The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

We use Action-Process-Object-Schema (APOS) theory to study students' geometric understanding of partial derivatives of functions of two variables. This study contributes to research on the teaching and learning of differential multivariable calculus and its didactics. This is an important area due to its multiple applications in science,…

This article presents several activities suitable for a transition to proofs course. In addition, this article surveys literature in support of active learning in the transition to proofs course and discusses how these activities have been successfully implemented in one such course.

This research contributes to the need to identify and expand learning environments that encourage undergraduate students to develop collaborative work skills and apply their classroom knowledge to solve real-world problems. Using qualitative methods, we examine the effects of the interaction between two teams of students when solving a…

In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in a classroom setting. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students…

In activities based on proof without words (PWW), we developed, students are given a PWW--a diagram that alludes to the proof of a mathematical theorem. The students work collaboratively to construct a proof alluded by the PWW, and then each student writes and submits a proof attempt. In a 3-year design-based study, we investigate and develop…

This article discusses Experience First, Formalize Later (EFFL), an approach to teaching and learning that empowers students to build strong conceptual understanding of concepts, redefining how students experience mathematics class, and ultimately leading to more equitable learning opportunities. Traditional lecture-based models for mathematics…

Classroom stories show how using technology to investigate the wage gap provided opportunities to develop students' identities and agency and enabled a classroom culture of sharing and risk-taking. This article illustrates how technology can (a) support students' engagement in case-based reasoning by helping them organize and analyze data; (b)…

This paper explores peer interactions in an elementary mathematics classroom (ages 9-10) where the teacher intentionally shared authority with her students and supported them in learning to share authority with one another. Authors examine how students shifted between shared, concentrated, and contested social and intellectual authority relations…

Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving…

Students often perceive mathematics as a challenging and abstract subject, leading to disengagement and anxiety. To address these challenges, educators have increasingly turned to math games as a pedagogical tool to make learning more interactive and enjoyable. This paper explores the potential of math games, particularly Bachet's game, as…

Out-of-class activities play a crucial role in student learning. However, student opinions on the design of these activities are rarely measured across several different classes. The purpose of this study is to understand students' preferences and attitudes towards new "Engaged Mathematics Labs" in which professors and teaching…

Collaborative problem solving (CPS) has been shown to both engage and benefit students' learning of mathematics. However, there is evidence that group work is not always easy to facilitate, in part because educators lack details about learners' engagement during group work: the processes of problem solving involved, and how these are engaged. In…

The first calculus course in the province of Quebec (Canada) is taught in the first year of college (17-18 year-old students) before university. Statistics show that this course is the most difficult one for students at the collegial level and that it prompts many to drop out of school. The literature has highlighted the cognitive problems…

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.