There is an ongoing need to support students' learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We…

Mathematical knowledge for teaching is a complex web of knowledge domains. In this article, we share findings from an 18-month professional development project that aimed to improve middle school mathematics teachers' mathematical knowledge for teaching (MKT) of proportional reasoning by focusing on the critical analysis of mathematical tasks and…

Many South African educational institutions are adopting learning management systems (LMS) into their daily teaching and learning practice. The Western Cape Education Department piloted Modular Object-Oriented Dynamic Learning Environment (Moodle), an LMS for improving teaching and learning. The objective of the research reported on here was to…

Mathematical Knowledge for Teaching (MKT), comprising Mathematics Content Knowledge (MCK) and Mathematics Pedagogy Content Knowledge (MPCK), is essential for pre-service teachers. However, numerous studies have shown that pre-service teachers are weak in content and difficult to plan to teach. Therefore, a shifting effort dealing with the learning…

Teaching Pasifika learners effectively to improve their educational outcomes is an education priority in New Zealand. New ways to maximise learning are needed. This article shows how dance, a cultural experience of many Pasifika learners, offers strong opportunities for enhancing learning across the curriculum while impacting positively on…

Children are innately mathematical and explore mathematical concepts through play. However, educator beliefs about mathematics can impact the inclusion of mathematics in early childhood education (ECE). Recent research has suggested that spatial reasoning is a key concept which forms the foundations of mathematics learning. The theoretical…

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

The purpose of this study is to examine the effects of concrete and technology-assisted learning tools on developing the conception of place value, mathematical achievement and arithmetical performance of primary school 4th graders. The study group was comprised of three different primary schools. There were no group differences prior to…

The aim of the study was to determine the effects of a dialogical argumentation instructional model (DAIM) on pre-service teachers' ability to solve conceptual maths-in-physics (MIP) problems. Using a quasi-experimental design the study included two equal groups of pre-service teachers (N = 40) to follow two instructional methods in which the…

Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

We discuss an implementation of the research-based Pathways precalculus curriculum in a large-lecture format supported by recitations, clickers, and online homework. We describe our approach to adapting the implementation of Pathways precalculus from a small class to a large lecture instructional format. We report data on student learning and…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors' beliefs associated with…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…