Marketing

Rational number

Praxeology

Linguistics

Mathematics education

Philosophy

Service (business)

Discrete mathematics

Danish

Archaeology

Economics

Business

Neoclassical economics

Mathematics

Geography

Decimal

Epistemology

Natural (archaeology)

Sociology

Indonesian

Arithmetic

Eurasia Journal of Mathematics Science and Technology Education

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.

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