The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

This paper reports on university students' responses to an inverse proportion question. The authors conclude that inverse proportion is a difficult concept that requires constant reinforcement, using approaches to teaching that facilitate deeper conceptual understanding.

Due to the growing interest in the integration of ethnomathematics in mathematics education, we undertook a systematic literature review and bibliometric analysis of research on the incorporation of ethnomathematics in geometry teaching from 2011 to 2021. The search for 37 relevant research articles was done on Google Scholar, Scopus, and by hand…

The mathematics curricula of Australia (ACARA, 2019), Scotland, England and America all require an understanding of proof by contradiction. Specifically, proof by contradiction is included as a Geometry topic in Specialist Mathematics (Version 8.4). In Specialist Mathematics, it is expected that students construct proofs in a variety of contexts…

In this article, the authors share one approach to Number Talks that may help more students participate, increase access to and learning of mathematics, and provide some variation in routines. Number Talks are commonplace in the elementary mathematics classroom, thanks to Parker and Humphreys (e.g., 2018) and Parrish (e.g., 2011). They are a…

Mathematical modelling (MM) plays a pivotal role in the integration of Science, Technology, Engineering and Mathematics (STEM) into school studies. This current empirical study suggests using a four-step solution plan as a scaffolding tool during the instruction of MM tasks in a STEM context in formal school mathematics. The study goals are…

Making sense of algebraic expressions in context is multifaceted and extends beyond representing real-world situations using algebra. As part of Project MathTalk, the authors created videos that feature a pair of Grade 9 algebra 1 students coming to understand algebraic expressions in context. The students found three aspects of making sense of…

Background: The debate on using concrete versus abstract materials in learning mathematics has been longstanding. For decades, research has focused on the physical characteristics of materials when defining them as concrete or abstract. Aims: This study extends the field by proposing a two-dimensional classification, which defines materials as…

This holistic, mixed-methods action research case study aimed to determine the influence of professional development on participants' mathematical teaching practices and how the changes influenced students' opportunities for discourse. In this two-year study, participants engaged in two professional development phases and implemented new…

In order to learn more about student understanding of the structure of proofs, we generated a novel genre of tasks called "Proof Without Claim" (PWC). Our work can be viewed as an extension of Selden and Selden's (1995) construct of "proof framework"; while Selden and Selden discuss how the structure of a proof can be discerned…

Proof validation plays a significant role in students' understanding and learning of mathematical proofs. Recent studies have shown that university students were lacking skills in proof validation and were challenged by the implementation of the appropriate acceptance criteria when validating proofs. Drawing on Habermas' construct and rational…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

Reform in teacher education seeks to engage preservice teachers (PSTs) in authentic classroom situations that explore equitable practices by connecting theory to professional practice. One way for PSTs to examine how equity and inequity operate in schools is with the aid of equity-related case-based instruction. This study reports on mathematics…

Over the past ten years, interest in game-based learning has increased. This increase stems from the results of research that demonstrate the potential for increased mathematical learning and engagement when game-based learning was implemented. It has been noted that the most frequent way game-based learning is included in research is with drill…

The coordinate system is a fundamental tool for many daily activities, yet it is usually taught to children in middle school. Research suggests that children should be exposed to the coordinate system at a younger age, using methods appropriate to their developmental level. This paper presents a set of instructional activities designed to teach…