In this important new book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help teachers become more effective professionals. By opening up new windows to seeing young children and the inherent delight and curiosity behind their mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying level of knowledge and thinking of their classes and the individuals within them as key in serving the needs of all children. In straightforward, no-nonsense language, this book summarizes what is known about how children learn mathematics, and how to build on what they know to realize more effective teaching practice. It will help teachers understand the learning trajectories of early mathematics and become quintessential professionals.

Value Learning Trajectories: Theory, Method, Context provides a theoretical, methodological and contextual framing of value learning alongside individual life trajectories in a diverse range of international educational settings. It brings together philosophical approaches on value learning with empirical research findings from Australia, Austria, Ethiopia, Estonia, Finland, Germany, Iran, the Netherlands and the United Kingdom. A critical interdisciplinary bridge between value learning and life trajectory research, the volume gathers together contributions from leading and emergent researchers to facilitate evidence-informed insights and future collaborations in the field.

Educators in the professions have always had unique demands placed upon them. These include the need to keep pace with rapidly evolving knowledge bases, developing skills and attitudes appropriate to practice, learning in the workplace and fostering public confidence. For twenty years, these new demands have created additional educational imperatives. Public accountability has become more intensive and extensive. Practitioners practice in climates more subject to scrutiny and less forgiving of error. The contexts in which professionals practice and learn have changed and these changes involve global issues and problems. Often, professionals are the first responders who are required to take an active stance in defining and solving problems. This book explores the pedagogic implications of these challenges internationally for a wide range of professions which include: accountants, military company commanders, surgeons, nurse practitioners, academic, managers, community physicians and dentists. The established view of professional development is about what the professional knows and can do. The authors broaden this view to include the systemic and contextual factors that affect learning, and the conditions necessary for effective practice and identity development across the professional lifespan. Authors examine the unique particularities and requirements of diverse professional groups. The editors emphasize new ideas and learning that emerges across the professions. As readers use this book as a pathway to their own innovations in scholarship and pedagogic research, they join their colleagues in supportingnew directions in learning, teaching and assessment across professions. This book was awarded the ‘Outstanding Research Publication award’ for 2012 by the American Educational Research Association’s Division I: ‘Education in the Professions’. “/p>

Designed to strengthen the teaching of mathematics in the elementary grades, this book focuses on helping teachers engage in instruction based on learning trajectories (LTs). Renowned scholars, including professional development researcher Hilda Borko, examine four exemplary projects with details on professional development design, teacher learning, and project implementation. Contributors include Hilda Borko, Douglas H. Clements, Susan B. Empson, Victoria R. Jacobs, and Julie Sarama. “This is an amazingly important and valuable resource for mathematics teachers and leaders at any level. It provides the background and understandings so critical for teachers and teacher leaders to regularly consider and use learning trajectories to inform teacher planning and instruction.” —Dr. Francis (Skip) Fennell, professor emeritus, McDaniel College, and past president of the Association of Mathematics Teacher Educators and the National Council of Teachers of Mathematics “This is the first book that I’ve come across that unpacks what it means to have a framework for student learning at the center of one’s instruction.” —Mary Kay Stein, University of Pittsburgh School of Education “I find this book useful for mathematics educators interested in framing learning trajectories across several domains—including tasks, discourse, curriculum, learners’ understanding, and assessment—to support professional development. Learning trajectories help us make connections among the domains and deepens professional knowledge and understanding.” —Robert Q. Berry III, University of Virginia, and president of the National Council of Teachers of Mathematics

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.

Learning Trajectories, Violence and Empowerment amongst Adult Basic Skills Learners offers deep insights into the lives of marginalised communities and the link between learning, literacy and violence, not previously carried out in-depth in a small scale study. It breaks the negative stereo-types of adults who struggle to read and write, who are often labelled and stigmatised by dominant discourses, and in doing so exposes why and how Basic Skills Learners often find themselves in marginal positions. The structural inequalities many face from childhood to adulthood across the private and public domains of their lives are revealed and probed, thus challenging neo-liberalism claims of an apparently egalitarian social field. The learners’ narratives expose the contradiction, complexities and ambivalences they experience in their daily lives, and how they try to make sense of them from their structural positioning as basic skills learners in a society based on inequality of opportunity and choice. Applying a feminist, qualitative, longitudinal, ethnographic and participatory approach, the book offers a critical perspective, drawing on Bourdieu’s work as the theoretical framework, as well as using a range of feminist, sociologists of education, literature on the ethics of care and critical literacy pedagogy, including the New Literacy Studies. The author’s personal position as an ’insider’ with ‘insider knowledge’ of marginalised communities is also woven throughout the chapters and offers insights into the struggles, conformity and resistance faced by the participants in the study. The book contributes to the debate on the impact of violence on learning and its link to class, gender and basic skills as well opening up a discussion on the power of a critical curriculum to empower people across the domains of their lives. It will be valuable reading for trainee teachers, teachers, education and sociology students, postgraduate students, as well as literacy specialists, researchers, academics, policy makers and managers of public services.

The purpose of this special issue is to present several research perspectives on learning trajectories with the intention of encouraging the broader community to reflect on, better define, adopt, adapt, or challenge the concept. The issue begins by briefly introducing learning trajectories. The remaining articles provide elaboration, examples, and discussion of the construct. They purposefully are intended to be illustrative, exploratory, and provocative with regard to learning trajectories construct; they are not a set of verification studies.