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This fifth volume of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles in RCME are peer-reviewed for two major features: (1) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their own students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics. The volume begins with a study from Mexico of the cross-cutting concept of variable followed by two studies dealing with aspects of calculus reform. The next study frames its discussion of students' conceptions of infinite sets using the psychological work of Efraim Fischbein on (mathematical) intuition. This is followed by two papers concerned with APOS theory and other frameworks regarding mathematical understanding. The final study provides some preliminary results on student learning using technology when lessons are delivered via the Internet. Whether specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas they can use. ... Read more

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The new edition of this best-selling text includes a new focus on active and collaborative learning, while maintaining its emphasis on developing skills and concepts. With a wealth of pedagogical tools, as well as relevant discussions of standard curricula and assessments, this book will be a valuable textbook and reference for future teachers. With this revision, two new chapters are included to address the needs of future middle school teachers, in accordance to the NCTM Focal Points document. ... Read more

Customer Reviews (3)

classified correctly
This book is a nice supplement to a math library.Some of the examples are excellent.

Math Book
I really enjoyed using this book and the content within is something every adult should know

Good Resource
I hate math, but know that I will need to understand it to teach it.This book was very helpful in learning concepts. ... Read more

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When it comes to effective math assessment, these handbooks offer both practical advice and teacher-tested inspiration. You'll find solid, workable assessment strategies with specific pointers on selecting, developing, and using various management tools. Includes samples of effective assessment tasks, scoring rubrics, checklists, observation forms, additional resources, correspondence templates, teaching tips, and much more. Grades K-12. ... Read more

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This anthology, consisting of two volumes, is intended to equip background researchers, practitioners and students of international mathematics education with intimate knowledge of mathematics education in Russia.

Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It examines the history of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics Education: Programs and Practices will examine specific Russian programs in mathematics, their impact and methodological innovations. Although Russian mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that. ... Read more

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“It is fun to figure out the puzzle of how children go about making sense of mathematics and then how to help teachers help kids.”  John A. Van de Walle, Late of Virginia Commonwealth University

This is the philosophy behind Elementary and Middle School Mathematics:  Teaching Developmentally.  John A. Van de Walle wrote this book to help students understand mathematics and become confident in their ability to teach the subject to children in kindergarten through eighth grade.  Although he could not have foreseen the changes in mathematics teaching over the last three decades, he was at the forefront of the movement towards a constructivist view of teaching, or teaching developmentally.  Constructivism says that children construct their own knowledge.  They are not blank slates waiting to absorb whatever the teacher tells them.  Teachers must understand both mathematics itself and how students learn mathematics in order to teach it effectively. 

Learning through problem solving is another major theme of this book.  Students solve problems not just to apply mathematics, but also to learn new mathematics.  Effective problems will take into account where students are, the problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn and not be diluted by non-mathematical activities such as cutting or pasting, and the problem must require justifications and explanations for answers and methods.  Learning then becomes an outcome of the problem solving process. 

The book also addresses in more detail than any other book on the market the effect that the trends of standards-based education, increased pressure to test, and increased teacher accountability have had on teaching mathematics.  He addresses the 2000 NCTM Standards in depth, in Chapter 1 on Teaching Mathematics in the Era of the NCTM Standards, through the NCTM icon that appears in the margins throughout the text, and in two appendices in the back of the book.  Chapter 5 on Building Assessment into Instruction has also been heavily revised to focus on increased testing pressure, creating more explicit links between objectives and assessment, and including assessments for students with special needs. Additionally, samples of Pearson's reformed-based curricula, Connnected Math Project  (5-8) as well as Investigations (K-4),  are featured in the text and on the myeducationlab site.

Elementary and Middle School Mathematics:  Teaching Developmentally is a book for doing math today–for both students who want to become teachers, and the students they will eventually teach. 

New To This Edition:

NEW!  Revises Chapter 5 on assessment--Discusses increased testing pressure and accountability, adds more information on equitable assessments, creates more explicit links between objectives and assessment, and includes assessments for students with special needs.

NEW!  Updates the Literature Connections feature to remove all out of print children’s literature and include more non-fiction, poetry, and other types of readings.

NEW!  Weaves the Focal Points throughout the chapters as well as links them with the Big Ideas feature–Focal Points have also been added to the Appendix. 

NEW!  Includes expanded coverage of working with diverse learners. 

NEW!  Gives greater emphasis on dealing with math anxiety.

Customer Reviews (39)

Great Resource
This book provides an excellent insight, strategies and activities that can be utilize intermediately in the classroom

wonderful resource for elementary teachers
This book has revolutionized my concept of teaching math.Usually I keep my books in perfect shape so I can sell them back, but I'm highlighting and bookmarking all through this text.I plan to keep it forever!

Great book for Teachers
There are some great tips and ideas for teaching math.It's a slow read, but good.

Want kids to 'understand' mathematics? This resource is the best!
John Van de Walle was a leader in teaching mathematics for understanding.I have been teaching secondary Mathematics since 1982 and taught middle school students for five years prior to that. I have used his materials since the second edition of this book was published in the mid-1980s and I am only sorry that I did not know about them sooner.John's ideas are usable with kids at any level who struggle and the readings provide insight into what educators should look for in diagnosing the misunderstandings that lead to difficulties with mathematical concepts.If we emphasized concepts as well as process we would have vastly more students progressing through upper levels mathematics than is currently the case.If you want to make a difference in student math achievement, check the book out.

Elementary and middle school math
This product arrived in a timely fashion and It was in better condition than described! Thanks! ... Read more

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This exciting text for the pre-service elementary teacher provides hands on mathematics lessons they can use to introduce mathematical concepts and skills that students find particularly challenging. Each chapter is divided into four sections:

By providing models of what excellent lessons on a given topic look like, knowledge of the mathematics involved, and a concrete lesson plan structure this much-needed resource is the definitive mathematics planning vehicle that every teacher will want before they set foot in their own elementary classroom.

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Breaking the Barriers shows how increased career awareness and exposure to mentors and role models can help students see science and math-related careers as desirable and viable options. It explains how test preparation, activity-based instruction, cooperative learning, and tutoring can help to improve academic outcomes.

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"Breaking the Barriers" breaks the molds
Admittedly, math and science are not my primary fields of interest.However, as a woman and an educator, I was immediately drawn into this book.

The importance of women and minorities in these fields is clearlydocumented, as are the factors that otherwise dissuade them fromparticipating.Perhaps more importantly, though, the authors outline stepsthat should be taken to remedy this problem.Guidelines for teachers andadministrators, as well as outside program directors, are well organizedand easily accessible within the chapters.We learn the best techniquesand environments for teaching, as well as names and goals of programsalready established to give examples of these theories in practice.

Myone problem with the book is that at times, it seemed to stereotype andgeneralize a bit too much, which is unfortunate, given the tone of advocacyof the book.However, the book is easily forgiven and extremely helpful.

If you're a teacher, this book reminds you that you have a diverse andrich audience, and should teach accordingly.If you're a principal, itreminds you what values to instill in your staff.And if you're a student,it reminds you that you should expect only the best, both from youreducators and from yourself, no matter who you are or what you've beentold. ... Read more

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Early childhood mathematics is vitally important for young children's present and future educational success. Research has demonstrated that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success.
Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.
... Read more

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This book discusses mathematics learners in transition and their practices in different contexts; the institutional and socio-cultural framing of the transition processes involved; and the communication and negotiation of mathematical meanings during transition. Providing both empirical studies and significant theoretical reflections, it will appeal to researchers and postgraduate students in mathematics education, cultural psychology, multicultural education, immigrant and indigenous education.

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The central question addressed in Foundations for the Future in Mathematics Education is this:
 
What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that are emphasized in mathematics classrooms and tests, and those that are needed for success beyond school in the 21st century?
 
This is an urgent question. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem-solving activities has changed dramatically during the past twenty years, as powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields.
 
For K-12 students and teachers, questions about the changing nature of mathematics (and mathematical thinking beyond school) might be rephrased to ask: If the goal is to create a mathematics curriculum that will be adequate to prepare students for informed citizenship—as well as preparing them for career opportunities in learning organizations, in knowledge economies, in an age of increasing globalization—how should traditional conceptions of the 3Rs be extended or reconceived? Overall, this book suggests that it is not enough to simply make incremental changes in the existing curriculum whose traditions developed out of the needs of industrial societies. The authors, beyond simply stating conclusions from their research, use results from it to describe promising directions for a research agenda related to this question.
 
The volume is organized in three sections:
*Part I focuses on naturalistic observations aimed at clarifying what kind of “mathematical thinking” people really do when they are engaged in “real life” problem solving or decision making situations beyond school.
*Part II shifts attention toward changes that have occurred in kinds of elementary-but-powerful mathematical concepts, topics, and tools that have evolved recently—and that could replace past notions of  “basics” by providing new foundations for the future. This section also initiates discussions about what it means to “understand” the preceding ideas and abilities.
*Part III extends these discussions about meaning and understanding—and emphasizes teaching experiments aimed at investigating how instructional activities can be designed to facilitate the development of the preceding ideas and abilities.
 
Foundations for the Future in Mathematics Education is an essential reference for researchers, curriculum developers, assessment experts, and teacher educators across the fields of mathematics and science education. ... Read more

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The economic and social challenges confronting the nation today demand that all citizens acquire and learn to use complex reasoning and thinking skills. "Education and Learning to Think" confronts the issues facing our schools as they take on this mission. This volume reviews previous research, highlights successful learning strategies, and makes specific recommendations about problems and directions requiring further study. Among the topics covered are the nature of thinking and learning, the possibilities of teaching general reasoning, the attempts to improve intelligence, thinking skills in academic disciplines, methods of cultivating the disposition toward higher order thinking and learning, and the integral role motivation plays in these activities. ... Read more

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What would it cost the education system to adopt policies that emphasize science literacy for all students?How can we ensure that tests measure what educators, parents, and others want them to?How can universities set admissions policies that motivate K-12 institutions to produce science literate graduates?Project 2061 of the American Association for the Advancement of Science believes that serious efforts to reform the K-12 curriculum in this country require an understanding of the whole of education.To gain this kind of perspective, Project 2061 commissioned experts to prepare reports on a dozen areas of the education system that would have implications for the implementation of the reforms defined in their earlier volumes Science for All Americans and Benchmarks for Science Literacy.Blueprints for Reform is a summation of those reports offering teachers, parents, policymakers, business leaders, and others a starting point for their exploration of the education system and its response to reform.

Blueprints for Reform includes discussions of equity, assessment, teacher education, policy, finance, school organization, curriculum connections, family and community, research, materials and technology, and business and industry.A chapter is devoted to each of these topics providing an overview of the issue and some recommendations on how to move forward.The idea behind this strategy is to bring current research together in one place so anyone working in the area of science education and reform can have complete access to the latest information, methods, and debates.

To spark the kind of thoughtful debate that can lead to meaningful change, Blueprints for Reform also has an on-line component providing summaries of the chapters in the book, as well as a database of bibliographies and science- and education-related topics.Through Blueprints On-Line, anyone with a stake in improving science education can share experiences with peers, find information on interrelated facets of the education system, or air their views on how best to go about systemic change.Blueprints for Reform offers a bold new examination of the current system to determine what changes are desirable and possible in science education, and how best to ensure our children are prepared for life in the twenty-first century. ... Read more

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This book puts a spotlight on the practices of teachers across the nation who have implemented effective mathematics instruction for students of different ethnicities. Among the ethnic groups represented are African Americans, Latinos, Native Americans, Haitians, Arab Americans, and Euro-Americans. ... Read more

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A volume in Research in Mathematics EducationSeries Editor Barbara J. Dougherty, Iowa State UniversityMarketing description: Issues of language in mathematics learning and teaching are important for bothpractical and theoretical reasons. Addressing issues of language is crucial for improving mathematicslearning and teaching for students who are bilingual, multilingual, or learning English. These issues are alsorelevant to theory: studies that make language visible provide a complex perspective of the role of languagein reasoning and learning mathematics. What is the relevant knowledge base to consider when designingresearch studies that address issues of language in the learning and teaching of mathematics? Whatscholarly literature is relevant and can contribute to research? In order to address issues of language inmathematics education, researchers need to use theoretical perspectives that integrate current views ofmathematics learning and teaching with current views on language, discourse, bilingualism, and secondlanguage acquisition. This volume contributes to the development of such integrated approaches to research on language issues in mathematicseducation by describing theoretical perspectives for framing the study of language issues and methodological issues to consider when designingresearch 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), andassessment (Solano-Flores). This volume offers graduate students and researchers new to the study of language in mathematics education anintroduction to resources for conceptualizing, framing, and designing research studies. For those already involved in examining language issues, thevolume provides useful and critical reviews of the literature as well as recommendations for moving forward in designing research. Lastly, the volumeprovides a basis for dialogue across multiple research communities engaged in collaborative work to address these pressing issues. ... Read more

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This text provides a critical overview of current thinking about equity issues in the teaching and learning of mathematics. Grounded in feminist theories of curriculum change and a broad range of cultural perspectives, the new approaches described here go beyond "special programmes" and "experimental treatments" designed to correct perceived problems and deficits. Instead they establish how improved instructional practices and a fuller understanding of the nature of the mathematical enterprise can overcome the systemic obstacles that have thwarted women's participation in this important field. This book will appeal to all those who are interested in the mathematical education of women, including teachers, parents, administrators and researchers. ... Read more

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"The Equity Equation deals candidly, thoroughly, and objectively with issues for women in science, engineering, and mathematics?This much-needed study not only investigates the institutional causes of gAnder inequity, but lays out the research, policy, and programs needed to change the status quo."
-- James Duderstadt, president, University of Michigan and former member, National Science Board

... Read more

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While the federal government and the nation's school systems have made strides toward improving mathematics education, the knowledge base supporting these efforts has been weak. In response, the RAND Mathematics Study Panel has proposed an R&D program supporting the improvement of mathematics proficiency among U.S. school students. The panel identified three areas for focused R&D development of teachers' mathematical knowledge, teaching and learning of skills for mathematical thinking and problem solving, and teaching and learning of algebra from kindergarten through grade 12. ... Read more

Customer Reviews (1)

A (sadly) revolutionary idea in math education...Research!
The following quote gives a fair summary of this wonderful book's goal: "Within such a community [as proposed in the book] we hope that debate among those with varying and competing views concerning standards of proficiency, curriculuar designs, pedagogical styles, and assessment methods will evolve into a discourse that is based _less_on_ideology_and_more_on_evidence_."

It should be clear from the title of this book that its brief 93 pages would be about mathematical proficiency for all students.Further, its subtitle would lead us to believe it will develop this through a proposal for a research and development program within mathematics education.In the first few pages, it becomes perfectly clear that the Research and Development Program the authors are suggesting doesn't vary much from the R&D Programs that private sector businesses are continually running.

At first, you'll wonder why this book was ever written.Haven't we been doing research about mathematics education for as long as we've been educating students about mathematics?The answer is a quiet "not really."To be exact, this book is revolutionary because it considers a program that would bring real, scientific data about mathematics education to educators in a meaningful way.

By focusing a realistically considered budget, the author proposes a program researching three key areas: The development and use of teachers' mathematical knowledge, teaching and learning mathematical practices, and teaching and learning algebra in kindergarten through 12th grade.The proposed program would focus its energy on these three areas and develop useful theories, curricula, and materials over the course of a 10-15 year period.At the end of this time, the group would have developed all of the knowledge necessary to help all teachers teach algebra effectively to all students.

This book is absolutely wonderful.The book is only a blueprint for this program, and hence doesn't offer solutions.Rather it provides an extremely well thought out path to reach these solutions.I would highly recommend it to anyone in the field of mathematics education, as we should all hope that this will be the future of mathematics education. ... Read more

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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 Principles and Standards for School Mathematics. Despite the substantial amount of curriculum development activity over the last 15 years and growing scholarly interest in their use, the book represents the first compilation of research on teachers and mathematics curriculum materials and the first volume with this focus in any content area in several decades.