The Language of Mathematics

Taking the reader on a wondrous journey through the invisible universe that surrounds us--a universe made visible by mathematics--Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, and ...

The Language of Mathematics

Taking the reader on a wondrous journey through the invisible universe that surrounds us--a universe made visible by mathematics--Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, and allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers--all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture.

Language and Mathematics Education

In this chapter, I submit the notion that four views of language—as a process, system, structure, and factor—shape how researchers of different orientations investigate language and its relation to mathematics.

Language and Mathematics Education

Issues of language in mathematics learning and teaching are important for both practical and theoretical reasons. Addressing issues of language is crucial for improving mathematics learning and teaching for students who are bilingual, multilingual, or learning English. These issues are also relevant to theory: studies that make language visible provide a complex perspective of the role of language in reasoning and learning mathematics. What is the relevant knowledge base to consider when designing research studies that address issues of language in the learning and teaching of mathematics? What scholarly literature is relevant and can contribute to research? In order to address issues of language in mathematics education, researchers need to use theoretical perspectives that integrate current views of mathematics learning and teaching with current views on language, discourse, bilingualism, and second language acquisition. This volume contributes to the development of such integrated approaches to research on language issues in mathematics education by describing theoretical perspectives for framing the study of language issues and methodological issues to consider when designing research studies. The volume provides interdisciplinary reviews of the research literature from four very different perspectives: mathematics education (Moschkovich), Cultural-Historical-Activity Theory (Gutiérrez, Sengupta-Irving, & Dieckmann), systemic functional linguistics (Schleppegrell), and assessment (Solano-Flores). This volume offers graduate students and researchers new to the study of language in mathematics education an introduction to resources for conceptualizing, framing, and designing research studies. For those already involved in examining language issues, the volume provides useful and critical reviews of the literature as well as recommendations for moving forward in designing research. Lastly, the volume provides a basis for dialogue across multiple research communities engaged in collaborative work to address these pressing issues.

The Language of Mathematics

In order to reason logically about things, mathematicians have developed a particular language with particular characteristics. That language—the Language of Mathematics—and other languages developed by human societies—such as ...

The Language of Mathematics

A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.

The Language of Mathematics

We will now give an informal description of the language of mathematics, and highlight some of the major issues that arise to confront a theory of mathematical language. No systematic survey of this kind exists in the literature, ...

The Language of Mathematics

The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. "The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers

Language and Mathematics

So, in a sense this book is about the cognitive science of language and mathematics, but it does not necessarily imply that cognitive science has found the light at the end of the tunnel, so to speak. As mentioned in the preface, ...

Language and Mathematics

This book explores the many disciplinary and theoretical links between language, linguistics, and mathematics. It examines trends in linguistics, such as structuralism, conceptual metaphor theory, and other relevant theories,to show that language and mathematics have a similar structure, but differential functions, even though one without the other would not exist.

The Language of Mathematics

response to these questions lies in one of the conclusions reached the evidence of language: mathematics emerges from communiI. During communication people use natural language full of ding metaphors based on common embodied experience.

The Language of Mathematics

The book emerges from several contemporary concerns in mathematics, language, and mathematics education. However, the book takes a different stance with respect to language by combining discussion of linguistics and mathematics using examples from each to illustrate the other. The picture that emerges is of a subject that is much more contingent, much more relative, much more subject to human experience than is usually accepted. Another way of expressing this, is that the thesis of the book takes the idea of mathematics as a human creation, and, using the evidence from language, comes to more radical conclusions than most writers allow.

The Mathematics of Language

This volume contains a selection of papers presented at the 10th and 11th Meeting of the Association for Mathematics of Language, held in Los Angeles, CA, USA in July 2007 and in Bielefeld, Germany, in August 2009.The 19 revised papers ...

The Mathematics of Language

This volume contains a selection of papers presented at the 10th and 11th Meeting of the Association for Mathematics of Language, held in Los Angeles, CA, USA in July 2007 and in Bielefeld, Germany, in August 2009.The 19 revised papers presented together with 3 invited speeches were carefully selected from numerous submissions. The papers in this collection reflect a wide range of theoretical topics relating to language and computation including papers on the intersection of computational complexity, formal language theory, proof theory, and logic, as well as phonology, lexical semantics, syntax and typology.

The Language Issue in the Teaching of Mathematics in South Africa

achievement in English reading, language and mathematics. It was confirmed that there was a significant positive relationship between the learners' literacy in the Arabic language and achievement in English reading, language and ...

The Language Issue in the Teaching of Mathematics in South Africa

The book is the result of a five-year project that culminated (within the first three years) in doctoral research interrogating language competency for meaningful mathematics instruction at upper primary level conducted at University of Stellenbosch in 2017; and this book in the succeeding two years. The initial research project received countrywide coverage in several South African media outlets including Times Live and Radio 2000.

Language and Communication in Mathematics Education

learning of mathematics is linked to the learning of language. Pimm sees mathematics as similar to a foreign language which certain people cannot speak, albeit one clearly differentiated from natural languages like German or English.

Language and Communication in Mathematics Education

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.

Academic Language in Diverse Classrooms Mathematics Grades 3 5

Promoting Content and Language Learning Margo Gottlieb, Gisela Ernst-Slavit. One of the eight CCSS mathematical practices, “attend to precision” (Number 6), is open to multiple interpretations of the term precision.

Academic Language in Diverse Classrooms  Mathematics  Grades 3   5

Make every student fluent in the language of learning. The Common Core and ELD standards provide pathways to academic success through academic language. Using an integrated Curricular Framework, districts, schools and professional learning communities can: Design and implement thematic units for learning Draw from content and language standards to set targets for all students Examine standards-centered materials for academic language Collaborate in planning instruction and assessment within and across lessons Consider linguistic and cultural resources of the students Create differentiated content and language objectives Delve deeply into instructional strategies involving academic language Reflect on teaching and learning

Academic Language in Diverse Classrooms Mathematics Grades 6 8

Promoting Content and Language Learning Margo Gottlieb, Gisela Ernst-Slavit. One of the eight CCSS mathematical practices, “attend to precision” (Number 6), is open to multiple interpretations of the term precision.

Academic Language in Diverse Classrooms  Mathematics  Grades 6   8

Make every student fluent in the language of learning. The Common Core and ELD standards provide pathways to academic success through academic language. Using an integrated Curricular Framework, districts, schools and professional learning communities can: Design and implement thematic units for learning Draw from content and language standards to set targets for all students Examine standards-centered materials for academic language Collaborate in planning instruction and assessment within and across lessons Consider linguistic and cultural resources of the students Create differentiated content and language objectives Delve deeply into instructional strategies involving academic language Reflect on teaching and learning

Strategies for Connecting Content and Language for ELLs Mathematics eBook

It has often been said that mathematics is a universal language. Universal, in the sense, that it is the only common language shared by individuals regardless of gender, culture, or ethnicity. Mathematics describes abstract concepts ...

Strategies for Connecting Content and Language for ELLs  Mathematics eBook

Develop English language learners' academic language in mathematics through the strategies presented in this digital resource. Encourage students to make academic language connections through listening, speaking, reading, and writing. This practical guide provides research-based instructional strategies to ensure comprehensible input and helps promote students' oral language development. By implementing the strategies in this e-book, teachers will be empowered with the knowledge and guidance they need to create the rich and rigorous learning environment all students deserve. Digital resources are included with students reproducibles.

Encyclopedia of Mathematics Education

LANGUAGE AND MATHEMATICS INTHE CLASSROOM LANGUAGE AND MATHEMATICS IN THE CLASSROOM LANGUAGE AND MATHEMATICS INTHE. Students first meet Lagrange's work in calculus when they apply the Lagrange multiplier method to the problem of ...

Encyclopedia of Mathematics Education

First published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.

Mathematics Education from an Asian Perspective Penerbit USM

The probable reason could be that linguistically denser items impose a higher degree of reading and higher demand of understanding the language of the mathematics word problem items (Irujo, 2007). When English language proficiency ...

Mathematics Education from an Asian Perspective  Penerbit USM

This book presents an exceptional collection of 11 articles on contemporary research studies that address current and critical issues of researches, theories and practices in the fields of mathematics education at various levels from primary to tertiary education. In addition, the book covers various innovative research studies from both local and abroad such as cognitive diagnostic assessment (CDA) and assessment for learning (AfL), teaching and learning of mathematics using the dynamic geometry software (DGS), action-process-object-schema (APOS) theory and relationship mapping and inverse (RMI) principle, as well as mathematics lesson structure (MLS) and collaborative lesson research (CLR). The contents of this book should be of interest to both national and international researchers and scholars, particularly mathematics educators, mathematics education researchers, teacher trainers, university students, teachers, curriculum planners, as well as policymakers.

Tep Vol 29 N4

Mathematics as language is primary in guiding individuals' mathematical development by engaging them in problems, facilitating the sharing of their solutions, observing and listening carefully to their ideas and explanations, ...

Tep Vol 29 N4

Teacher Education and Practice, a peer-refereed journal, is dedicated to the encouragement and the dissemination of research and scholarship related to professional education. The journal is concerned, in the broadest sense, with teacher preparation, practice and policy issues related to the teaching profession, as well as being concerned with learning in the school setting. The journal also serves as a forum for the exchange of diverse ideas and points of view within these purposes. As a forum, the journal offers a public space in which to critically examine current discourse and practice as well as engage in generative dialogue. Alternative forms of inquiry and representation are invited, and authors from a variety of backgrounds and diverse perspectives are encouraged to contribute. Teacher Education & Practice is published by Rowman & Littlefield.

Diversity Dimensions in Mathematics and Language Learning

Students use academic language, which involves vocabulary, grammatical structures, and linguistic functions, to learn knowledge and perform tasks in a specific discipline (e.g., mathematics; Cummins, 2000).

Diversity Dimensions in Mathematics and Language Learning

Wie hängen sprachliche und mathematische Entwicklung zusammen? Dieser Frage wird derzeit mit großem Interesse aus unterschiedlichen Perspektiven nachgegangen. Dieser Sammelband vereint Erkenntnisse aus Psychologie, Neurowissenschaften, Mathematikdidaktik, (Psycho-)Linguistik und Mehrsprachigkeitsforschung. Der interdisziplinäre Ansatz bietet einen umfassenden Blick auf den aktuellen Forschungsstand, dargestellt von national und international renommierten Forschenden. Das Buch gliedert sich in drei Teile. Der erste Teil „Modelle und Theorien“ fasst theoretische Überlegungen zusammen und stellt Strukturen für Forschung und Praxis bereit. Dieser Teil dient dazu, den Grundstein für die anderen Teile sowie für zukünftige Forschung zu legen. Der zweite Teil „Kindergartenalter“ sowie der dritte Teil „Grundschulalter“ decken empirische Befunde über die Korrelation zwischen Sprache und mathematischem Lernen in der jeweiligen Altersgruppe ab. Ein besonderer Fokus liegt hierbei auf dem Aspekt der Mehrsprachigkeit. Damit bietet dieser Sammelband eine große Bandbreite fachspezifischen Wissens für Bildungswissenschaftler*innen, Lehramtsstudierende, Psycholog*innen und Forschende zur Mehrsprachigkeit.

Teaching Mathematics to English Language Learners

50 Strategiesfor teaching English language learners. (3rd edn.). Upper Saddle River, NJ: Pearson. Although not specifically designed for mathematics teachers, this book contains 50 specific teaching strategies along with examples and ...

Teaching Mathematics to English Language Learners

Today's mathematics classrooms increasingly include students for whom English is a second language. Teaching Mathematics to English Language Learners provides readers a comprehensive understanding of both the challenges that face English language learners (ELLs) and ways in which educators might address them in the secondary mathematics classroom. Framed by a research perspective, Teaching Mathematics to English Language Learners presents practical instructional strategies for engaging learners that can be incorporated as a regular part of instruction. The authors offer context-specific strategies for everything from facilitating classroom discussions with all students, to reading and interpreting math textbooks, to tackling word problems. A fully annotated list of math web and print resources completes the volume, making this a valuable reference to help mathematics teachers meet the challenges of including all learners in effective instruction. Features and updates to this new edition include: An updated and streamlined Part 1 provides an essential overview of ELL theory in a mathematics specific context. Additional practical examples of mathematics problems and exercises make turning theory into practice easy when teaching ELLs New pedagogical elements in Part 3 include tips on harnessing new technologies, discussion questions and reflection points. New coverage of the Common Core State Standards, as well as updates to the web and print resources in Part 4.

Language mathematics and linguistics

I have tried to help the linguist reader by emphasizing the language-like attributes of mathematics, most of which are not recognized as such by mathematicians because they have no specialist's knowledge of language.

Language  mathematics  and linguistics


Mathematics Education and Language

Clearly, this is true not only of practical mathematics but also of any representation of any mathematical phenomena. An act of mathematics can be seen as an act of construction where I simultaneously construct in language mathematical ...

Mathematics Education and Language

Contemporary thinking on philosophy and the social sciences has primarily focused on the centrality of language in understanding societies and individuals; important developments which have been under-utilised by researchers in mathematics education. In this revised and extended edition this book reaches out to contemporary work in these broader fields, adding new material on how progression in mathematical learning might be variously understood. A new concluding chapter considers how teachers experience the new demands they face.

Handbook of Multicultural School Psychology

Scaffolding or Supporting Academic Language of Mathematics Language and Mathematics Academic language is the language through which an academic subject is taught and evaluated (Schleppegrell, 2012). Although many researchers and ...

Handbook of Multicultural School Psychology

The second edition of the Handbook of Multicultural School Psychology continues the mission of its predecessor, offering a comprehensive, interdisciplinary view of the field of multicultural school psychology and addressing the needs of children and families from diverse cultural backgrounds. The revised organizational structure includes the following: History and Professional Issues; Consultation and Collaboration; Interventions Focused on Academic and Mental Health Issues; Data-based Decision Making; Systems-based Issues; Training and Research; and Future Perspectives. Nineteen of the volume's twenty-three chapters are completely new to this edition, while the rest have been effectively revised and updated. Comprehensive—In seven sections, this book covers theoretical, research, and practical concerns in a wide range of areas that include multicultural and bilingual issues, second language acquisition, acculturation, parent collaboration, research, and systemic issues. Chapter Structure—Chapter authors follow a uniform structure that includes theoretical and research issues and implications for practice. Recent practice and training guidelines including Blueprint for Training and Practice III (2006), NASP Model for Comprehensive and Integrated School Psychological Services (2010), and APA Multicultural Guidelines (2003) are covered. Interdisciplinary Perspective—Contributing authors are from a wide range of related fields that include school psychology, special education, general education, early childhood education, educational psychology, clinical psychology, counseling, and mental health, thus exposing readers to theory and research from various approaches. Changes—New to this edition is a section focusing on systemic issues such as overrepresentation of culturally and linguistically diverse (CLD) students in special education, prejudice, response to intervention (RTI) for CLD students and English Language Learners (ELL), and end-of-chapter discussion questions. This book is ideal for graduate courses and seminars on multicultural school psychology. It is also a useful reference for researchers and practicing school psychologists and the libraries that serve them.