Despite the prominence of analogies in mathematics, little attention has been given to exploring students' processes of analogical reasoning, and even less research exists on revealing how students might be empowered to independently and productively reason by analogy to establish new (to them) mathematics. I argue that the lack of a cohesive…

In this paper, we are interested in a dynamic vision of diagrams, focusing on their evocative power, their force in mathematical activity and their potential for interaction with mathematical objects. We are inspired by the work of C. S. Pierce to see diagrams as "inscriptions that organise space and articulate relations" and that of the…

An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving…

The Action-Process-Object-Schema (APOS) theory is applied to study student understanding of implicit differentiation in the context of functions of one variable. The APOS notions of Schema and schema development in terms of the intra-, inter-, and trans-triad are used to analyze semi-structured interviews with 25 students who had just finished…

In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a…

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…

Although counting problems are easy to state and provide rich, accessible problem-solving situations, there is much evidence that students struggle with solving counting problems correctly. With combinatorics (and the study of counting problems) becoming increasingly prevalent in K-12 and undergraduate curricula, there is a need for researchers to…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

The aim of the research presented in this paper is to contribute to our knowledge about problem solving in mathematics. My purpose in this paper is to compare, from this point of view, two very different institutions in the French tertiary education system, with the intention to interpret the chronic inequality of performance in problem solving…

Our research is concerned with teacher's knowledge, and especially with teacher's processes of learning, in the classroom, from observing and interacting with students' work. In the first part of the paper, we outline the theoretical framework of our study and distinguish it from some other perspectives. We argue for the importance of…