The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

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.…

While translation was once a key component of language teaching, throughout the twentieth century, it largely gave way to methods and approaches with a greater focus on communicative competence. However, efforts have been made in the past few decades to return translation and more generally multilingual language learning to classrooms. In the…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

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…

The purpose of the study is to evaluate how prospective mathematics teachers (PMTs) modify tasks to facilitate students' learning of pattern generalization through the use of their mathematical knowledge for teaching. Case study, which is a type of qualitative research method, was used to determine the mathematical characteristics that PMTs use…

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.…

Children's Approaches to Learning (AtL) represents how children seek learning opportunities in their classrooms. It can include children's persistence, attention, and initiative. It has often been studied using a composite of a teacher-rated scale. However, person-centered approaches may account for heterogeneity in children's learning approaches,…

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…

Cognitively demanding tasks provide important opportunities for students to develop an understanding of mathematics; however, they are challenging to launch and implement. The authors designed a secondary methods unit on launching tasks. Participants in the study were enrolled in five different methods courses. Using a noticing framework, findings…

Why are so many teachers around the world moving towards adopting task-based language teaching? This teacher-friendly guide to understanding and implementing task-based language teaching (TBLT) provides a brief and clear introduction to the key elements of TBLT and highlights practical guidelines for teachers. Read about the essential pedagogical…

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…

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…