Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in…

In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain instructions to perform mathematical actions, often in the form of imperatives, which are common both in mathematical practice and in undergraduate mathematics textbooks. We consider in detail a…

One can identify at least three different types of relationships between mathematics and crises. First, "mathematics can picture a crisis." This is in accordance with the classic interpretation of mathematical modelling, which highlights that a mathematical model provides a representation of a piece of reality, a reality that could be a…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students' listening is examined, using data from an educational design research study in an upper secondary…

Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers' professional mathematical modeling competencies in three different…

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…

Part of the international reflection on the use of history in mathematics teaching consists in a quest of frameworks and models suitable for empirical studies. Following this demand, this paper explores the way Balacheff's cK? model, a model taken from the didactics of mathematics, can be used in the analysis of learning at student level. In the…

Maturity and citizenship in a democracy require that laypersons are able to critically evaluate experts' use of mathematics. Learning to critically reflect on the use of mathematics, including the acquisition of the mathematical knowledge and skills required to that end, has been repeatedly postulated as an indispensable goal of compulsory…

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students…

In this paper, we present and discuss a framework for considering the quality of primary teachers' mediating of primary mathematics within instruction. The "mediating primary mathematics" framework is located in a sociocultural view of instruction as mediational, with mathematical goals focused on structure and generality. It focuses on…

We offer criteria that an observer can use to determine whether an argument that uses an example to argue for a general claim appeals to that example generically. We review existing literature on generic example and note the strengths of each contribution, as well as inconsistencies among uses of the term. We offer several examples from the…

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher's mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and…

The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…

In this volume, Wolff-Michael Roth provides a critical but partial reading of Tony Brown's book "Mathematics Education and Subjectivity". The reading contrasts Brown's approach with Roth's own conception of subjectivity as derived from the work of Vygotsky, in which Roth aims to "reunite" psychology and sociology. Brown's book, however, focuses on…