This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of…

Prior research highlights the role of number manipulation activities in fostering the early mathematical development of children. This study (N = 1,491) explored the effect of a bear-themed intervention on enhancing arithmetic abilities in kindergarten students. Utilizing a pre- and post-test design, the study compared the advancements of children…

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…

On the lookout for and with a vested interest in Canadian mathematics education matters, this article is dedicated to hockey cards. More specifically, the statistics found on the back of hockey cards. The combination of taking a trip down memory lane, thrifting in British Columbia, traipsing around Toronto, and having coffee (one cream) at Tim…

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…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

Derek Holton and Duncan Symons present the first in a series of three papers that address sequences and their patterns. Their explorations lead to classroom teaching suggestions that involve creative thinking.

Diagrams and in general the use of visualization and manipulative material play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an…

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

We study the ideas about teaching and learning mathematics that undergraduate students generate when they encounter tasks designed to embed approximations of teaching practice in mathematics courses taken by a general population of students. These tasks attend to the dual goals of developing an understanding of mathematics content and an…

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means…

In this commentary, we explore tensions between engaging students in authentic disciplinary mathematical activity and insights from critical theorists who analyze equity in mathematics education. The tensions arise as engaging students in authentic mathematical activity usually involve having students adopt the language and norms of another…

This article investigates the potential mathematical learning opportunities arising from a digital activity designed to enhance students' comprehension of equations. Employing a commognitive-oriented lens, the analysis explores the potential mathematical discourses that could emerge from students' interactions with a digital scale inspired by the…

Building upon the blockbuster success of "Building Thinking Classrooms in Mathematics," Peter Liljedahl has joined forces with co-author Maegan Giroux to bring the Building Thinking Classrooms (BTC) framework to life in this new book, "Mathematics Tasks for the Thinking Classroom, Grades K-5." But this book is so much more than…