The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…

The concept of the Citizen Scholar highlights the potential for universities to act as vehicles for social change by supporting the development of active, engaged graduates who are geared to respond to current and future global challenges. This demands a radical shift in teaching towards more interactive pedagogies, which may prove difficult for…

Many general and special education teachers teach mathematics word problems by defining problems as a single operation and linking key words to specific operations. Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. This article lists eight common…

Problem solving in groups can be rich with tension for students. This tension may arise from conflicting approaches (conceptual and/or epistemological) and/or from conflict emerging in the social relations among group members. Drawing on video records of undergraduate students working collaboratively, we use three cases to illustrate the…

Data-based problem solving within a multi-tiered system of support (MTSS) can help state education agencies and local education agencies (LEAs) improve graduation rates for students with disabilities. To facilitate problem solving within an MTSS, states and LEAs need efficient systems and processes for analyzing and integrating data across…

As outlined by many of the social and political movements happening around us today, now more than ever, youth need to be critically conscious of their world in order to navigate it successfully. The Toronto District School Board, where Armen Shahnazarian teaches uses the hybrid model of culturally responsive and relevant pedagogy (CRRP), based on…

This paper outlines a seven-step process for developing problem-solving tasks informed by cognitive load theory. Through an example of a task developed for Year 2 students, we show how this approach can be used to produce challenging mathematical tasks that aim to optimise cognitive load for each student.

In this article, the author describes a collaborative problem-based inquiry project with eighty-three secondary students. The students attended a large high school situated in a medium size town, surrounded by farmland and smaller rural towns. Demographically, nearly half of the students identified as Latina/o, while the slight majority of the…

It is hard to imagine that, eight hundred years on, the study of Fibonacci could affect the lives of teenagers in Australia. Or is it? A mathematics class of more able Year 9 students in a regional city of Western Australia feels that it has happened to them. Thirty-two students submitted a Fibonacci task as a mathematics assessment, with many of…

Many dance artists in their first encounters with improvisational dance making begin not only to learn how to compose spontaneously, but also to gain skills for coping with the uncertainties inherent in the form. This article suggests helpful dance scores for beginning students of physical improvisation and those who teach improvisational…

Most students can follow this simple procedure for division of fractions: "Ours is not to reason why, just invert and multiply." But how many really understand what division of fractions means--especially fraction division with respect to the meaning of the remainder. The purpose of this article is to provide an instructional method as a…

Long before the release of the Common Core State Standards (CCSSI 2010), the Mathematical Tug-of-War was engaging students in the type of reasoning and problem solving described by the Standards for Mathematical Practice (SMP). In this updated version of a Marilyn Burns task, students use algebraic reasoning to determine the outcome of a contest…

The classical "brachistochrone" problem asks for the path on which a mobile point M just driven by its own gravity will travel in the shortest possible time between two given points "A" and "B." The resulting curve, the cycloid, will also be the "tautochrone" curve, i.e. the travelling time of the mobile…

Solving non-routine problems is a key competence in a world full of changes, uncertainty and surprise where we strive to achieve so many ambitious goals. But the world is also full of solutions because of the extraordinary competences of humans who search for and find them. We must explore the world around us in a thoughtful way, acquire knowledge…

For many educators, the inspiration to teach comes from a desire to make a positive difference in students' lives. As they seek to guide students toward their big goals through trying times, teachers need resources that strengthen social and emotional skills. Facing this very challenge, Allison Silverman, a teacher at Port Chester Middle School in…