Extensions of number systems: continuities and discontinuities revisited

Sebastian Rezat (1)

1 Mathematisches Institut der Universität Paderborn

The extension of number systems from natural to rational and real numbers and related arithmetic is a prominent theme in mathematics from primary to upper secondary education. In parallel to the development of the number concept and the extension of number systems, students need to proceed from arithmetic to algebra. Students’ difficulties in mastering both, the extension from one number system to another and the progression from arithmetic to algebra are well documented. The paper focuses on the extension from natural numbers to integers with a particular interest in the relationship to the progression from arithmetic to algebra. Continuities and discontinuities in the alignment of these two parallel curricular developments are analyzed from three different perspectives, namely an epistemological, a psychological, and a pedagogical perspective. This analysis will include work from TWG02 “Arithmetic and Number Systems”, which gives a flourishing account of the multifaceted issues related to the teaching and learning of different number systems since its foundation at CERME7 in 2011 and also draws on the work of TWG03 “Algebraic Thinking”. Finally, conclusions will be drawn from the analysis of the relationship between the extension from natural numbers to integers and algebraic thinking in terms of the construction of a more coherent curriculum regarding these two developments.

Mots clés: number systems; integers; negative numbers; algebraic thinking; coherence

Domaines: Mathématiques [math]; Education

Sebastian Rezat. Extensions of number systems: continuities and discontinuities revisited. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. ⟨hal-02436283⟩