How to teach and assess whole number arithmetic: some international perspectives

Jarmila Novotná, Berinderjeet Kaur, Ann Gervasoni, Michael Askew, Michiel Veldhuis, Catherine Pearn, Xu Hua Sun

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther


This chapter focusses on the diverse theoretical and methodical frameworks that capture the complex relationship between whole number arithmetic (WNA) learning, teaching and assessment. Its aim is to bring these diverse perspectives into conversation. It comprises seven sections. The introduction is followed by a narrative of a Macao primary school lesson on addition calculations with two-digit numbers, and this sets the context for the subsequent three sections that focus on the development of students’ mathematical and metacognitive strategies during their learning of WNA. Apart from examining the impact of teachers’ knowledge of pedagogy, learning trajectories, mathematics and students on children’s learning of WNA, learning theories are also drawn on to interpret the lesson in the Macao Primary School. Two interpretations of the variation theory (VT), an indigenous one and a Western perspective, provide much needed lenses for readers to make sense of the lesson. In addition, the theory of didactical situations (TDS) is also applied to the lesson. The chapter also includes a reflection on possible classroom assessment and the role of textbooks, both of which were less apparent in the lesson, for the teaching and learning of WNA.

Original languageEnglish
Title of host publicationBuilding the Foundation
Subtitle of host publicationWhole Numbers in the Primary Grades: The 23rd ICMI Study
EditorsMaria G. Bartolini Bussi, Xu Hua Sun
Place of PublicationCham Switzerland
Number of pages36
ISBN (Electronic)9783319635552
ISBN (Print)9783319635545
Publication statusPublished - 2018
EventInternational Commission on Mathematical Instruction (ICMI) Study Conference 2015 - University of Macau, Macau, Macao
Duration: 3 Jun 20157 Jun 2015
Conference number: 23rd

Publication series

NameNew ICMI Study Series
ISSN (Print)1387-6872
ISSN (Electronic)2215-1745


ConferenceInternational Commission on Mathematical Instruction (ICMI) Study Conference 2015
Abbreviated titleICMI Study 2015
Internet address

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