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…

Students at the elementary level should have opportunities to critique the world through mathematics and to see themselves as capable doers of mathematics. The lesson described in this article prompted students to consider how to use mathematics to organize an emergency evacuation. In this article, the authors show how small changes to a task…

This article aims to outline the important role of the summary phase within a mathematics instructional model and provide six strategies to support teachers to move beyond "share time." By drawing upon good teaching strategies during the summary phase, teachers can enhance the learning experience for themselves and for their students.…

Given the positive effect of teaching idiomatic expressions using the conceptual metaphor (CM) view, and the many benefits of using language tasks in English as a second or foreign language context, this article aims to help teachers design and develop tasks on the basis of CM and task-based language teaching (TBLT). In this study, a series of…

In response to the COVID-19 pandemic, school closures across the country have altered the way educators teach and provide services to students. Engaging technologies in learning environments have become the primary mechanism delivering curriculum and maintaining the intellectual wellbeing of students. With the accelerated expansion of technologies…

Advocates of using songs and music in English as a second language (EL2) teaching and learning contexts emphasize the educational benefits of song lyrics. To make the full potential of using songs more visible and accessible to EL2 teachers, this article presents a methodological framework that can be used when planning a song unit for learners.…

This article provides information to educational leaders about how to address the challenge of supporting students who are emergent multilingual--i.e., those identified as English Learners (ELs) by their schools--in middle grades mathematics classes. The ideas in this article draw on research and collaborations with hundreds of teachers across the…

This article provides six fundamental steps for using a task analysis to teach emergent literacy skills to young learners with autism spectrum disorder (ASD). Compared to general education peers, students with ASD score lower on reading measures and often have difficulty acquiring literacy skills via the instruction methods used in typical…

A simple throwing task is described to illustrate various aspects of projectile motion. The task was to throw a tennis ball in a waste paper bin about 2 m away. Success depends on skill, but it also depends on the physics of the problem. If the ball is thrown underarm, then success depends primarily on the throw speed, which must be controlled to…

The goal of this paper is to illustrate different ways that cardsorting activities (or "card stacks") can be implemented in the introductory physics classroom, along with various tips and resources for getting started. My first attempt at developing a card stack came about from simply wanting to try out a fun way to change student…

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

As teachers are increasingly asked to respond to assessment and evaluation demands in their schools, the aim of this article is to provide suggestions and scales for singing accuracy. A description of each step in the assessment design process is provided, along with specific suggestions for a singing development scale and a singing accuracy scale.

How might teachers transform routine tasks into non-routine ones? The purpose of this article is to address this question. The article opens with a discussion of why non-routine problems require creative and original thought. Specifically, I discuss how non-routine problems require students to confront uncertainty and how uncertainty can serve as…

The inspection of mistakes can play a powerful role in an individual's learning process (Boaler 2015). The purpose of this article is to support the reader in selecting mistakes that can be leveraged to benefit the learning of all students. Specifically, the authors focus on "which" and "why": "which" mistakes to…

Special educators can play an essential role in the development of students' understanding of and capacity to do mathematics. Whether a special education teacher's goal is to help kindergartners develop counting skills or to support 10th graders in constructing geometric proofs and whether instruction will occur in co teaching, consulting, or…