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…

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…

This article discusses algebraic thinking regarding positive integers and rational numbers when students, 6 to 9 years old in multilingual classrooms, are engaged in an algebraic learning activity proposed by the El'konin and Davydov curriculum. The main results of this study indicate that young, newly arrived students, through tool-mediated joint…

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…

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged…

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and…

The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were tape-recorded and fully transcribed, the students were encouraged to explore strategies for winning a…

We describe the "somatic marker hypothesis" proposed by Damasio (1996) to account for the ability of most people to make decisions quickly and continually in the course of their lives. We relate this hypothesis to two other theoretical constructs, emotional orientations and purposes, which we have used in our research on students' reasoning and…