Models-and-modeling perspective (MMP) is a problem-solving and learning perspective in mathematics education. Although modeling processes have been addressed widely in the international discussion on mathematical modeling, a homogeneous understanding has not been established yet. Hence, the field needs studies addressing the epistemological…

Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this…

The goal of this article is to investigate Davydov's concept of the concept against the backdrop of its philosophical system, namely, dialectical materialism. In the first part, after briefly sketching the context of Davydov's work, I consider some ontological and epistemological ideas on which Davydov bases his concept of the concept. I pay…

A great deal of progress has been made in dealing with the multiplicity and diversity of theories in mathematics education. However, relatively little attention has been paid to the opportunities offered by conflicts, tensions, and paradoxes among accepted yet opposing theoretical perspectives for theory building and theory advancement. In this…

Epistemological beliefs are considered to play an important role in processes of learning and teaching. However, research on epistemological beliefs is confronted with methodological issues as for traditionally used self-report instruments with closed items, problems with social desirability, validity, and capturing domain-specific aspects of…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

This manuscript focuses on how students make sense of proofs. Participants were students who engaged in peer-review conferences of each other's attempted proofs in a graduate-level real analysis course for mathematics teachers. Building on the concept of distance from conversational analysis, we distinguish how three types of distance (epistemic,…

What are the effects of teaching the dominant mathematics on the wholeness and integrity of the cultural, social and linguistic resources of diverse communities? In this text, I seek to capture the risks associated with utilising non-Western resources in the teaching of the dominant mathematics in order to elucidate possible types of harms that…

The COVID-19 pandemic has changed the agenda of mathematics education. This change will be analyzed by looking at three trends in mathematics education: the use of digital technology, philosophy of mathematics education, and critical mathematics education. Digital technology became a trend in mathematics education in response to the arrival of a…

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…

Language, which plays a special role for the learning of mathematics, is investigated in this article for the specific discourse practice of explaining during whole-class discussions: On the one hand, explaining is a medium for learning since school cannot be thought of without communication. On the other hand, students at the beginning of…

Preparing students for their lives beyond schooling appears to be a universal goal of formal education. Much has been done to make mathematics education more "realistic," but such activities nevertheless generally remain within the institutional norms of education. In this article, we assume that pedagogic relations are also an integral…

There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students' conceptual developments in mathematics. We problematize…

Two questions about certainty in mathematics are asked. First, is mathematical knowledge known with certainty? Second, why is the belief in the certainty of mathematical knowledge so widespread and where does it come from? This question is little addressed in the literature. In explaining the reasons for these beliefs, both cultural-historical and…

A theoretical reflection on epistemology is presented. The important role of epistemological analysis in research in mathematics education is discussed. I analyze the epistemological evolution as a consequence of the changes in the mathematical culture and demonstrate how the epistemological analysis is tightly linked to the cultural dimension.…