In this chance, I am going to tell you, particularly all mathematics educators, about what kind of books that you need, or have to read. There are a lot of books these days, but we have to be smart enough to chose what the most important to read among them. Furthermore, there are several books that you have to pay to get it. There is no other choice. But, in the other side, there are several mathematics teachers or students that do not have enough budget to deal with. So, based upon this fact, I was searching on the internet and finally found the links for several important books for mathematics educators. The links are provided by the other people, not me. So, I am very happy that he/she makes education even better by providing e-books for free.

Then, I make a list and give a short explanation about the books either taken from the web or from the book itself. You can also download it through the links for free. Here they are.

**1. ****Educational Design Research**

Educational design research is the systematic study of designing, developing and evaluating educational programs, processes and products. It can be an invaluable process, yielding considerable insight into how to optimize educational interventions and better understand teaching and learning. However, the fact that such investigations are typically carried out in naturalistic settings – with all the color and complexity that accompanies real classrooms and schools – presents researchers with significant methodological challenges, and scientific rigor can be difficult to maintain. This book addresses a clear and growing need to better understand and address the challenges faced by educational design researchers.

Educational Design Research has been written to appeal to the rapidly growing international audience of educational researchers who situate their studies in practice. The publication contains four main parts, plus supplementary materials available on a companion website. First, a mixture of substantive information is presented for those interested in learning about the essence of design research. The second part of the book features examples of design research, and in the third, researchers share their views on quality assurance. Finally, policy implications are offered and discussed, with particular attention paid to understanding and evaluating design research work. The chapters of this volume are revised, updated and expanded versions of presentations and dialogue shared at a seminar sponsored by the Netherlands Organization for Scientific Research (NWO). The intentions were to clarify exactly what design research entails, to articulate quality standards and reach an understanding of how to judge research proposals and products. Leading scholars form Europe and North America were invited to share their views on design research and advance understanding of how academic standards should be guarded when using this approach. Altogether, this book provides an informative and instructive platform for considering the domain of design research in education. Anyone with an interest in educational research will find it essential reading.

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**2. ****Young mathematician at Work – Constructing Algebra**

The first three volumes of this popular series help teachers support children’s development in number sense and operation, from addition and subtraction through fractions, decimals, and percents. Catherine Twomey Fosnot and Maarten Dolk’s signature approach uses classroom vignettes to illustrate the investigations and minilessons students engage in as they build their mathematical knowledge. The hallmarks of their approach include: Supporting children as they construct mathematical strategies and big ideas Creating realistic contexts and representational models that develop children’s capacity to mathematize their world Building a collaborative community of mathematical thinkers engaged in inquiry For the fourth volume Catherine teams up with Bill Jacob to offer a comfortably familiar and characteristically rich extension to the earlier work. In Constructing Algebra Catherine and Bill provide a landscape of learning that helps teachers recognize, support, and celebrate their students’ capacity to structure their worlds algebraically. They identify for teachers the models, contexts, and landmarks that facilitate algebraic thinking in young students. This volume will be a welcome resource for classroom teachers, math supervisors, and curriculum coordinators alike. Preparing young children for success in algebra is a crucial topic. Constructing Algebra provides the insightful and practical methods from the most trusted source for teaching mathematics to young students from Kindergarten through grade 8. Book study groups and professional learning communities, click here to SAVE 15% when you order 15 copies of Constructing Algebra. Save $56.25! “When children are given the chance to structure number and operation in their own way, they can make sense of algebra not as a funny set of rules that mixes up letters and numbers but as a language for describing the structure and relationships they uncover.

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**3. ****Young Mathematician at Work – Constructing Number Sense, Addition, and Subtraction**

This is a must read for any k-2 teacher. Primarily focused on K-2 teachers this book offers a direct and explicit document to base investigative math. It also gives clear research into the development of young mathematicians (the why). It is a short and concise book that gives you the framework to change your mind-set on teaching math. There is new support materials available as well. Read it and raise your teaching to the next level.

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**4. ****Young Mathematician at Work – Constructing Multiplication and Division**

In this second volume in a series of three, Fosnot and Dolk focus on how to develop an understanding of multiplication and division in grades 3-5.

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**5. ****Young Mathematician at Work – Constructing Fractions, Decimals and Percents**

In our efforts to reform mathematics education, we’ve learned a tremendous amount about young students’ strategies and the ways they construct knowledge, without fully understanding how to support such development over time. The Dutch do. So, funded by the National Science Foundation and ExxonMobil, Mathematics in the City was begun, a collaborative inservice project that pooled the best thinking from both countries. In Young Mathematicians at Work, Catherine Fosnot and Maarten Dolk reveal what they learned after several years of intensive study in numerous urban classrooms.

In this third volume in a series of three, Fosnot and Dolk focus on how children in grades 5-8 construct their knowledge of fractions, decimals, and percents. Their book:

- describes and illustrates what it means to do and learn mathematics.
- contrasts word problems with true problematic situations which support and enhance investigation and inquiry.
- provides strategies to help teachers turn their classrooms into math workshops.
- explores the cultural and historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies.
- defines and gives examples of modeling, noting the importance of context.
- discusses calculation using number sense and the role of algorithms in computation instruction.
- describes how to strengthen performance and portfolio assessment.
- focuses on teachers as learners by encouraging them to see themselves as mathematicians.

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**6. ****Elementary and Middle School mathematics: teaching Developmentally, 6th Edition**

This leading K-8 math methods text has the most coverage of the NCTM standards, the strongest coverage of middle school mathematics, and the highest student approval of any text currently available. Elementary and Middle School Mathematics provides an unparalleled depth of ideas and discussion to help students develop a real understanding of the mathematics they will teach. John Van de Walle, one of the foremost experts on how children learn mathematics, finds that 80 percent of the students who purchase this book keep it for reference when they begin their professional teaching careers. This text reflects the NCTM Principles and Standards and the benefits of constructivist-or student-centered-mathematics instruction. Moreover, it is structured for maximum flexibility, offering 24 brief, compartmentalized chapters that may be mixed and matched to fit any course or teaching approach.

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**7. ****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’ theoretical and empirical frameworks are learning trajectories – detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking.Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.

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**8. ****Early Childhood Mathematics, 3rd Edition**

This NCTM Standards-based book encourages the teacher or future teacher to create an active learning environment that fosters curiosity, confidence, and persistence in children as they learn math. Because the knowledge of important mathematical relationships, number sense, and the ability to solve problems are three key ingredients to the successful acquisition of math in the early years, this book pays special attention to helping teachers foster those skills and ways of thinking.

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**9. ****Revisiting Mathematics Education: China Lectures**

This is neither preface nor introduction but rather an apology and a warning: the present book adds nothing but itself to work that I have published in the past in various places. I have renounced originality, I have refrained from offering the reader any new experiences, aspects, or ideas he might feel entitled to expect reason to apologise. Resuming old ideas, my aim is now one of comprehensiveness,

not by compiling but by selecting and streamlining, by including essentials and eliminating contradictions. Views, even when supported by evidence, are susceptible to change. My present viewpoint is “here and now”, that of review rather than of overview. I felt prompted by two experiences. Negative: reading dated quotations from my own work where I did not recognise myself. Positive: a visit to China, where in lectures, seminars, and discussions I tried to display and illustrate my view on mathematics education in all its aspects. The present book somehow reflects these talks, albeit in no way textually. Therefore the subtitle, meant as an homage to my listeners who, by their critical curiosity, induced me to improve on clarity and concreteness.

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**10. ****Theories of Mathematics Education: Seeking New Frontiers (Advances in Mathematics Education)**

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building.

This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

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**11. ****Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research**

This book has a two-fold purpose. First, it was intended as a description of the development and testing of a primary school fraction program, presently in practice. This project seeks to develop a realistic alternative to the teaching and learning of fractions. The second purpose was to produce a theory on the teaching and learning of fractions that could be an example for a theory of realistic mathematics education.

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**12. ****Handbook of International Research in Mathematics Education**

This state-of-the-art Handbook brings together important mathematics education research that makes a difference in both theory and practice, organized around three key themes: life-long democratic access to powerful mathematical ideas, advances in research methodologies, and influences of advanced technologies.

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