In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

The Programme of International Student Assessment (PISA) has instigated domestic policy debate aimed at improving education systems' quality and efficiency. Its high performers are often described as knowledge-based legitimation tools that have become reference societies. This article analyses if and the extent to which PISA affects the choice of…

This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics…

Many international studies focus empirically on integrating the history of mathematics in mathematics education. Over the last 2 decades, some studies also revealed theoretical elements concerning the implementation of learning sessions and/or their didactical analysis and effectiveness. This paper has the aim of complementing these empirical…

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…

Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students,…

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…

Background: Young children's mathematics abilities may be divided between symbolic and non-symbolic skills. Lower performance of SES disadvantaged versus advantaged children has already been established in symbolic math. Aim: This study aimed to verify the effect of children's SES category on non-symbolic mathematical (numerical) performance.…

During this digital era, France, like many other countries, is undergoing a transition from paper-based assessments to digital assessments in education. There is a rising interest in technology-enhanced items which offer innovative ways to assess traditional competencies, as well as addressing problem solving skills, specifically in mathematics.…

Numeration units (ones, tens, hundreds, etc.) are an epistemological foundation for place value. Here, we assume that they are a didactic support in countries where spoken numbers are incongruent with written numbers. In France, teaching practices neglect the relations between units, and numeration units are typically used only to designate the…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from…