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

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.

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.

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.

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.

Educators require constructive information that details their students’ comprehension and can help them to advance the learners' education. Accurate evaluation of students at all educational levels and the implementation of comprehensive assessment strategies are essential for ensuring student equality and academic success. The Handbook of Research on Formative Assessment in Pre-K Through Elementary Classrooms is an essential research publication that addresses gaps in the understanding of formative assessment and offers educators meaningful and comprehensive examples of formative assessment in the Pre-K through elementary grade levels. Covering an array of topics such as literacy, professional development, and educational technologies, this book is relevant for instructors, administrators, education professionals, educational policymakers, pre-service teachers, academicians, researchers, and students.

At a time when ICTs are proliferating various facets of society and human interactivity, optimizing the use of these tools and technologies not only enhances learning but also transforms learning experiences all together, resulting in an increase of effectiveness and quality of education around the globe. As such, teachers are being challenged to implement a wide range of tools, such as mobile learning and augmented reality, to create smarter learning environments inside and outside of the classroom. Cases on Smart Learning Environments explores the potential of SLE tools for enhanced learning outcomes as experienced by educators, learners, and administrators from various learning institutions around the world. This publication presents cases on the real-world implementation of SLEs in 11 countries that span the continents of Asia, Africa, Europe, and North and South America. Featuring coverage on a broad range of topics such as learner engagement, teacher training, and intelligent agent technology, this book is ideally designed for academicians, instructors, instructional designers, librarians, educational stakeholders, and curriculum developers.