In this article we review the research on the flexible or adaptive use of solution strategies in school mathematics, with a focus on the most recent work in the field. After a short introduction, we provide an overview of the various ways in which strategy flexibility has been conceptualized and investigated in the research literature. Then we…

This study focused on improving students' learning mathematical of proofs and proving by using combinations of proof strategies that span different levels of understanding of proof structure; we refer to these as 'level-spanning proof-production strategies'. We analysed the level-specific proof-production strategies evident in the lessons and…

If students are to pursue the mathematical strategies they devise, teachers must be able to notice these strategies in-the-moment, attending to what a student did and interpreting what they understand. Otherwise, teachers might urge students to pursue a different approach. Novice teachers may find it particularly challenging to notice strategies…

In this book Bill Hanlon provides examples and recommends highly effective and practical instructional and assessment strategies that classroom teachers can immediately implement and that school administrators can readily observe. These high yield strategies build on accepted practices and directly address the needs of struggling students or…

This study investigated effects of feedback and exposure to alternative strategies on strategy change in children (N = 106, age range = 7;3-10;0) learning about mathematical equivalence. Children's strategies were evaluated before and after a brief instructional intervention. During the intervention, children either were exposed to a set of 4…

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.

Preschool children are learning so many skills--how to cut with scissors, zip zippers, recognize the alphabet and their names, and share toys with others. A strong academic curriculum also requires that children learn more about math (National Council of Teachers of Mathematics [NCTM], 2000). By following the five easy principles outlined here,…

We illustrate and exemplify how the idea of reflection is framed by the enactive concept of "deliberate analysis". In keeping with this frame, we do not attempt to define reflection but rather work on the question of "how do we do reflecting?" within such a frame. We set out our enactivist theoretical stance, in particular pointing to implications…

The purpose of this study was to explore teaching styles and how frequently teachers with a variety of teaching styles incorporate multiple representations, such as manipulatives, drawings, counters, etc., in the middle school mathematics classroom. Through this explanatory mixed methods study it was possible to collect the quantitative data in…

The purpose of this study was to investigate the effectiveness of explicit, direct, and generative strategy training and working memory capacity (WMC) on mathematical word problem-solving accuracy in elementary schoolchildren. In this study, children in third grade ("N" = 82) identified as at risk for math difficulties (MD) were randomly…

By any measure, Singapore's educational system has generated an extraordinary record of achievement over the past two or three decades. In this article, we report on one key component of a broader three year investigation into why Singapore has done so well, and explore the logic, strength, resilience and limits of the underlying pedagogical model…

Incorporating and using technology in teaching mathematics can encourage students to become active participants in the classroom. This paper gives a brief overview of several technologies that can be used to enhance learning and motivate students to become engaged in the learning process. The technologies discussed include graphing calculators and…

The theme for the 62nd annual conference of the Association of Literacy Educators and Researchers was Educating for a Just Society. Connie Briggs, previous Program Chair, reminded us that, "Education has always been the foundation of a democratic nation. It is important that our students understand the principles upon which our nation was…

Nearly every state has signed on to use the Common Core State Standards as a framework for teaching English/language arts and mathematics to students. Translating them for the classroom, however, requires schools, teachers, and students to change the way they approach teaching and learning. This report examines the progress some states have made…

In this article, the author explores the theme of inclusion. Inclusion is one of the themes within the recent Qualifications and Curriculum Authority (QCA) publication: "Engaging mathematics for all learners" and the author had the good fortune to participate in this project. This involved working with five schools which, frivolously, all had a…