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The way in which teachers communicate with their students partly determines what they communicate. This book addresses the communication issue by building on a series of papers whose first versions were presented in 1992 at the Sixth International Congress of Mathematics Education in Quebec. Papers include: (1) "Crossing the Gulf between Thought and Symbol: Language as (Slippery) Stepping-Stones" (Susan E.B. Pirie); (2) "Three Epistemologies, Three Views of Classroom Communication: Constructivism, Sociocultural Approaches, Interactionism" (Anna Sierpinska); (3) "Verbal Interaction in the Mathematics Classroom: A Vygotskian Analysis" (Maria G. Bartolini Bussi); (4) "Discourse and Beyond: On the Ethnography of Classroom Discourse" (Falk Seeger); (5) "From 'Stoffdidaktik' to Social Interactionism: An Evolution of Approaches to the Study of Language and Communication in German Mathematics Education Research" (Heinz Steinbring); (6) "Examining the Linguistic Mediation of Pedagogic Interactions in Mathematics" (Clive Kanes); (7) "Pupil Language-Teacher Language: Two Case Studies and the Consequences for Teacher Training" (Albrecht Abele); (8) "Teacher-Student Communication in Traditional and Constructivist Approaches to Teaching" (Maria Luiza Cestari); (9) "Alternative Patterns of Communication in Mathematics Classes: Funneling or Focusing?" (Terry Wood); (10) "Students Communicating in Small Groups: Making Sense of Data in Graphical Form" (Frances R. Curcio and Alice F. Artzt); (11) "Communication and Learning in Small-Group Discussions" (Kaye Stacey and Anne Gooding); (12) "Mathematical Communication through Small-Group Discussions" (Marta Civil); (13) "Formats of Argumentation in the Mathematics Classroom" (Gotz Krummheuer); (14) "Teaching without Instruction: The Neo-Socratic Method" (Rainer Loska); (15) "The Role of Natural Language in Prealgebraic and Algebraic Thinking" (Ferdinando Arzarello); (16) "How Students Interpret Equations: Intuition versus Taught Procedures" (Mollie MacGregor); (17) "Epistemological and Metacognitive Factors Involved in the Learning of Mathematics: The Case of Graphic Representations of Functions" (Maria Kaldrimidou and Andreas Ikonomou); (18) "Making Mathematics Accessible" (Megan Clark); (19) "Itineraries through Logic To Enhance Linguistic and Argumentative Skills" (Giancarlo Navarra); and (20)"Communication in a Secondary Mathematics Classroom: Some Images" (Judith Fonzi and Constance Smith). (ASK)
This book considers some of the outstanding questions regarding language and communication in the teaching and learning of mathematics – an established theme in mathematics education research, which is growing in prominence. Recent research has demonstrated the wide range of theoretical and methodological resources that can contribute to this area of study, including those drawing on cross-disciplinary perspectives influenced by, among others, sociology, psychology, linguistics, and semiotics. Examining language in its broadest sense to include all modes of communication, including visual and gestural as well as spoken and written modes, it features work presented and discussed in the Language and Communication topic study group (TSG 31) at the 13th International Congress on Mathematical Education (ICME-13). A joint session with participants of the Mathematics Education in a Multilingual and Multicultural Environment topic study group (TSG 32) enhanced discussions, which are incorporated in elaborations included in this book. Discussing cross-cutting topics it appeals to readers from a wide range of disciplines, such as mathematics education and research methods in education, multilingualism, applied linguistics and beyond.
This stimulating study focuses on mathematics as a language with its own rules and conventions and explores the implications of this for classroom practice.
This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.
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.
Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.
Classroom Innovations through Lesson Study is an APEC EDNET (Asia-Pacific Economic Cooperation Education Network) project that aims to improve the quality of education in the area of mathematics. This book includes challenges of lesson study implementation from members of the APEC economies.Lesson study is one of the best ways to improve the quality of teaching. It is a model approach for improvement of teacher education across the globe. This book focuses on mathematics education, teacher education, and curriculum implementation and reforms.
Students learning math are expected to do more than just solve problems; they must also be able to demonstrate their thinking and share their ideas, both orally and in writing. As many classroom teachers have discovered, these can be challenging tasks for students. The good news is, mathematical communication can be taught and mastered. In Teaching Students to Communicate Mathematically, Laney Sammons provides practical assistance for K–8 classroom teachers. Drawing on her vast knowledge and experience as a classroom teacher, she covers the basics of effective mathematical communication and offers specific strategies for teaching students how to speak and write about math. Sammons also presents useful suggestions for helping students incorporate correct vocabulary and appropriate representations when presenting their mathematical ideas. This must-have resource will help you help your students improve their understanding of and their skill and confidence in mathematical communication.
Writing in Math Class presents a clear and persuasive case for making writing a part of math instruction. Author and master teacher Marilyn Burns explains why students should write in math class, describes five different types of writing assignments for math, and offer tips and suggestions for teachers. In her usual engaging style, Marilyn Burns tells what happened in actual classrooms when writing was incorporated into math lessons. Illustrated throughout with student work. With a foreword by Susan Ohanian.
"This book offers an international perspective on the current and future state of the research specifically focused on the role and use of language in mathematics school teaching and learning. It focuses on the development of a unified view of the languages of the learners, of the teachers and of mathematics by considering the role of language in the learning, teaching and doing of mathematics in the classroom, and the current richness and pluralness of language and culture. Twelve contributions show together how views of language and of language research in mathematics education have importantly changed in the last decades, and how they will continue to change and become even more complex and challenging in the era of diversity. All these contributions by leading scholars are grouped into two sections for emphasis on issues of: Theorising the complexity of language in mathematics teaching and learning Opening spaces of learning with mathematics classroom research on language This book will be of great interest to mathematics teachers, teacher educators, curriculum developers and mathematics education researchers who deal with the study and implementation of pedagogies of mathematics teaching and learning, specifically in world regions culturally and sociolinguistically diverse"--