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Mathematical Thinking and Communication (eBook)

Access for English Learners

By Mark Driscoll, Johannah Nikula, Jill Neumayer DePiper

Starting from the perspective that English learners are capable of mathematical thinking. Mathematical Thinking and Communication outlines four principles for designing instruction: challenging tasks, multimodal representations, development of mathematical communication, and repeated structured practice.


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Full Description

Language is deeply involved in learning mathematics as students both communicate and think about mathematical ideas. Because of this, teachers of English learners have particular challenges to overcome. Mathematical Thinking and Communication addresses perhaps the most significant challenge: providing access to mathematics for these students.

For all students—and English learners in particular—access means finding effective, authentic ways to make language clear and thinking visible so they can reason more, speak more, and write more in mathematics. Based on extensive research and collaboration with teachers, coaches, and schools, Mark Driscoll, Johannah Nikula, and Jill Neumayer DePiper outline four principles for designing instruction that creates this kind of access: challenging tasks, multimodal representations, development of mathematical communication, and repeated structured practice.

Starting from the perspective that English learners are capable of mathematical thinking (even as they are learning to express their ideas verbally), the authors highlight techniques for using gestures, drawings, models, manipulatives, and technology as tools for reasoning and communication. By embedding these visual representations into instruction—and encouraging their regular use—teachers support engagement in problem solving, facilitate mathematical dialogue, and notice evidence of students’ thinking that propels them to create more engaging and equitable instruction.

Enhanced by an extensive online collection of companion professional development resources, this book highlights classroom-ready strategies and routines for fostering mathematics success in all students and helping them recognize their potential.

Additional Resource Information

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In Depth

To move from the status quo to the win-win solution, mathematics teachers of ELs have particular challenges to overcome, especially two commonly held opinions. First, there is a widespread belief that students need English proficiency in order to do mathematics reasoning tasks. A related conviction holds that the best way to create access to mathematics tasks for ELs is to lighten the cognitive demand of the tasks. Neither the “English first” nor the “lighten the cognitive demand” strategies about mathematics tasks for English learners is necessary for building proficiency in mathematical reasoning. Instead, we suggest remembering that ELs are thinking when working on mathematics tasks, and by letting that thinking become more visible and audible, teachers can nurture the productive potential in that thinking, as well as help adjust any faulty or misinformed thinking.

This book is intended to be a resource for mathematics teachers whose students include ELs. Furthermore, because this book explores the roles that language plays in the learning of mathematics, we also believe it can be useful to all teachers of mathematics, regardless of the particular collection of students in their classrooms. But these strategies, tailored in ways to meet the needs of different students, are absolutely essential for ELs. To meet ELs’ needs it is necessary to nurture mathematics teaching practices that “specifically address the language demands of students who are developing skill in listening, speaking, reading, and writing in a second language while learning mathematics” (Celedón-Pattichis and Ramirez 2012, 1). In other words, although ELs must gain facility in using English to express themselves mathematically, in order to succeed in mathematics, the learning can and should happen “while learning mathematics.”



“Have you ever asked yourself: How do I give my English learners access to the concepts and the language of the mathematics they are learning? Mark, Johannah, and Jill provide us with a simple, elegant, and brilliant answer that debunks two myths that plague English learners’ educational experience—that “English first” and “lowering the cognitive demand of tasks” are necessary for reasoning about mathematics. Any teacher using the robust framework presented here—along with the connected routines—can be sure that all his students, but most important his English learners, will develop a positive mathematical identity as doers of mathematics. The way these routines provide students access by using language as a tool for thinking makes the book an invaluable asset for teachers of English learners.”

—Harold Asturias, Director of the Center for Mathematics Excellence and Equity, University of California, Berkeley

Mathematical Thinking and Communication is based on over a decade of research and development focused on meeting the needs of middle school English Learners in mathematics. Driscoll, Nikula, and DePiper present engaging examples to illustrate how teachers can put research-based recommendations for teaching ELs in mathematics into practice. As a mathematics educator who studies English Learners in mathematics classrooms, I was most impressed with how the authors distilled their extensive work into practical, yet flexible, strategies and techniques that others can use. I look forward to using this resource in my teaching and professional development with middle school mathematics teachers.”

—Bill Zahner, Assistant Professor, San Diego State University

“Unlike most professional development, Mathematical Thinking and Communication does practice what it preaches. It uses visual and structured methods for helping teachers create access for English learners throughout the book. This is a great resource not only for teachers of students learning a second language, but also special educators working with students with communication challenges.”

—Andrew Gael, special education teacher, New York City, blogs at The Learning Kaleidoscope