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…

The aim of this article is to carry out a work of networking theories which combines two perspectives on the mathematical activity involved in a modelling process, in order to answer the following question: To what extent does the application of the onto-semiotic tools complement the analysis from a cognitive perspective of a mathematical…

Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM…

Since the introduction by Kermack and McKendrick in 1927, the Susceptible-Infected-Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious…

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…

Offering explanations is a central part of teaching mathematics, and understanding those explanations is a vital activity for learners. Given this, it is natural to ask what makes a good mathematical explanation. This question has received surprisingly little attention in the mathematics education literature, perhaps because the field has no…

Cognitively demanding tasks have been shown to support students' understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers…

This article presents several activities suitable for a transition to proofs course. In addition, this article surveys literature in support of active learning in the transition to proofs course and discusses how these activities have been successfully implemented in one such course.

Learning mathematics is often justified as supporting students to make rational decisions, an important goal given the misinformation spread through social media every day. However, when asking preservice teachers to engage in a critical mathematics education activity in which they had to produce an argumentation that would persuade people to…

The aim of this qualitative study was to explore the thoughts of primary and secondary prospective mathematics teachers about educating mathematically gifted students. For this purpose, this research was conducted with 40 prospective mathematics teachers, 17 of whom were secondary mathematics prospective teachers, and 23 were primary mathematics…

Previous studies highlight the importance of investigate the construction in video-recorded learning situations. The aim of this study is to investigate how video-recordings can be used to enhance pre-service teachers' abilities to identify children's exploration of mathematics in preschools. Even if some previous studies have focused the use of…

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f…

This study focuses on connections between linear functions and their graphs that were made by tertiary remedial algebra students. In particular, we describe students' work on a Task designed to examine the connection between points on a graph and the equation of a line. The data consist of 63 responses to a written questionnaire and individual…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…

Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…