Theories of Mathematics Education

1. Front Matter

   Pages I-XXX

   PDF

2. Surveying Theories and Philosophies of Mathematics Education

   1. Front Matter

      Pages 1-1

      PDF

3. Part I

   1. Preface to Part I

      • Jeremy Kilpatrick

      Pages 3-5

   2. Surveying Theories and Philosophies of Mathematics Education

      • Bharath Sriraman, Lyn English

      Pages 7-32

4. Reflections on Theories of Learning

   1. Front Matter

      Pages 33-33

      PDF

5. Part II

   1. Preface to Part II Ernest’s Reflections on Theories of Learning

      • Bharath Sriraman, Nick Haverhals

      Pages 35-38

   2. Reflections on Theories of Learning

      • Paul Ernest

      Pages 39-47

   3. Commentary 1 on Reflections on Theories of Learning by Paul Ernest

      • Simon Goodchild

      Pages 49-52

   4. Commentary 2 on Reflections on Theories of Learning

      • Paul Ernest

      Pages 53-61

6. On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education

   1. Front Matter

      Pages 63-63

      PDF

7. Part III

   1. Preface to Part III

      • Lyn D. English

      Pages 65-66

   2. On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education

      • Frank K. Lester Jr.

      Pages 67-85

   3. Commentary on On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education

      • Guershon Harel

      Pages 87-94

8. Theories of Mathematics Education: Is Plurality a Problem?

   1. Front Matter

      Pages 95-95

      PDF

9. Part IV

   1. Preface to Part IV

      • Norma Presmeg

      Pages 97-98

   2. Theories of Mathematics Education: Is Plurality a Problem?

      • Stephen Lerman

      Pages 99-109

   3. Commentary on Theories of Mathematics Education: Is Plurality a Problem?

      • Eva Jablonka, Christer Bergsten

      Pages 111-117

10. Re-conceptualizing Mathematics Education as a Design Science

    1. Front Matter

       Pages 119-119

       PDF

11. Part V

    1. Preface to Part V

       • Lyn D. English

       Pages 121-122

    2. Re-conceptualizing Mathematics Education as a Design Science

       • Richard Lesh, Bharath Sriraman

       Pages 123-146

Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The Inter- tional Journal on Mathematics Education (formerly known as Zentralblatt für - daktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on c- tral sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the ?eld forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking ins- ration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority.

• Mathematica
• Mathematics Education
• complexity
• mathematics
• modeling
• philosophy
• problem solving

From the reviews:

“Theories of Mathematics Education: Seeking New Frontiers is the first book in the series titled ‘Advances in Mathematics Education.’ The book contains 20 chapters, 16 prefaces, and 23 commentaries … . if you are interested and ready to join, as a listener, an interesting and informative conversation among the leaders in the field of ME, to follow their contemplations and become exposed to their arguments and disagreements, then this book will provide you with plenty.” (Roza Leikin and Rina Zazkis, Journal for Research in Mathematics Education, Vol. 43 (2), March, 2012)

“The series intends to ‘integrate, synthesize, and extend’ work in the field so that promising ideas can be improved and built upon. The seed for this inaugural book was the 2005 meeting of the International Group of the Psychology of Mathematics Education. … The ultimate test of the value of the ideas in this book is whether they or their progeny help solve the problems that teachers, administrators, and policymakers face as they work to improve mathematics teaching and learning.” (Kristin L. Umland, The Mathematical Intelligencer, Vol. 33 (2), March, 2011)

“Book addresses much more, including teachers’ pedagogical actions and the politicization of mathematics education, and offers an intriguing look at covert ways of knowing. … provides vocabularies to use, pronouncements to respond to, and examples to consider for researchers and graduate students who wish to discuss what MER theory is and should be. For these reasons, the book will be of most interest to expert, novice, and aspiring researchers who are using, crafting, refining, or reflecting upon theories for their own current and future research.” (Robert Ely, Educational Studies in Mathematics, May, 2010)

“I like this book!! It is the flagship book announcing a new Springer series Advances in Mathematics Education, and as such it does a wonderful jobintroducing readers to the field, at the same time laying it out clearly and extending it in many different directions. It provides a valuable perspective on the field. … a valuable resource for anyone interested in learning about the many facets of the field. … I highly recommend it for the library of any serious mathematics education researcher.” (Libby Knott, Mathematics Education Research Journal, Vol. 22 (3), 2010)

“Volume is organized into 19 parts, each of which, after the initial overview … typically contains a brief preface, a substantial essay, and from one to three commentaries on the essay. … This is an excellent format … suited for discussions of theory. … researchers will find themselves provoked to react to various perspectives; those embarking on their careers will find introductions to a wide range of areas. All will be provoked to react, and that … is a fitting reward for reading the book.” (Alan H. Schoenfeld, ZDM Mathematics Education, Vol. 42, 2010)

"A very impressive new book, "Theories of Mathematics Education" (Springer) edited by Sriraman and English is meant to inaugurate a new series, "Advances in Mathematics Education" . This first book in the series is a massive and ambitious undertaking, a very wide-ranging survey written in a dialogic format. " (Reuben Hersh)

• Dept. Mathematical Sciences, University of Montana-Missoula, Missoula, U.S.A.

  Bharath Sriraman

• Centre for Learning Innovation, Queensland University of Technology, Kelvin Grove, Australia

  Lyn English

Policies and ethics