Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations. A range of classroom…

This study aimed to design and analyze activities that enable students to investigate the probabilities of compound events and the equiprobability bias by a perception-based design that foregrounds sample sets. Drawing on historical insights and prior research, we designed activities to guide students in exploring the probabilities of compound…

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…

Parents' math anxiety may hinder their engagement in math activities with their children. This study investigated when this impact occured by examining the association between parental math anxiety and the frequency of home-based math activities among parents of preschool-aged children, and investigating whether this parental math anxiety-activity…

This article examines what constitutes a 'good' mathematical problem and proposes to conceptualize the notion of "collective mathematical problems" as phenomena that arise through and by way of the inter-actions enabled by the collective itself. The author examines how these collective mathematical problems can emerge in the classroom…

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 article shares activities that engage students in quality peer dialogue to build up and break down networks, revealing underlying structure and equivalence. These investigations offer students three kinds of mathematical arguments: (1) proofs of impossibility; (2) proofs by induction; and (3) proofs by exhaustion. The authors describe a…

Students' sense of belonging in the mathematics classroom can be supported and increased by building mathematics tasks that connect to and incorporate aspects of students' identities and sense of selves (e.g., their names, images, and ages). This article shares one commonly used mathematics task and highlights how it can be used to create…

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…

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…

English Learners benefit from rich opportunities to explore and engage with peers. We describe pattern-seeking and argument-constructing activities that support partners as they co-construct representations of networks, such as social networks connecting people. Such activities allow all students to explore relationships between vertices, edges,…

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…

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…