perceived as nonessential. However, our teaching and learning are unavoidably embedded in history, language and culture, from which we draw to organize our educational systems. Such factors can remain hidden but can also provide us with opportunities to gain a deeper understanding of constraints that are taken for granted. This chapter provides a meta-level analysis and synthesis of the what and why of whole number arithmetic (WNA). The summary provides background for the whole volume, which identifies the historical, cultural and linguistic foundations upon which other aspects of learning, teaching and assessment are based. We begin with a historical survey of the development of pre-numeral and numeral systems. We then explore the epistemological and pedagogical insights and highlight the differences between linguistic practices and their links with the universal decimal features of WNA. We investigate inconsistencies between spoken and written numbers and the incompatibility of numeration and calculation and review a number of teaching interventions. Finally, we report the influence of economics and business, academic mathematics, science and technology and public and private stakeholders on WNA to understand how and why curriculum changes are made, with a focus on the fundamental losses and gains.

DOI10.1007/978-3-319-63555-2_5
URLView the original
Language英語English
ISBN978-3-319-63554-5
Scopus ID2-s2.0-85067918207
Fulltext Access
Citation statistics
Document TypeBook chapter
CollectionFaculty of Education
Affiliation1.Faculty of Education,University of Macau,Macao,China
2.Laboratoire de didactique André Revuz,Université de Cergy-Pontoise,Cergy,France
3.Stockholm University,Stockholm,Sweden
4.University of Hong Kong,Pokfulam, Hong Kong,China
5.Weizmann Institute of Science,Rehovot,Israel
6.University of Geneva,Geneva,Switzerland
7.Pontificia Universidad Católica Madre,Santiago de los Caballeros,Germany
8.Portland State University,Portland,United States
9.University Yahia Fares Medea,Medea,Algeria
10.University of Alberta,Edmonton,Canada
11.Laboratoire de didactique André Revuz,Université de Rouen-Normandie,Rouen,France
12.Aarhus University,Aarhus,Denmark
First Author AffilicationFaculty of Education
Recommended Citation
GB/T 7714
Sun,Xu Hua,Chambris,Christine,Sayers,Judy,et al. The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes[M]. Building the Foundation: Whole Numbers in the Primary Grades - The 23rd ICMI Study:Springer, Cham, 2018, 91-124.
APA Sun,Xu Hua., Chambris,Christine., Sayers,Judy., Siu,Man Keung., Cooper,Jason., Dorier,Jean Luc., de Lora Sued,Sarah Inés González., Thanheiser,Eva., Azrou,Nadia., McGarvey,Lynn., Houdement,Catherine., & Ejersbo,Lisser Rye (2018). The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes. Building the Foundation: Whole Numbers in the Primary Grades - The 23rd ICMI Study, 91-124.
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