Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia

Zetra Hainul Putra

doi:10.29333/ejmste/105867

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Zetra Hainul Putra ¹ ² ^*

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¹ University of Copenhagen, Department of Science Education, Copenhagen, DENMARK² University of Riau, Faculty of Teacher Training and Education, Pekanbaru, INDONESIA^* Corresponding Author

Abstract

The present study aims to introduce the notion of praxeological change, developed based on the Anthropological Theory of the Didactic, to describe a necessity of changing mathematical praxeologies when passing from natural to rational numbers. It is applied to study and compare Danish and Indonesian pre-service teachers’ (PSTs) knowledge of the density of rational numbers. They work in pairs to solve and discuss a hypothetical teacher task, which involves both mathematical and didactical tasks, related to the density of rational numbers. The findings highlight significant differences of the mathematical and didactical knowledge which are shared by the Danish and Indonesian PSTs. In particular, the Danish PSTs are more successful than the Indonesian PSTs in proposing didactical praxeologies to support pupils’ praxeological change. They use the mathematical idea of converting fractions into decimals or vice versa and representing fractions and decimals on the same number line, while the Indonesian pairs tend to suggest pupils to order fractions and decimals based on the ordering properties of natural numbers.

Keywords

praxeological change
anthropological theory of the didactic
hypothetical teacher task
density of rational numbers

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 15, Issue 5, May 2019, Article No: em1711

https://doi.org/10.29333/ejmste/105867

Publication date: 21 Mar 2019

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Article Downloads: 1354

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How to cite this article

APA

Putra, Z. H. (2019). Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 15(5), em1711. https://doi.org/10.29333/ejmste/105867

Vancouver

Putra ZH. Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia. EURASIA J Math Sci Tech Ed. 2019;15(5):em1711. https://doi.org/10.29333/ejmste/105867

AMA

Putra ZH. Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia. EURASIA J Math Sci Tech Ed. 2019;15(5), em1711. https://doi.org/10.29333/ejmste/105867

Chicago

Putra, Zetra Hainul. "Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 5 (2019): em1711. https://doi.org/10.29333/ejmste/105867

Harvard

Putra, Z. H. (2019). Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 15(5), em1711. https://doi.org/10.29333/ejmste/105867

MLA

Putra, Zetra Hainul "Praxeological Change and the Density of Rational Numbers: The Case of Pre-service Teachers in Denmark and Indonesia". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 5, 2019, em1711. https://doi.org/10.29333/ejmste/105867