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…

This article aims to illustrate how the collective resolution of routine mathematical tasks can give rise to uncertainties, fostering and supporting a rich and authentic mathematical activity. While solving routine tasks may not typically be classified as problem-solving, the research presented in this paper shows that, at the collective level,…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

We outline the use and evaluation of a video presentation about variance and covariance developed to motivate students to process the topics and to enhance their skills. We outline the structure and the content of the video presentation and present data of an evaluation study. Students in different subjects who must pass statistics courses…

The aim of this paper is to discuss preservice mathematics teachers' in-the-moment noticing of mathematical opportunities and how they reflected on those opportunities both orally and in writing. A faculty-school collaboration program was set up to enable preservice teachers to work with students in a school setting throughout a year. Ten…