This volume highlights theories that influence mathematical education theory building. It also includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory and networking theories.

Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDMThe 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 (18541912), 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.

Inaugural volume of the new series "Advances in Mathematics Education" Forward-looking monograph highlighting theories that influence mathematical education theory building Top researchers in their field are contributing Includes supplementary material: sn.pub/extras

Inhalt
I.- Preface to Part I.- Surveying Theories and Philosophies of Mathematics Education.- II.- Preface to Part II Ernest's Reflections on Theories of Learning.- Reflections on Theories of Learning.- Commentary 1 on Reflections on Theories of Learning by Paul Ernest.- Commentary 2 on Reflections on Theories of Learning.- III.- Preface to Part III.- On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education.- Commentary on On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education.- IV.- Preface to Part IV.- Theories of Mathematics Education: Is Plurality a Problem?.- Commentary on Theories of Mathematics Education: Is Plurality a Problem?.- V.- Preface to Part V.- Re-conceptualizing Mathematics Education as a Design Science.- Commentary 1 on Re-conceptualizing Mathematics Education as a Design Science.- Commentary 2 on Re-conceptualizing Mathematics Education as a Design Science.- Commentary 3 on Re-conceptualizing Mathematics Education as a Design Science.- VI.- Preface to Part VI.- The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks.- Commentary on The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks.- VII.- Preface to Part VII.- Symbols and Mediation in Mathematics Education.- Commentary on Symbols and Mediation in Mathematics Education.- VIII.- Problem Solving Heuristics, Affect, and Discrete Mathematics: A Representational Discussion.- Commentary on Problem Solving Heuristics, Affect, and Discrete Mathematics: A Representational Discussion.- IX.- Preface to Part IX.- Problem Solving for the 21 Century.- Commentary 1 on Problem Solving for the 21 Century.- Commentary 2 on Problem Solvingfor the 21 Century.- X.- Preface to Part X.- Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education.- Commentary on Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education.- XI.- Preface to Part XI.- DNR-Based Instruction in Mathematics as a Conceptual Framework.- Commentary on DNR-Based Instruction in Mathematics as a Conceptual Framework.- XII.- Appreciating in Qualitative Research.- XIII.- Preface to Part XIII.- Understanding a Teacher's Actions in the Classroom by Applying Schoenfeld's Theory : Reflecting on Goals and Beliefs.- Commentary on Understanding a Teacher's Actions in the Classroom by Applying Schoenfeld's Theory : Reflecting on Goals and Beliefs.- XIV.- Preface to Part XIV.- Feminist Pedagogy and Mathematics.- Commentary 1 on Feminist Pedagogy and Mathematics.- Commentary 2 on Feminist Pedagogy and Mathematics.- Commentary 3 on Feminist Pedagogy and Mathematics.- XV.- Preface to Part XV.- Networking of TheoriesAn Approach for Exploiting the Diversity of Theoretical Approaches.- Commentary on Networking of TheoriesAn Approach for Exploiting the Diversity of Theoretical Approaches.- XVI.- Preface to Part XVI.- On Networking Strategies and Theories' Compatibility: Learning from an Effective Combination of Theories in a Research Project.- Modalities of a Local Integration of Theories in Mathematics Education.- Commentary on On Networking Strategies and Theories' Compatibility: Learning from an Effective Combination of Theories in a Research Project.- Commentary on Modalities of a Local Integration of Theories in Mathematics Education.- XVII.- Preface to Part XVII.- Complexity Theories and Theories of Learning: Literature Reviews andSyntheses.- XVIII.- Preface to Part XVIII.- Knowing More Than We Can Tell.- Commentary on Knowing More Than We Can Tell.- XIX.- Politicizing Mathematics Education: Has Politics Gone too Far? Or Not Far Enough?.- Commentary on Politicizing Mathematics Education: Has Politics Gone too Far? Or Not Far Enough?.