Facilitator S Guidebook For Use Of Mathematics Situations In Professional Learning
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Facilitator's Guidebook for Use of Mathematics Situations in Professional Learning
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.
Mathematical Understanding for Secondary Teaching
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.
Handbook of Design Research Methods in Education
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.