Example-generation tasks have been suggested as an effective way to both promote students' learning of mathematics and assess students' understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we…

This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable…

This paper explores the specialized knowledge mobilized by a mathematics teacher in the selection and use of examples for teaching sequences. Taking an experimental case study approach, we analyse the examples deployed in a series of third-year secondary level lessons on sequences and identify the different knowledge subdomains activated according…

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students (N = 49) were randomly assigned to a business-as-usual (BAU)…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

This research reports the implementation of an evaluation instrument of the slope concept in high school students. The design of this study was based on four dimensions: Skills, Properties, Uses and Representations (SPUR model; Thompson & Kaur, 2011) and on three conceptualizations: constant ratio, behavior indicator and trigonometric…

The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year…

This article presents an instructional technology-based cycle model intended to support and facilitate the teaching and learning of mathematics, particularly calculus. The study used quantitative methods with quasi-experimental research that uses non-randomised assignments of the study group that are categorised into experimental and control…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

When teaching a novel mathematical concept, should we present learners with abstract or concrete examples? In this experiment, we conduct a critical replication and extension of a well-known study that argued for the general advantage of abstract examples (Kaminski, Sloutsky, & Heckler, 2008a). We demonstrate that theoretically motivated yet…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

How teachers interpret and express fractions critically influences their teaching and their students' fraction knowledge. Internationally, the mathematics education community has been studying ways to enhance preservice elementary teachers' rational number knowledge, particularly fractions. To address the challenge of augmenting pre-service…

Prior research in mathematics education confirms the significance of representations as an integral part of curriculum standards. The effective teaching of representations is related to teachers' content and pedagogical knowledge. A teacher must know the salient features of the mathematical concept as well as the attributes of various…

This research addressed increasing understanding of how players make meaning during play of a complex STEM game and explores to what extent player mental models of STEM concepts shift as a result of interacting with the game simulation. Game based learning is attracting increased attention and interest as a novel platform for experiential…

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report "why" such a model is used, "what" types of models are used, and "when" they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a…