This paper presents an extended project that offers, through American football, an application of concepts from enumerative combinatorics and an introduction to proofs course. The questions in this paper and subsequent details concerning equivalence relations and counting techniques can be used to reinforce these new topics to students in such a…

Our goal with this paper is three-fold. We want to increase awareness of inquiry-based learning by presenting the strategy we use to develop and implement lessons and activities. We describe our approach to structuring lessons in mathematics in a way that engages the students by using language and constructs with which they are familiar from other…

This article reports the results of a study that investigated pre-service mathematics teachers' modelling processes in terms of representational fluency in a modelling activity related to a cassette player. A qualitative approach was used in the data collection process. Students' individual and group written responses to the mathematical modelling…

This paper identifies binary oppositions in the discourse of mathematics education and introduces a binary-epistemic model for (re)conceptualising these oppositions and the epistemic-pedagogic problems they represent. The model is attentive to the contextual relationships between pedagogically relevant binaries (e.g., traditional/progressive,…

This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…

In Calculus, students are often both presented problems with and taught to use three interconnected types of representations: symbolic, graphic, and numeric. However, students often fail to notice the relationship between mathematical objects (and even the same object) that are presented using different types of representations. Using the APOS…

One of Martin Gardner's most famous columns introduced John Conway's game of Life. The inverse problem, finding a previous generation in the Game of Life given some extra constraints, was introduced a few years ago and is referred to as Retrolife. In this paper we present a puzzle played on a chessboard that is isomorphic to a variation of…

In this paper, I present and discuss critically the main elements of Mario Bunge's philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge's systemic emergent materialism.

The numerical range, easy to understand but often tedious to compute, provides useful information about a matrix. Here we describe the numerical range of a 3 x 3 magic square. Applying our results to one of the most famous of those squares, the Luoshu, it turns out that its numerical range is a piece of cake--almost.

The purpose of the current study was to investigate the effect of micro-teaching practices with concrete models on the pre-service teachers' self-efficacy beliefs about using concrete models and to determine the opinions of the pre-service teachers about this issue. In the current study, one of the mixed methods, the convergent design (embedded)…

Many preservice teacher (PST) programs throughout the world are preparing students to implement the Core Standards, which require deeper conceptual understandings of mathematics and an informed approach for teaching. In this qualitative multi-case study, researchers explored the teaching methods for two university instructors and changes in PSTs…

This study examines whether creating a mathematics-based digital story increases pre-service teachers' understanding of the problem solving process, the relationship among visual, auditory and verbal representation in critical thinking/problem solving in mathematics. Survey results indicated that pre-service teachers were unfamiliar with the uses…

This paper outlines a STEM (Science, Technology, Engineering and Mathematics) learning experience for children in the early years of school. It builds on STEM education in early childhood with a shared purpose, "to help children to explore and make sense of their world using childrelevant and appropriate contexts" (Preston, 2018 p. 137).…

This paper discusses the implementation and evaluation of an innovative professional development program that supported 8th grade mathematics teachers in designing learning activities that assisted students in developing a conceptual understanding of mathematics. Funded by an Investing in Innovation (i3) grant from the U.S. Department of…

Because math knowledge begins to develop at a young age to varying degrees, it is important to identify foundational cognitive and academic skills that might contribute to its development. The current study focused on two important, but often overlooked skills that recent evidence suggests are important contributors to early math development:…