Programming-based activities are becoming more widespread in curricula. Our theoretical and empirical investigation seeks to identify appropriate ways to connect computer programming and algorithmics to mathematical learning. We take the intermediate value theorem as our starting point, as it is covered by the French school curriculum, and because…

In this article, I present the eighteenth century's polemic of Bernoulli and d'Alembert concerning the smallpox epidemic and a prevention method called inoculation. Through an analysis of the polemic and the related resources, I show that this historical debate has various interests for mathematics education; and more specifically it can help…

The study presented in this article takes a closer look at how French and German high-school students deal with a mathematical modeling problem, what blockages they encounter and how differences in the modeling processes between students from both nations can be explained by differences between the teaching and learning of mathematical modeling in…

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof--statement, proof, and theory--suggested by…

"Attribute" and "measurement" are two fundamental concepts in mathematics and physics. Teaching these concepts is essential even in elementary school, but numerous studies have pointed out pupils' difficulties with them. These studies emphasized that pupils must learn about attributes before being taught how to measure these…

Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many…

The evolution of indexing sequences and series has been little studied so far, although this topic presents difficulties for students. This symbolisation signified, however, an important means for operating more generally with finite and infinite series. This paper investigates the first steps during the eighteenth century and then the different…

Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric…

In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from…

We examine teachers' classroom activities with the spreadsheet, focusing especially on episodes marked by improvisation and uncertainty. The framework is based on Saxe's cultural approach to cognitive development. The study considers two teachers, one positively disposed towards classroom use of technology, and the other not, both of them…

Simplicity arguments are to be found in most geometrical works, from those of Proclus in his "Commentaries on the First Book of Euclid's Elements," up to those of contemporary manuals. Our goal is to read these arguments in their historical contexts to analyze agreements, disagreements and the multiplicity of points of view. For a better…

In this paper, we use the theory of didactic situations to characterize a mathematics teaching practice, currently used in secondary schools in France, which we have called "interactive synthesis discussion." We have studied this practice in ordinary classes, i.e. classes where the researcher intervenes neither in the preparation nor in…

This paper outlines some theoretical categories (i.e. the "meso-", "topo-", "chrono-geneses," the "milieu," the didactical contract and the learning games), providing a "model" to study mathematics teacher's action. In order to show what this model brings to the didactical analysis, we present the…

Time is a constraint but also a condition of operating within a didactic system. Don't we need to distinguish several kinds of times? Our study will focus on teachers' time management strategies. We will identify these strategies by taking into account two temporal dimensions--didactic time and time capital--and the rate at which the former…