A practice-based engineering degree, in which students worked on real-world, team-based projects from day one and throughout their course, was designed to address the need for employability skills in a rapidly changing world. Teaching mathematics in this way required a very different approach to the lecture-exam based model prevalent in most…

This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and…

The multiplicative reasoning that students should develop in elementary school is a key area of research in contemporary mathematics education. Researchers employ various views including multiplication as arithmetic operation, multiplicative structures, and multiplicative relationships. They also propose various classifications of multiplicative…

In this paper, we share details of a South African early grades' number intervention informed by aspects of Davydov's writing on early number teaching and learning. A key part of Davydov's approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number…

One of the topics within the course of Essential Concepts in School Mathematics (ECSM) for prospective mathematics teachers concerns maximum and minimum problems. This type of problems requires mathematization, i.e., the activity of transforming a problem into a symbolic mathematics problem and of reorganizing within the mathematical system, in…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…

Posing problems in the mathematics classroom can enhance students' learning experiences and allow them to produce problems in a realistic context. Students do not always associate positive feelings with mathematics. Problem-posing activities can positively impact students' mathematical understanding while allowing for freedom of expression.…

The aim of this study is to examine studies on mathematics teaching anxiety thematically. For this purpose, 44 research articles on mathematics teaching anxiety published between 2000-2020 were examined. Studies were collected through document review and evaluated in terms of publication year, sample type, method, data collection tools, purpose…

In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

This article presents a series of open-ended tasks exploring the development of algebraic expressions suitable for exploration with Year 7 students. The tasks use a familiar tool, the hundreds chart, to aid the transition between representational tools and abstract ways of working. The tasks outline a developmental progression of patterns and…

This theoretical paper examines views about the role of language and mathematical discourse in learning mathematics. Current research is still addressing what constitutes a mathematical discourse. As new conceptions of the purpose of language use in mathematics are explored, and associated ontological and epistemic positions are revealed, one…

The focus of this dissertation is on students' thinking regarding the function concept in the context of abstract algebra, focusing on the properties of well- and everywhere-definedness. This dissertation follows a three-paper format, where each paper has a different yet related focus. In the first paper, I analyze (non-)examples found in…

Noticing children's mathematical thinking is foundational to teaching that is responsive to children's thinking. To better understand the range of noticing expertise for teachers engaged in multiyear professional development, we assessed the noticing of 72 upper elementary school teachers using three instructional scenarios involving fraction…

Understanding and reasoning with functions permeates mathematics education standards at all grade levels. Research shows students take multiple approaches to building functions. Deep content knowledge of functions may affect how pre-service teachers link student reasoning with mathematical ideas. To extend and connect the research literature on…

Preparing graduates for employment is the goal of postsecondary education. In response to the national quantitative reasoning deficiency, institutions have joined nationwide to align college math content and learning outcomes to meet the needs of common careers and everyday life. The problem addressed in this study is that traditional college math…