This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable…

Tensions between constructivist learning theories and objectivist learning theories in online courses implicate a need for a theoretical balance. This article describes organizing and enacting tasks that elicit constructivist learning of mathematics in an online mathematics teacher education course. The results focus on a conceptual framework that…

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

Among many consequences of the pandemic was an abrupt switch to virtual instruction coupled with feelings of isolation around mandated lockdowns. This situation pushed us to humanize our mathematics classes in ways we had not done previously. Our takeaway from this experience is that community building must be done intentionally and actively. The…

The author presents a child-centered approach to teaching, developed through longtime connections with colleagues, which concentrates on the children and provides them time to make their own connections, to learn, to think, and to develop at their own pace with the support of their classmates. Two examples of how mathematics interlaced into…

In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

In this article, the authors share two examples of student engagement in visible, mathematical thinking through a Chalk Talk within the four walls of the classroom, as well as the connected spaces of online learning. Five steps for facilitating the Chalk Talk are outlined, with descriptions of teacher moves for each step. The silent thinking…

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

In this article, the author will demonstrate how gestures--often used in combination with offloading information on scratch paper--can be used to help students with difficulties in mathematics succeed with secondary level algebra. The authors will provide key examples from three studies of the algebra learning of students with mathematics…

The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to…

Begun in the mid-90s, computers have long been a staple in teaching mathematics to engineering students. In recent years, with the effects of the COVID-19 pandemic and the arrival of Generation Z in tertiary education, the role of blended learning has increased. This paper highlights some of the greater challenges and successes of the transition…

This article focuses on implementing the Science of Math through a culturally responsive framework designed to support culturally and linguistically diverse students in math classrooms. We consider the influence of (second) language acquisition and instructional environments for students in addition to specific ways to increase instructional…

Area should be experienced, not simply calculated. This task invites students to physically experience areas and the spatial relationships between them, as well as their own community.

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…