Critique of research methods and methodology is one of several key features of the regular dialogue between researchers. This critique takes place formally at conferences and seminars, and regularly in universities. Published critique is normally separated from the original work. This book brings together the writing of researcher and independent critique. Thus the book exposes to wider scrutiny the dialogue that exists between researchers. It will be of interest to all who are concerned to understand the nature and substance of this critique.

The volume comprises a collection of accounts of classroom studies, each complemented by the reaction of an eminent researcher. The accounts and reactions are written to expose the nature of methodology of classroom research. It argues that methodology encompasses the choice of methods and the researchers' beliefs and values.

A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the "boy problem," with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.

The diversity of research in mathematics education has been addressed as both, a problem and a strength. When manifested through adherence to different intellectual roots and theoretical orientations, diversions constitute `refractions' of mathematics education. The collection and analysis of empirical data in a study are by necessity refracted through the specific analytical lens employed, as well as the aim of the study itself. Refractions can also refer to looking at old phenomena through new lenses. The chapters in this book are refracted through philosophical, political, mathematical and personal lenses by distinguished authors in the field, addressing issues about the elusive experience of doing mathematics, purification of texts, refractions, mathematics and ethnomathematics, political messages in textbook tasks, mathematics education policy debate, the political in mathematics education research, philosophy and mathematics, meanings and representations, identity of mathematical modeling, and dilemmas in the teaching of calculus. An ancient Sanskrit adage states that Knowledge is something that grows when shared, but shrinks when hoarded. Academics engaged in the generation of new Knowledge are blessed with both the time and the freedom to engage in pursuits that allow for intellectual pleasure. As a phenomenon of the Zeitgeist many have succumbed to the increased corporatization of academic work, engaging in activities for monetary and self advancement purposes. Are there any real intellectuals left in academia, a la Adorno, Bourdieu, Chomsky, Foucault, among others? This Festschrift is dedicated to academics that don't bother with self promotion or aggrandizement of themselves or their ideas in simplistic terms.

This book addresses engineering learning in early childhood, spanning ages 3 to 8 years. It explores why engineering experiences are important in young children's overall development and how engineering is a core component of early STEM learning, including how engineering education links and supports children's existing experiences in science, mathematics, and design and technology, both before school and in the early school years. Promoting STEM education across the school years is a key goal of many nations, with the realization that building STEM skills required by societies takes time and needs to begin as early as possible. Despite calls from national and international organisations, the inclusion of engineering-based learning within elementary and primary school programs remains limited in many countries. Engineering experiences for young children in the pre-school or early school years has received almost no attention, even though young children can be considered natural engineers. This book addresses this void by exposing what we know about engineering for young learners, including their capabilities for solving engineering-based problems and the (few) existing programs that are capitalising on their potential.

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 fur - 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 Poincare (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."

This book addresses engineering learning in early childhood, spanning ages 3 to 8 years. It explores why engineering experiences are important in young children's overall development and how engineering is a core component of early STEM learning, including how engineering education links and supports children's existing experiences in science, mathematics, and design and technology, both before school and in the early school years. Promoting STEM education across the school years is a key goal of many nations, with the realization that building STEM skills required by societies takes time and needs to begin as early as possible. Despite calls from national and international organisations, the inclusion of engineering-based learning within elementary and primary school programs remains limited in many countries. Engineering experiences for young children in the pre-school or early school years has received almost no attention, even though young children can be considered natural engineers. This book addresses this void by exposing what we know about engineering for young learners, including their capabilities for solving engineering-based problems and the (few) existing programs that are capitalising on their potential.

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 fur - 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 Poincare (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."

The diversity of research in mathematics education has been addressed as both, a problem and a strength. When manifested through adherence to different intellectual roots and theoretical orientations, diversions constitute `refractions' of mathematics education. The collection and analysis of empirical data in a study are by necessity refracted through the specific analytical lens employed, as well as the aim of the study itself. Refractions can also refer to looking at old phenomena through new lenses. The chapters in this book are refracted through philosophical, political, mathematical and personal lenses by distinguished authors in the field, addressing issues about the elusive experience of doing mathematics, purification of texts, refractions, mathematics and ethnomathematics, political messages in textbook tasks, mathematics education policy debate, the political in mathematics education research, philosophy and mathematics, meanings and representations, identity of mathematical modeling, and dilemmas in the teaching of calculus. An ancient Sanskrit adage states that Knowledge is something that grows when shared, but shrinks when hoarded. Academics engaged in the generation of new Knowledge are blessed with both the time and the freedom to engage in pursuits that allow for intellectual pleasure. As a phenomenon of the Zeitgeist many have succumbed to the increased corporatization of academic work, engaging in activities for monetary and self advancement purposes. Are there any real intellectuals left in academia, a la Adorno, Bourdieu, Chomsky, Foucault, among others? This Festschrift is dedicated to academics that don't bother with self promotion or aggrandizement of themselves or their ideas in simplistic terms.

A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the "boy problem," with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.