Mathematical Thinking and Communication: Access for English Learners

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.

Mark Driscoll is a nationally recognized leader in mathematics education who designs instructional resources and professional development materials that build mathematics teachers' capacity to enhance students' understanding and improve their learning outcomes. He is the author of Mathematical Thinking and Communication (2016), Fostering Geometric Thinking (2007), Fostering Algebraic Thinking (1999), as well as The Fostering Geometric Thinking Toolkit (2008) - all published by Heinemann. Mark is the Managing Project Director of Leadership for Learning Innovation at Educational Development Center (EDC) in Waltham, MA. He received his Ph.D. in mathematics (differential geometry) from Washington University in St. Louis and taught mathematics at Logos School, an alternative high school in inner-city St. Louis. He has been a member of the writing team for NCTM's Assessment Standards for School Mathematics and served as Editor of Mathematics Education Leadership, the journal of the National Council of Supervisors of Mathematics, from 2003 - 2007. Mark has been named the recipient of the Ross Taylor/Glenn Gilbert National Leadership Award from the National Council of Supervisors of Mathematics (NCSM). The award recognizes Mark's contributions to mathematics education over four decades as well as his work at EDC.

Johannah Nikula is a coauthor of a number of Heinemann professional development books and staff development materials. Her most recent are Lesson Study in Practice: A Mathematics Staff Development Course (2010) and the companion, A Mathematics Leaders Guide to Lesson Study in Practice (2010). She also coauthored Fostering Geometric Thinking (2007) and its professional development companion, the Fostering Geometric Thinking Toolkit (2008), both published by Heinemann. Her work has focused on professional development for middle and high school mathematics teachers that is grounded in the work of teaching through analysis of artifacts that reveal students' mathematical thinking and through the Japanese lesson-study process.

Jill Neumayer DePiper is a Senior Research Associate at Education Development Center (EDC) in Waltham, MA and the coauthor of Mathematical Thinking and Communication. Her focus is mathematics learning and teaching, and identifying strategies to support the academic success of English Learners. She is currently contributing to initiatives targeted to deepen mathematics teachers' understanding of effective instructional practices for students who are English learners. She is a senior research associate on Visual Access to Mathematics (VAM), a project focused on designing professional development for mathematics teachers of English learners to support them in their use of visual representations for mathematical problem-solving and specific language strategies to support their students. Before joining EDC, Jill served as a researcher and instructor in the Center for Mathematics Education at the University of Maryland, College Park. She has provided professional development for teachers, including courses specifically focused on instruction for English learners. She was also a recipient of the the Mid-Atlantic Center for Mathematics Teaching and Learning doctoral fellowship, an NSF-funded award to increase the number of graduate students who become leaders in mathematics education.