Eminent scholars from around the globe gathered to discuss how educational systems would change if the prevailing principles of constructivism were applied to three major aspects of those systems -- knowledge and learning, communication, and environment. This volume provides documentation of the proceedings of this important meeting - - the Early Childhood Action Group of the Sixth International Congress on Mathematics Education. This international assembly, representing such diverse disciplines as mathematics and math education, epistemology, philosophy, cognitive science, psycholinguistics, and science education, is the first to examine early childhood mathematics education from constructivist and international perspectives in addition to formulating recommendations for future work in the field.

With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.

This practical and popular guide to children’s common errors and misconceptions in primary mathematics is an essential tool for teachers and trainees. It supports them in planning for and tackling potential errors and enhances their understanding of the difficulties encountered in mathematical development. This fourth edition explores how a Growth Mindset approach works alongside an awareness of children′s errors and how mistakes themselves are powerful learning tools. This edition includes 50 new identifiable misconceptions children have of mathematics. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions. Key features: Linked to the new National Curriculum and covers every objective Provides an essential tool for planning primary mathematics lessons Explores how common misconceptions can be anticipated and addressed

‘Lively and thought provoking...at a key time in the development of primary mathematics teaching and learning. It offers a very much richer model of mathematics learning than is available to many young learners and has the potential to have a real impact on the way mathematics is taught.’ - Jan Winter, Bristol University, UK What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? Under-pinned by findings from the largest research programme into primary mathematics funded in recent years, Transforming Primary Mathematics offers a clear, practical approach to implementing fundamental change in curriculum, classroom environment and teaching styles. It offers an inspiring, sometimes controversial, and often unconventional look at the subject of mathematics, by: Endorsing the use of a ‘new mathematics’ – one based on problem solving, modelling and inquiry, not on abstract rules, memorising, and regurgitation Arguing that there is more to maths teaching than ‘death by a thousand worksheets’ Challenging norms, such as the practice of sorting children into sets based on their perceived mathematical ability Advocating an environment where teachers are encouraged to take risks Looking at how best to prepare learners for an unknown future Encouraging reflection on teachers’ own beliefs and values about mathematics. Transforming Primary Mathematics is for all primary school teachers who want to make mathematics welcoming, engaging, inclusive and successful.

During the past two decades, Chris Confer and Marco Ramirez have worked to deepen and improve mathematics instruction at schools around the country. The authors identify eight tested principles that transform what can be an overwhelming process into a set of comprehensible and concrete steps. Each phase of the change process is brought to life through the stories and perspectives of teachers, coaches, and principals. When teachers make sense of math, students learn to make sense of math, and that can profoundly change the entire culture of a school. In one vivid illustration, the authors tell the story of Pueblo Gardens Elementary School in Tucson, Arizona, where Marco, as principal, and Chris, as instructional coach, worked alongside a group of dedicated teachers. A few years into the change process, Pueblo Gardens--a school with 96 percent of its students at the poverty level and a high percentage of English language learners--had 94 percent of students meeting or exceeding state standards in third-grade mathematics. Over time, other grades achieved similarly high scores. And once the test scores rose, they were sustained at high levels.

This book builds on the Teachers Empowered to Advance Change in Mathematics (TEACH Math) project, which was an initiative that sought to develop a new generation of preK-8 mathematics teachers to connect mathematics, children’s mathematical thinking, and community and family knowledge in mathematics instruction – or what we have come to call children’s multiple mathematical knowledge bases in mathematics instruction, with an explicit focus on equity. Much of the work involved in the TEACH Math project included the development of three instructional modules for preK-8 mathematics methods courses to support the project’s goals. These activities were used and refined over eight semesters, and in Fall 2014 shared at a dissemination conference with other mathematics teacher educators from a variety of universities across the United States. Chapter contributions represent diverse program and geographical contexts and teach prospective and practicing teachers from a variety of socioeconomic and ethnic backgrounds, in particular providing accounts of supports, challenges, and tensions in implementing equity-based mathematics teacher education. The chapters supply rich evidence and illustrative examples of how other mathematics teacher educators and professional developers might make the modules work for their unique practices, courses, workshops, and prospective teachers/teachers. It promises to be an important resource for offering guidance and examples to those working with prospective teachers of mathematics who want to create positive, culturally responsive, and equity-based mathematics experiences for our nation’s youth.

This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.