This book is written primarily for pre-service and in-service teachers of Literacy/English Language Arts, school administrators, literacy graduate education students, and literacy education researchers, and addresses the myriad of questions regarding the implementation of the Common Core State Standards. Classroom teachers and pre-service teachers are currently confronting questions such as how they can teach the Common Core State Standards to make sure they are fully addressing them; how they can have the time to teach students to have deeper understandings of the skills and concepts addressed in the Standards; what they can do to meet the learning needs of diverse students such as English language learners and students with learning disabilities; whether teachers of content areas are required to add reading instruction to their teaching responsibilities; whether the Standards tell teachers what to teach; and whether the document tells teachers how to implement the Standards in the classroom, among others. This book is designed to answer these questions and many others. Each chapter contains instructional practices, examples, vignettes, and illustrations that connect the Common Core State Standards to classroom practices, and thereby provide pre-service and in-service teachers with meaningful, relevant, and practical teaching strategies to prepare culturally, academically, and linguistically diverse students in California and other states of the nation for both career and college. In this regard, readers of this book will find that the authors have provided a pathway to better understand the Common Core State Standards, and will be able to use what they learn in the pages of this book to provide more effective instruction for their students across the disciplines to read, analyse, and critique complex texts and apply knowledge to solve practical, real-life problems.
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The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics—how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings—and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories. A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionallygrounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessmentdriven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.) This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children’s mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories’ evolutionfrom smallscale daytoday conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.
This volume examines how several key components of the mathematics education system in the United States fail to provide teachers with adequate and effective tools to teach mathematics in K-12 classrooms. These components consist of teachers’ own learning experiences as students in K-12 classrooms, their undergraduate or graduate trainings in mathematics, and their in-service professional development trainings. Newton argues that unless we improve these system components as a whole and recognize the importance of teaching future mathematics teachers explicitly and rigorously the topics they are expected to teach, teachers will continue to recycle a body of incoherent and incomprehensible mathematical knowledge to their students, because these are the only types of mathematical knowledge they have at their disposal, both in terms of what they themselves have learned as K-12 students and in terms of the mathematical resources available to them, including the textbooks they rely on to teach as mathematics teachers.