Three mathematics education researchers discuss their findings on the use of diagrams in math instruction for English language learners. The authors show how diagrams can help students who are English learners better develop mathematical thinking and communicate their mathematical understanding.

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…

We propose that there exists mathematical knowledge for teaching (MKT) specific to visual representations (VRs), abbreviated MKT-VR. We define a VR as a graphic creation, such as a diagram or drawing, which illustrates quantities and shows quantitative relationships or which illustrates geometric properties of figures and shows geometric…

Teachers' confidence and facility with strategies that position and support students who are English learners (ELs) as active participants in middle grades mathematics classrooms are key to facilitating ELs' mathematics learning. The Visual Access to Mathematics (VAM) project developed and studied teacher professional development (PD) focused on…

Although there are increasing numbers of professional development (PD) materials intended to foster teachers' mathematical knowledge for teaching within the topics of number and algebra, little attention has been given to geometry. In this article we describe the Learning and Teaching Geometry project's approach to the development of PD materials…

Because the author and his colleagues at the Center for Leadership and Learning Communities believe that instructional coaching is one of the most exciting developments in education in a long time, they have examined the questions this new strategy has raised for education leaders: Should coaching replace some traditional forms of teacher…

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these…

Instructional tips help educators carry out recommendations contained in IES Educator's Practice Guides. The tips translate these recommendations into actionable approaches that educators can try in their classrooms. These tips are based on a practice guide authored by Sybilla Beckmann, Mark Driscoll, Megan Franke, Patricia Herzig, Asha Jitendra,…

This book was written as a resource for middle and high school teachers hoping to ease their students' transition to algebra. Drawing on experiences with three professional development programs, key "habits of thinking" that characterize the successful learning and use of algebra are outlined. Strategies teachers can use to cultivate…

Instructional tips help educators carry out recommendations contained in IES Educator's Practice Guides. This summary describes the research evidence that supports the use of the instructional tips in classrooms and is based on a practice guide authored by Sybilla Beckmann, Mark Driscoll, Megan Franke, Patricia Herzig, Asha Jitendra, Kenneth R.…

Increased attention has been given to issues of assessment in recent years. Teachers of mathematics have been working to change both the way they elicit evidence of their students' mathematical thinking and the way they use that evidence to monitor students' progress and guide instructional decision making. This publication is based on work done…

This toolkit contains a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. A core belief underlying the Toolkit is that good mathematics teaching begins with understanding how mathematics is learned, so these materials…

This brief paper reports the results of two observational studies examining the impact of fines for youth tobacco possession on public smoking among youth. Preliminary findings are presented that suggest that when police issued warnings and tickets to reduce underage youth possession of tobacco, in both towns the number of youth smoking in public…