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The Language of Mathematics Education

An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning

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Shannon W. Dingman, Laura B. Kent, Kim K. McComas and Cynthia C. Orona

The Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field.

The authors provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.

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Edited by Dianne Siemon, Tasos Barkatsas and Rebecca Seah

The relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time.

This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered.

Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.

STEM of Desire

Queer Theories and Science Education

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Edited by Will Letts and Steve Fifield

STEM of Desire: Queer Theories and Science Education locates, creates, and investigates intersections of science, technology, engineering, and mathematics (STEM) education and queer theorizing. Manifold desires—personal, political, cultural—produce and animate STEM education. Queer theories instigate and explore (im)possibilities for knowing and being through desires normal and strange. The provocative original manuscripts in this collection draw on queer theories and allied perspectives to trace entanglements of STEM education, sex, sexuality, gender, and desire and to advance constructive critique, creative world-making, and (com)passionate advocacy. Not just another call for inclusion, this volume turns to what and how STEM education and diverse, desiring subjects might be(come) in relation to each other and the world.

STEM of Desire is the first book-length project on queering STEM education. Eighteen chapters and two poems by 27 contributors consider STEM education in schools and universities, museums and other informal learning environments, and everyday life. Subject areas include physical and life sciences, engineering, mathematics, nursing and medicine, environmental education, early childhood education, teacher education, and education standards. These queering orientations to theory, research, and practice will interest STEM teacher educators, teachers and professors, undergraduate and graduate students, scholars, policy makers, and academic libraries.

Contributors are: Jesse Bazzul, Charlotte Boulay, Francis S. Broadway, Erin A. Cech, Steve Fifield, blake m. r. flessas, Andrew Gilbert, Helene Götschel, Emily M. Gray, Kristin L. Gunckel, Joe E. Heimlich, Tommye Hutson, Kathryn L. Kirchgasler, Michelle L. Knaier, Sheri Leafgren, Will Letts, Anna MacDermut, Michael J. Reiss, Donna M. Riley, Cecilia Rodéhn, Scott Sander, Nicholas Santavicca, James Sheldon, Amy E. Slaton, Stephen Witzig, Timothy D. Zimmerman, and Adrian Zongrone.

Critical Mathematics Education

Can Democratic Mathematics Education Survive under Neoliberal Regime?

Bülent Avci

Drawing on rich ethnographic data, Critical Mathematics Education: Can Democratic Mathematics Education Survive under Neoliberal Regime? responds to ongoing discussions on the standardization in curriculum and reconceptualizes Critical Mathematics Education (CME) by arguing that despite obstructive implications of market-driven changes in education, a practice of critical mathematics education to promote critical citizenship could be implemented through open-ended projects that resonate with an inquiry-based collaborative learning and dialogic pedagogy. In doing so, neoliberal hegemony in education can be countered. The book also identifies certain limitations of critical mathematical education and suggests pedagogic and curricular strategies for critical educators to cope with these obstacles.

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Edited by Tasos Barkatsas, Nicky Carr and Grant Cooper

The second decade of the 21st century has seen governments and industry globally intensify their focus on the role of science, technology, engineering and mathematics (STEM) as a vehicle for future economic prosperity. Economic opportunities for new industries that are emerging from technological advances, such as those emerging from the field of artificial intelligence also require greater capabilities in science, mathematics, engineering and technologies. In response to such opportunities and challenges, government policies that position STEM as a critical driver of economic prosperity have burgeoned in recent years. Common to all these policies are consistent messages that STEM related industries are the key to future international competitiveness, productivity and economic prosperity.
This book presents a contemporary focus on significant issues in STEM teaching, learning and research that are valuable in preparing students for a digital 21st century. The book chapters cover a wide spectrum of issues and topics using a wealth of research methodologies and methods ranging from STEM definitions to virtual reality in the classroom; multiplicative thinking; STEM in pre-school, primary, secondary and tertiary education, opportunities and obstacles in STEM; inquiry-based learning in statistics; values in STEM education and building academic leadership in STEM.
The book is an important representation of some of the work currently being done by research-active academics. It will appeal to academics, researchers, teacher educators, educational administrators, teachers and anyone interested in contemporary STEM Education related research in a rapidly changing globally interconnected world.

Contributors are: Natalie Banks, Anastasios (Tasos) Barkatsas, Amanda Berry, Lisa Borgerding, Nicky Carr, Io Keong Cheong, Grant Cooper, Jan van Driel, Jennifer Earle, Susan Fraser, Noleine Fitzallen, Tricia Forrester, Helen Georgiou, Andrew Gilbert, Ineke Henze, Linda Hobbs, Sarah Howard, Sylvia Sao Leng Ieong, Chunlian Jiang, Kathy Jordan, Belinda Kennedy, Zsolt Lavicza, Tricia Mclaughlin, Wendy Nielsen, Shalveena Prasad, Theodosia Prodromou, Wee Tiong Seah, Dianne Siemon, Li Ping Thong, Tessa E. Vossen and Marc J. de Vries.

Edited by Jacqueline Leonard, Andrea C. Burrows and Richard Kitchen

There is a critical need to prepare diverse teachers with expertise in science, technology, engineering, and mathematics (STEM) with the skills necessary to work effectively with underrepresented K-12 students. Three major goals of funded STEM programs are to attract and prepare students at all educational levels to pursue coursework in the STEM content areas, to prepare graduates to pursue careers in STEM fields, and to improve teacher education programs in the STEM content areas. Drawing upon these goals as the framework for Recruiting, Preparing, and Retaining STEM Teachers for a Global Generation, the 15 chapters contained herein highlight both the challenges and successes of recruiting, preparing, and sustaining novice teachers in the STEM content areas in high-need schools.

Recruiting, retaining and sustaining highly-qualified teachers with expertise in STEM content areas to work in hard-to-staff schools and geographic areas are necessary to equalize educational opportunities for rural and urban Title 1 students. High teacher turnover rates, in combination with teachers working out-of-field, leave many students without highly-qualified teachers in STEM fields. Most of the chapters in this volume were prepared by scholars who received NSF funding through Noyce and are engaged in addressing research questions related to these endeavours.

Contributors are: Lillie R. Albert, Cynthia Anhalt, Saman A. Aryana, Joy Barnes-Johnson, Lora Bartlett, Brezhnev Batres, Diane Bonilla, Patti Brosnan, Andrea C. Burrows, Alan Buss, Laurie O. Campbell, Phil Cantor, Michelle T. Chamberlin, Scott A. Chamberlin, Marta Civil, Lin Ding, Teresa Dunleavy, Belinda P. Edwards, Jennifer A. Eli, Joshua Ellis, Adrian Epps, Anne Even, Angela Frausto, Samantha Heller, Karen E. Irving, Heather Johnson, Nicole M. Joseph, Richard Kitchen, Karen Kuhel, Marina Lazic, Jacqueline Leonard, Rebecca H. McGraw, Daniel Morales-Doyle, Sultana N. Nahar, Justina Ogodo, Anil K. Pradhan, Carolina Salinas, David Segura, Lynette Gayden Thomas, Alisun Thompson, Maria Varelas, Dorothy Y. White, Desha Williams, and Ryan Ziols.

The Narrative of Mathematics Teachers

Elementary School Mathematics Teachers’ Features of Education, Knowledge, Teaching and Personality

Edited by Dorit Patkin and Avikam Gazit

The issue of mathematics teaching and its impact on learners' attainments in this subject has continuously been on the public agenda. The anthology of chapters in this book consists of varied up-to-date studies of some of the best mathematics education researchers and mathematics teaching experts, exploring the varied aspects of this essential. The book depicts the elementary school mathematics teachers' world while relating to three aspects which comprise the professional environment of mathematics teachers: Teachers' education and teachers' knowledge, Teaching and Teachers' personality. The chapters are written on a level which addresses and might interest a wide readership: researchers, in-service teachers, pre-service teachers, parents and learners.

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Edited by Yeping Li and Rongjin Huang

While the importance of knowledge for effective instruction has long been acknowledged, and the concept and structure of mathematics knowledge for teaching are far from being new, the process of such knowledge acquisition and improvement remains underexplored empirically and theoretically. The difficulty can well associate with the fact that different education systems embody different values for what mathematics teachers need to learn and how they can be assisted to develop their knowledge. To improve this situation with needed consideration about a system context and policies, How Chinese Acquire and Improve Mathematics Knowledge for Teaching takes a unique approach to present new research that views knowledge acquisition and improvement as part of teachers’ life-long professional learning process in China. The book includes such chapters that can help readers to make possible connections of teachers’ mathematical knowledge for teaching in China with educational policies and program structures for mathematics teacher education in that system context.

How Chinese Acquire and Improve Mathematics Knowledge for Teaching brings invaluable inspirations and insights to mathematics educators and teacher educators who wish to help teachers improve their knowledge, and to researchers who study this important topic beyond a static knowledge conception.

Adults, Mathematics and Work

From Research into Practice

John J. Keogh, Theresa Maguire and John O’Donoghue

Adults use mathematics extensively in work even though they may deny it or dismiss their numerate behaviour as common sense. Their capacity for mathematics is invisible to them and confirms their ‘non-maths person’ self-perception, which has negative consequences for their life choices. In Adults, Mathematics and Work, the authors tackle and explain a number of paradoxes related to the curious relationship between adults and mathematics. It operationalises the benefits of workplace doctoral research by providing a set of the tools to review this mistaken self-perception in order to make workers’ abilities available for development. It also provides a systematic way of uncovering and recognising informal and non-formal learning to support employability and re-employability in an increasingly fluid work-landscape.

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Edited by Carolyn A. Maher and Dina Yankelewitz

This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.