Language in the Mathematics Classroom: An introduction to the papers and presentations within ETC 7

Research considering the role of language in the teaching and learning of mathematics continues to grow and develop, drawing on a range of theoretical, methodological and pedagogical approaches. In this introduction, we detail the discussions had and issues raised at the 7th ERME Topic Conference as a result of the bringing together of the theoretical perspectives, foci and findings of the papers presented that are included in these proceedings. These rich discussions also raised new challenges for those researching language and mathematics and identified new possibilities for the future work of the Mathematics and Language thematic working group. Keywords: Language and mathematics, multilingual contexts, meaning-making, interaction<br/

Walzebug, Anke (2015). Sprachlich bedingte soziale Ungleichheit. Theoretische und empirische Betrachtungen am Beispiel mathematischer Testaufgaben und ihrer Bearbeitung [Rezension]

Rezension von: Walzebug, Anke (2015). Sprachlich bedingte soziale Ungleichheit. Theoretische und empirische Betrachtungen am Beispiel mathematischer Testaufgaben und ihrer Bearbeitung

Innovativ utdanning i matematikk

I denne artikkelen beskrives et prosjekt ved NTNU som har som mål å modernisere undervisningen i grunnleggende matematikkemner for å øke studentenes læringsutbytte. Basert på spørreundersøkelser og intervjuer beskrives foreløpige erfaringer og funn fra prosjektet. Nøkkelord: Matematikkundervisning for ingeniører, video, databasert vurdering, veiledningstjeneste

Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations

This paper is based on data from two teaching sequences in primary school that are designed using principles from the theory of didactical situations (TDS). The following research question is addressed: “What opportunities can a teaching design based on TDS give a teacher to gain insight into pupils’ language use, and to use this insight to establish shared, and mathematically acceptable, knowledge in a group of primary school pupils?” Empirical data from one teaching sequence on geometrical shapes and another teaching sequence on combinatorial problems are used to answer this question. The research shows that a sharp focus on well-defned learning goals does not limit the pupils’ possibilities in expressing their thoughts and ideas in their own language. The research also shows that despite clear learning goals, the teacher has rich opportunities to build on pupils’ language to connect everyday and scientifc language for the purpose of developing a mathematically accepted discourse

Integral representations of bounded starlike functions

For α ≥ 0 let $ℱ_α$ denote the class of functions defined for |z| 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf'(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to $ℱ_0$. In general, it is only known that bounded starlike functions belong to $ℱ_α$ for α > 0

Innovativ utdanning i matematikk

This paper describes a project at NTNU where the aim is to modernize education in the basic mathematics subjects in order to increase students’ learning outcomes. Based on surveys and interviews, the paper reports on preliminary experiences and findings from the project

The Role of Fourier Series in Mathematics and in Signal Theory

This paper presents a praxeological analysis, based on ATD (Anthropological Theory of the Didactic), of the topic of Fourier series, as this topic is introduced and used in mathematics and in electrical engineering, more precisely in signal theory. The analysis is based mainly on one widely used textbook in mathematics for engineers, and a textbook and video lectures in signal theory. The aim of the analysis is to investigate possible differences in the motivation for introducing Fourier series in mathematics and in signal theory, as well as differences in the techniques used, and the justifications behind the techniques. This research is inspired by previous research showing lack of connection between mathematics courses and engineering courses applying mathematics. To get a wider perspective, the exposition in the textbook in mathematics for engineers is also compared to the exposition in more advanced books in mathematics. To add to the perspective, the historical origin of Fourier series is also discussed. The findings show that there are differences in the motivation for the topic both between mathematics and signal theory, but also between basic and more advanced mathematics. Within mathematics there are also differences in the underlying theories

Choice of representations in combinatorial problems

International audienceThis paper is based on classroom sessions where Norwegian 9-year-old (Grade 4) children work on combinatorial problems. The classroom sessions are part of a four-year long research project where the topic of multiplicative structures was central. I will investigate to what extent the pupils recognise the combinatorial problems as multiplicative and identify possible connections between the semiotic representations chosen in the solutions and in the formulation of the problems