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.

The aim of this book is to explore measures of mathematics knowledge, spanning K-16 grade levels. By focusing solely on mathematics content, such as knowledge of mathematical practices, knowledge of ratio and proportions, and knowledge of abstract algebra, this volume offers detailed discussions of specific instruments and tools meant for measuring student learning. Written for assessment scholars and students both in mathematics education and across educational contexts, this book presents innovative research and perspectives on quantitative measures, including their associated purpose statements and validity arguments.

School readiness is as much about schools recognizing the existing capabilities and knowledge each child has when they enter school as it is about supporting children and families in their preparation for entering formal learning environments. Effective approaches that address learning variability must take these differences into account, recognizing and leveraging opportunities inherent in the child’s ecosystem of resources. The Handbook of Research on Innovative Approaches to Early Childhood Development and School Readiness assembles the most current research and thought-leadership on the ways in which innovative education stakeholders are working together to impact the most critical years in a child’s life—the years leading up to and including kindergarten. Covering topics such as change agency, experience quality, and social-emotional development, this book is a crucial resource for educational researchers, child development professionals, school administrators, pre-K teachers, pre-service teachers, program managers, policymakers, non-profit service organizations, early childhood EdTech developers, curriculum developers, and academicians.

This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students’ mathematical thinking, thus contributing an alternative view of mathematical progression in which students are taught conceptually. The research-based volume presents a unique collaboration among researchers in special education, psychology, and mathematics education from around the world. It reflects an ongoing work by members of the International Group for the Psychology of Mathematics Education (PME) and the North American Chapter of the PME Working Groups. The authors of chapters in this book, who have been collaborating extensively over the past 7 years, are from Australia, Canada, the United Kingdom, and the United States.

This book expands upon the guiding principles at the heart of Math Recovery® instruction, exploring their connections with learning theory, practical application in the classroom and their wider links to agreed concepts of high-quality mathematics teaching. It provides a well-rounded overview of all major aspects of mathematics teaching including inquiry-based and constructivist approaches, planning and assessment, and strategies that offer children opportunities for reflection, satisfaction and increasing challenge. Particular focus is placed on equitable and inclusive practices in mathematics and how we can develop teaching that connects with the abilities, cultures, and lived experiences of all children. This is essential reading for all teachers familiar with the Math Recovery® approach and classroom mathematics teachers in elementary and primary schools everywhere seeking to enhance their own professional knowledge and understanding. Beth L. MacDonald is an associate professor in Early Childhood Mathematics Education in the School of Teaching and Learning at Illinois State University. Jonathan N. Thomas is an associate professor of mathematics education and the chairperson of the Department of STEM Education at the University of Kentucky.

Primary Mathematics: Integrating Theory with Practice is a comprehensive introduction to teaching mathematics in Australian primary schools. Closely aligned with the Australian Curriculum, it provides a thorough understanding of measurement, geometry, patterns and algebra, data and statistics, and chance and probability. The fourth edition provides support for educators in key aspects of teaching: planning, assessment, digital technologies, diversity in the classroom and integrating mathematics content with other learning areas. It also features a new chapter on the role of education support in the mathematics classroom. Each chapter has been thoroughly revised and is complemented by classroom snapshots demonstrating practical application of theories, activities to further understanding and reflection questions to guide learning. New in this edition are 'Concepts to consider', which provide a guided explanation and further discussion of key concepts to support pre- and in-service teachers' learning and teaching of the fundamentals of mathematics.

Gathering contributions from leading scholars around the world, this handbook offers a comprehensive resource on the most recent advances in research surrounding the theories, methodologies, and applications of science learning progressions. Researchers and educators have used learning progressions to guide the design and alignment of curriculum, instruction, and assessment, and to help students learn scientific knowledge and practices in a coherent and connected way across multiple years. This handbook lays out the development and current state of research in this field across four sections: learning progression theories and methodologies; learning progressions to promote student learning; teachers’ learning and use of learning progressions; and new technology in learning progression research. Featuring internationally-recognized experts in learning progression research as well as up-and-coming voices, the Handbook of Research on Science Learning Progressions offers a defining new resource for researchers, teachers and teacher educators, and curriculum and assessment developers in science education.

Primary Mathematics: Integrating Theory with Practice is a comprehensive introduction to teaching mathematics in Australian primary schools. Closely aligned with the Australian Curriculum, it provides a thorough understanding of measurement, geometry, patterns and algebra, data and statistics, and chance and probability. The fourth edition provides support for educators in key aspects of teaching: planning, assessment, digital technologies, diversity in the classroom and integrating mathematics content with other learning areas. It also features a new chapter on the role of education support in the mathematics classroom. Each chapter has been thoroughly revised and is complemented by classroom snapshots demonstrating practical application of theories, activities to further understanding and reflection questions to guide learning. New in this edition are 'Concepts to consider', which provide a guided explanation and further discussion of key concepts to support pre- and in-service teachers' learning and teaching of the fundamentals of mathematics.

Nursery World Professional Book of the Year 2022 Children are naturally mathematical in their play. They play with mathematics. Early years’ practitioners often struggle to make mathematics relevant and engaging for their young learners. In their play, children are naturally mathematical yet practitioners are often unsure about how to build on this or how this observed play ‘fits’ in with the mathematics they teach. This Nursery World Award Winning Book: *Empowers early years teachers to see the learning in this play and to remain committed to play based practice *Outlines recent research on how children best learn mathematics *Supports early years practitioners to know why preparation works better than planning and why ′thinking space′ matters more than you think