Mathematical modelling and modelling activities are important for making sense of mathematical concepts in different extracurricular and daily life contexts. However, teachers may have difficulties in designing these activities in a way to establish meaningful relationships with real life, in accordance with the modeling process and the objectives…

Using the sawtooth map as the basis of a coupled map lattice enables simple analytic results to be obtained for the global Lyapunov spectra of a number of standard lattice networks. The results presented can be used to enrich a course on chaos or dynamical systems by providing tractable examples of higher dimensional maps and links to a number of…

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…

As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

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…

This paper reports on a combined research-development project conducted in collaboration between researchers and preschool teachers in three Swedish preschools. The aim is to investigate how ongoing preschool activities may become the starting point for mathematics teaching in which toddlers are given the opportunity to distinguish necessary…

This study examined seventh-grade students' emergent and progressive financial literacy in the context of risk and reward while working on two mathematical modelling tasks. The participants were six seventh-grade students identified as 'good at mathematics' by their teachers. The data sources comprised videotaped group discussions, group…

We present an example of one of the modelling projects we assign to students in our differential equations classes. Students are asked to determine how to run a cost-efficient hot water heating system. We consider a cylindrical tank filled with water and heated by a heating element immersed in it. Together with students we discuss physical laws…

Playing board games and other math activities can provide young children with opportunities to develop their math skills. However, it is critical to understand for whom these activities may be most beneficial. In two studies, we examine the extent to which foundational cognitive skills moderate the effects of playing math games on math skills. In…

The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

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…

The authors discuss the use of "real life" activities that are interesting to children in the teaching of measurement and number concepts. In this article, they present a series of lessons targeting volume and capacity that seamlessly incorporate genuine "real-life" experiences with practical mathematical applications. In…

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…

The authors describe the benefit of launching mathematics lessons in ways that engage young learners. Short, meaningful introductions can motivate and focus students. Some features of interesting launches are drawn from Ben Dixon's Foundation classroom.

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…