### Integrating Research on the Graphical Representation of Functions

This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the…

Paperback – 2016-02-29

Routledge*Studies in Mathematical Thinking and Learning Series*### Rational Numbers

#### An Integration of Research

Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and…

Paperback – 2015-12-18

Routledge*Studies in Mathematical Thinking and Learning Series*### A Focus on Fractions

#### Bringing Research to the Classroom, 2nd Edition

A Focus on Fractions is a groundbreaking effort to make the mathematics education research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. Using extensive annotated samples of student work, as…

Paperback – 2015-07-27

Routledge*Studies in Mathematical Thinking and Learning Series*### Becoming a Reflective Mathematics Teacher.

#### A Guide for Observations and Self-Assessment, 3rd Edition

Ideal for preservice mathematics teachers who are taking methods courses or are student teaching, this research-based, activity-oriented guide offers a highly effective framework for teacher reflection and self-assessment. Highlighting inquiry-based, learner-centered teaching and grounded in a…

Paperback – 2015-06-17

Routledge*Studies in Mathematical Thinking and Learning Series*### Learning and Teaching Early Math

#### The Learning Trajectories Approach, 2nd Edition

In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child’s level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind…

Paperback – 2014-04-14

Routledge*Studies in Mathematical Thinking and Learning Series*### How Chinese Teach Mathematics and Improve Teaching

How Chinese Teach Mathematics and Improve Teaching builds upon existing studies to examine mathematics classroom instruction in China. It combines contributions from Chinese scholars with commentary from key Western scholars to offer a truly systematic examination of some important and distinctive…

Paperback – 2013-06-19

Routledge*Studies in Mathematical Thinking and Learning Series*### The Impact of Reform Instruction on Student Mathematics Achievement

#### An Example of a Summative Evaluation of a Standards-Based Curriculum

Summarizing data derived from a four-year combined longitudinal/ cross-sectional comparative study of the implementation of one standards-based middle school curriculum program, Mathematics in Context, this book demonstrates the challenges of conducting comparative longitudinal research in the…

Paperback – 2011-10-05

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics Teachers at Work

#### Connecting Curriculum Materials and Classroom Instruction

This book compiles and synthesizes existing research on teachers’ use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on – but not restricted to – those materials developed in the 1990s in response to the NCTM’s…

Paperback – 2011-08-12

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics Teacher Noticing

#### Seeing Through Teachers' Eyes

Mathematics Teacher Noticing is the first book to examine research on the particular type of noticing done by teachers---how teachers pay attention to and make sense of what happens in the complexity of instructional situations. In the midst of all that is happening in a classroom, where do…

Paperback – 2010-12-20

Routledge*Studies in Mathematical Thinking and Learning Series*### Transnational and Borderland Studies in Mathematics Education

Every year, significant numbers of immigrant children from Mexico enter classrooms in the United States. These immigrants comprise a heterogeneous group of students with diverse needs, abilities, and experiences. Transnational and Borderland Studies in Mathematics Education is the first…

Hardback – 2010-10-12

Routledge*Studies in Mathematical Thinking and Learning Series*### How We Think

#### A Theory of Goal-Oriented Decision Making and its Educational Applications

Teachers try to help their students learn. But why do they make the particular teaching choices they do? What resources do they draw upon? What accounts for the success or failure of their efforts? In How We Think, esteemed scholar and mathematician, Alan H. Schoenfeld, proposes a groundbreaking…

Paperback – 2010-10-05

Routledge*Studies in Mathematical Thinking and Learning Series*### Teaching and Learning Proof Across the Grades

#### A K-16 Perspective

A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics…

Paperback – 2010-08-11

Routledge*Studies in Mathematical Thinking and Learning Series*### The Mathematics That Every Secondary School Math Teacher Needs to Know

What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary…

Paperback – 2010-07-28

Routledge*Studies in Mathematical Thinking and Learning Series*### Knowing and Teaching Elementary Mathematics

#### Teachers' Understanding of Fundamental Mathematics in China and the United States, 2nd Edition

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching…

Paperback – 2010-01-25

Routledge*Studies in Mathematical Thinking and Learning Series*### Embracing Reason

#### Egalitarian Ideals and the Teaching of High School Mathematics

This book tells a single story, in many voices, about a serious and sustained set of changes in mathematics teaching practice in a high school and how those efforts influenced and were influenced by a local university. It includes the writings and perspectives of high school students, high school…

Paperback – 2009-12-21

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics Teaching, Learning, and Liberation in the Lives of Black Children

With issues of equity at the forefront of mathematics education research and policy, Mathematics Teaching, Learning, and Liberation in the Lives of Black Children fills the need for authoritative, rigorous scholarship that sheds light on the ways that young black learners experience mathematics in…

Paperback – 2009-06-03

Routledge*Studies in Mathematical Thinking and Learning Series*### Culturally Responsive Mathematics Education

At a time of rapid demographic change and amidst the many educational challenges facing the US, this critical new collection presents mathematics education from a culturally responsive perspective. It tackles the most crucial issues of teaching mathematics to an ethnically diverse school population…

Paperback – 2009-03-27

Routledge*Studies in Mathematical Thinking and Learning Series*### Learning and Teaching Early Math

#### The Learning Trajectories Approach

In this important new book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help teachers become more effective professionals. By opening up new windows to seeing young children and the inherent delight and curiosity behind…

Hardback – 2009-03-12

Routledge*Studies in Mathematical Thinking and Learning Series*### Early Childhood Mathematics Education Research

#### Learning Trajectories for Young Children

This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning…

Paperback – 2009-03-12

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematical Literacy

#### Developing Identities of Inclusion

Why do so many learners, even those who are successful, feel that they are outsiders in the world of mathematics? Taking the central importance of language in the development of mathematical understanding as its starting point, Mathematical Literacy explores students’ experiences of doing…

Paperback – 2008-10-06

Routledge*Studies in Mathematical Thinking and Learning Series*### Algebra in the Early Grades

This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics…

Paperback – 2007-09-14

Routledge*Studies in Mathematical Thinking and Learning Series*### The Origins of Mathematical Knowledge in Childhood

This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the…

Hardback – 2007-06-21

Routledge*Studies in Mathematical Thinking and Learning Series*### Bringing Out the Algebraic Character of Arithmetic

#### From Children's Ideas To Classroom Practice

Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic…

Paperback – 2006-08-17

Routledge*Studies in Mathematical Thinking and Learning Series*### Statistical Literacy at School

#### Growth and Goals

This book reveals the development of students' understanding of statistical literacy. It provides a way to "see" student thinking and gives readers a deeper sense of how students think about important statistical topics. Intended as a complement to curriculum documents and textbook series, it is…

Paperback – 2006-06-23

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics Success and Failure Among African-American Youth

#### The Roles of Sociohistorical Context, Community Forces, School Influence, and Individual Agency

No matter how mathematics achievement and persistence are measured, African Americans seem to lag behind their peers. This state of affairs is typically explained in terms of student ability, family background, differential treatment by teachers, and biased curricula. But what can explain…

Paperback – 2006-04-28

Routledge*Studies in Mathematical Thinking and Learning Series*### Number Theory in Mathematics Education

#### Perspectives and Prospects

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its…

Paperback – 2006-03-21

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics as a Constructive Activity

#### Learners Generating Examples

This book explains and demonstrates the teaching strategy of asking learners to construct their own examples of mathematical objects. The authors show that the creation of examples can involve transforming and reorganizing knowledge and that, although this is usually done by authors and teachers,…

Paperback – 2005-05-17

Routledge*Studies in Mathematical Thinking and Learning Series*### Understanding Mathematics and Science Matters

The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world.The National Center…

Paperback – 2005-02-17

Routledge*Studies in Mathematical Thinking and Learning Series*### Lesson Study

#### A Japanese Approach To Improving Mathematics Teaching and Learning

Lesson study is a popular professional development approach in Japan whereby teachers collaborate to study content, instruction, and how students solve problems and reach for understanding in order to improve elementary mathematics instruction and learning in the classroom. This book is the first…

Paperback – 2004-06-04

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematical and Analogical Reasoning of Young Learners

Mathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for…

Paperback – 2004-05-07

Routledge*Studies in Mathematical Thinking and Learning Series*### Teachers' Professional Development and the Elementary Mathematics Classroom

#### Bringing Understandings To Light

This book illustrates the experiences of elementary school teachers across one year's time as they participated in a teacher development seminar focused on mathematics, and as a result changed their beliefs, their knowledge, and their practices. It explores these experiences as a means of…

Paperback – 2004-04-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Standards-based School Mathematics Curricula

#### What Are They? What Do Students Learn?

The Curriculum and Evaluation Standards for School Mathematics published by the National Council of Teachers of Mathematics in 1989 set forth a broad vision of mathematical content and pedagogy for grades K-12 in the United States. These Standards prompted the development of Standards-based…

Paperback – 2003-09-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Engaging Young Children in Mathematics

#### Standards for Early Childhood Mathematics Education

Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and…

Paperback – 2003-07-01

Routledge*Studies in Mathematical Thinking and Learning Series*### The Development of Arithmetic Concepts and Skills

#### Constructive Adaptive Expertise

This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities,…

Paperback – 2003-01-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Experiencing School Mathematics

#### Traditional and Reform Approaches To Teaching and Their Impact on Student Learning, Revised and Expanded Edition

NORTH AMERICAN RIGHTS ONLY: This is a revised edition of Experiencing School Mathematics first published in 1997 by Open University Press, © Jo Boaler. This revised edition is for sale in North America only.The first book to provide direct evidence for the effectiveness of traditional and…

Paperback – 2002-09-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Beyond Classical Pedagogy

#### Teaching Elementary School Mathematics

The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students'…

Paperback – 2001-05-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Using Assessment To Reshape Mathematics Teaching

#### A Casebook for Teachers and Teacher Educators, Curriculum and Staff Development Specialists

This casebook is intended to support professionals who are working in a variety of contexts to use classroom-based assessment more effectively to support teacher learning and teaching change, and to enhance the opportunities for all students to develop mathematical power. It grows out of a…

Paperback – 2000-04-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics Classrooms That Promote Understanding

Mathematics Classrooms That Promote Understanding synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics. This research…

Paperback – 1999-04-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Word Problems

#### Research and Curriculum Reform

Research by cognitive psychologists and mathematics educators has often been compartmentalized by departmental boundaries. Word Problems integrates this research to show its relevance to the debate on the reform of mathematics education. Beginning with the different knowledge structures that…

Paperback – 1998-12-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Designing Learning Environments for Developing Understanding of Geometry and Space

This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight,…

Paperback – 1998-10-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Reflections on Statistics

#### Learning, Teaching, and Assessment in Grades K-12

An issue in the current push for reform in mathematics education is the call to address statistics at the precollege level. This volume represents the emerging findings of an interdisciplinary collaboration among a group of mathematics educators, cognitive scientists, teachers, and statisticians to…

Paperback – 1998-03-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematical Reasoning

#### Analogies, Metaphors, and Images

How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology,…

Paperback – 1997-07-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematics Teachers in Transition

This book addresses the need of professional development leaders and policymakers for scholarly knowledge about influencing teachers to modify mathematical instruction to bring it more in alignment with the recommendations of the current reform movement initiated by the National Council of Teachers…

Paperback – 1997-05-01

Routledge*Studies in Mathematical Thinking and Learning Series*### The Nature of Mathematical Thinking

Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How…

Paperback – 1996-09-01

Routledge*Studies in Mathematical Thinking and Learning Series*### The Emergence of Mathematical Meaning

#### interaction in Classroom Cultures

This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the…

Hardback – 1995-05-01

Routledge*Studies in Mathematical Thinking and Learning Series*### Mathematical Thinking and Problem Solving

In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different…

Paperback – 1994-09-01

Routledge*Studies in Mathematical Thinking and Learning Series*