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The depth and breadth of a mathematics teacher’s understanding of mathematics matter most as the teacher engages in the daily work of teaching. One of the major challenges to teachers is to be ready to draw on the relevant mathematical ideas from different areas of the school curriculum and from their postsecondary mathematics experiences that can be helpful in explaining ideas to students, making instructional decisions, creating examples, and engaging in other aspects of their daily work. Being mathematically ready and confident requires teachers to engage in ongoing professional learning that helps them to connect mathematics to events like those they live on a daily basis. The purpose of this volume is to provide teachers, teacher educators, and other facilitators of professional learning opportunities with examples of authentic events and tools for discussing those events in professional learning settings. The work shared in Facilitator’s Guidebook for Use of Mathematics Situations in Professional Learning (Guidebook) resulted from a collaborative effort of school mathematics supervisors and university mathematics educators. The collaborators joined their varied experiences as teachers, coaches, supervisors, teacher educators, and researchers to suggest ways to scaffold activities, encourage discussion, and instigate reflection with teacher–participants of differing mathematics backgrounds and with varying teaching assignments. Each guide has ideas for engaging and furthering mathematical thought across a range of facilitator and participant mathematics backgrounds and draws on the collaborators’ uses of the Situations with in-service and prospective teachers. The events and mathematical ideas connected to each event come from Situations in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations. A Situation is a description of a classroom-related event and the mathematics related to it. For each of six Situations, school and university collaborators developed a facilitator’s guide that presents ideas and options for engaging teachers with the event and the mathematical ideas. The Guidebook also contains suggestions for how teachers and others might develop new Situations based on events from their own classrooms as a form of professional learning. Both teacher educators and school-based facilitators can use this volume to structure sessions and inspire ideas for professional learning activities that are rooted in the daily work of mathematics teachers and students.
A perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level. The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice. Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.
This Handbook presents the latest thinking and current examples of design research in education. Design-based research involves introducing innovations into real-world practices (as opposed to constrained laboratory contexts) and examining the impact of those designs on the learning process. Designed prototype applications (e.g., instructional methods, software or materials) and the research findings are then cycled back into the next iteration of the design innovation in order to build evidence of the particular theories being researched, and to positively impact practice and the diffusion of the innovation. The Handbook of Design Research Methods in Education-- the defining book for the field -- fills a need in how to conduct design research by those doing so right now. The chapters represent a broad array of interpretations and examples of how today’s design researchers conceptualize this emergent methodology across areas as diverse as educational leadership, diffusion of innovations, complexity theory, and curriculum research. This volume is designed as a guide for doctoral students, early career researchers and cross-over researchers from fields outside of education interested in supporting innovation in educational settings through conducting design research.
This second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors looked back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and looked forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 3, Participants in Mathematics Teacher Education, focuses not only on prospective and practicing teachers as learners but also on school colleagues, teacher educators, researchers, and others who work to provide effective learning opportunities for teachers. The emphasis is on describing and analysing participants’ engagement in mathematics teacher education collaborations and contexts from various perspectives. Thus, as the third volume in the series, it further broadens our understanding of the development of mathematics teachers.
This resource will help school leaders and other professional development providers conduct ongoing, structured learning opportunities for mathematics teachers (K-12). The authors present models for professional development and the preparation of PD leaders designed and field-tested as part of two research projects supported by the National Science Foundation. The Problem-Solving Cycle model and the Mathematics Leadership Preparation model focus on topics of primary interest to mathematics teachers - mathematics content, classroom instruction, and student learning. They are intentionally designed so that they can be tailored to meet the needs and interests of participating teachers and schools. Through engaging vignettes, the authors describe the models, summarize key research findings, and share lessons learned. The book also includes detailed examples of workshop activities for both teachers and PD leaders.
This second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors look back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and look forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 2, Tools and Processes in Mathematics Teacher Education, describes and analyze various promising tools and processes, from different perspectives, aimed at facilitating the mathematics teacher learning and development. It provides insights of how mathematics teacher educators think about and approach their work with teachers. Thus, as the second volume in the series, it broadens our understanding of the mathematics teacher and their learning and teaching.
This edition is an essential resource for students, researchers, teacher educators and curriculum policy makers in the field of mathematics education.
Create a pathway to equity by detracking mathematics The tracked mathematics system has been operating in US schools for decades. However, research demonstrates negative effects on subgroups of students by keeping them in a single math track, thereby denying them access to rigorous coursework needed for college and career readiness. The journey to change this involves confronting some long-standing beliefs and structures in education. When supported with the right structures, instructional shifts, coalition building, and educator training and support, the detracking of mathematics courses can be a primary pathway to equity. The ultimate goal is to increase more students’ access to and achievement in higher levels of mathematics learning–especially for students who are historically marginalized. Based on the stories and lessons learned from the San Francisco Unified School District educators who have talked the talk and walked the walk, this book provides a model for all those involved in taking on detracking efforts from policymakers and school administrators, to math coaches and teachers. By sharing stories of real-world examples, lessons learned, and prompts to provoke discussion about your own context, the book walks you through: Designing and gaining support for a policy of detracked math courses Implementing the policy through practical shifts in scheduling, curriculum, professional development, and coaching Supporting and improving the policy through continuous research, monitoring, and maintenance. This book offers the big ideas that help you in your own unique journey to advance equity in your school or district’s mathematics education and also provides practical information to help students in a detracked system thrive.
"Provides readers with a compelling rationale for the process, offers experience-tested tools, and suggests ways to address commonly-occurring challenges. This book will assist teachers, and those who support them, in understanding and implementing all phases of lesson study, from initial planning through sharing with others what was learned." —Dennis Sparks, Executive Director National Staff Development Council "A powerful teacher professional development process that focuses collaborative teams directly on the classroom, and the perfect tool for teachers, professional developers, and team leaders. Gives you everything you need to use lesson study to support teachers in thinking deeply about practice." —Roberta Jaffe, Science Education Coordinator, New Teacher Center, University of California, Santa Cruz Use this team-centered approach to directly enhance teaching and learning in your school! First introduced in Japan, lesson study has gained enthusiastic advocates in US educational circles as a powerful, collaborative approach that brings teachers together as researchers into the science and craft of teaching and learning in their classrooms. Teachers work as teams to develop a lesson plan, teach and observe the lesson to collect data on student learning, and use their observations to refine their lesson. Participants build their sense of professional authority while discovering effective practices that result in improved learning outcomes for their students. This "how-to" guide provides teachers, administrators, and team leaders with practical strategies, models, and tools. The book leads a beginning team through the phases of the lesson study cycle and provides an experienced team with new perspectives. Using examples from U.S. classrooms, this handbook: Encourages educators to generate and share knowledge Inspires a teacher-researcher stance Illustrates both the process and substance of lesson study Encourages collaboration Provides guidelines for avoiding common pitfalls Leading Lesson Study is an excellent resource for both experienced and novice lesson study teams, administrators who want to start a lesson study program, and lesson study team facilitators such as instructional coaches and professional development providers.