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Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings
Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.ORCID iD: 0000-0002-6453-1623
2020 (English)In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704Article in journal (Refereed) Epub ahead of print
Abstract [en]

The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive and multiplicative relations have been theorized. We examine how the connections between these can be considered through a focus on number line representations and children positioning and comparing numbers. The responses of a cohort of South African Grade 1 learners’ (6- and 7-year-olds) to a numerical magnitude estimation task and to a numerical comparison task are analysed and the findings compared to those in the international literature, some of which argue that children’s early, informal, understandings of cardinality and ordinality are underpinned by an intuitive logarithmic model relating number order and size. A main finding presented here is that the responses from learners in this study exhibited a better fit with an exponential model of the relationship between cardinality and ordinality. These findings raise questions about whether some of the findings in previous research are as universal as sometimes claimed.

Place, publisher, year, edition, pages
Springer, 2020.
Keywords [en]
Cardinality, Ordinality, Relational understanding, Log-to-linear shift
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-47716DOI: 10.1007/s11858-020-01132-2ISI: 000507775800001Scopus ID: 2-s2.0-85078633092Local ID: ;HLKÖvrigtISOAI: oai:DiVA.org:hj-47716DiVA, id: diva2:1390953
Available from: 2020-02-03 Created: 2020-02-03 Last updated: 2020-02-18

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Venkat, Hamsa

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CiteExportLink to record
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