In our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' ("Teaching Children Mathematics", 21(1), 18-25) "13 Rules That Expire" article has been a useful resource for us to…

This paper examines the phenomenon of homogenization in higher mathematics education from three dimensions: textbooks, teaching methods, and assessment, identifying rigid educational policies, limited resources, and entrenched teacher mindsets as underlying causes. It proposes four reform pathways: differentiated instruction, diverse teaching…

The paper focuses exclusively on the famous geometry lesson given by Socrates to the slave-boy in Plato's Meno, providing an in-depth analysis that emphasizes the pedagogical aspects of the lesson. This approach allows for an examination of the lesson that teachers, educators and students alike--regardless of their interest in the philosophical…

Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

The Pirie-Kieren Model (PKM) was a paradigm shift in theories of learning by presenting a coherent, consistent theory compatible with complexity theory. PKM recognized that learning is non-linear, recursive, iterative, and emergent. PKM was one of the first theories to depart from the linear models of learning that dominated theories of learning…

The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…

In this theoretical article, we propose a conceptualisation of noticing, drawing on our enactivist perspective, which takes account of what is now known about human cognition, and from which we draw out implications for how noticing develops. We review past work on mathematics teacher noticing and note the dominance of a paradigm of taking…

Terence Mills introduces us to Keynsian probability and discusses its implications for teaching probability. The author considers it unlikely that Keynes's theory would replace how we teach probability, but argues that it may make us think more deeply about the use of terms such as chance and probability when used in our lessons.

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…

Undergraduate peer drop-in mathematics tutoring is a common form of support at the university level, yet research regarding how to train this specific group of tutors is underspecified. This paper aims to describe a training program for this population that is grounded in mathematics education research. It serves as a first step in conducting a…

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Language is a conduit for communicating and understanding mathematical ideas. In this article, the authors describe how literacy relates to modes of reading, writing, speaking, and listening. They then share a strategy for supporting student literacy in mathematics--judicious telling--and provide examples of what this approach looks like in the…

Teacher questioning impacts the level of student thinking that occurs during mathematical instruction. It is important to investigate how questioning is developed in secondary mathematics methods classes so that these environments can support the development effective questioning strategies. This article explores how two preservice teachers use…

The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The…