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Creating Change To Improve Science And Mathematics Education
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Book Synopsis Creating Change to Improve Science and Mathematics Education by : Chong Ho Yu
Download or read book Creating Change to Improve Science and Mathematics Education written by Chong Ho Yu and published by Springer Nature. This book was released on 2020-03-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the merits and potential shortcomings of Hong Kong STEM education from Grade 8 to Grade 12. Based on concurrent triangulated mixed-method methodology, which integrates both quantitative and qualitative procedures, it describes various change models and proposes new models that are considered compatible with Western cultures.
Book Synopsis Designing Professional Development for Teachers of Science and Mathematics by : Susan Loucks-Horsley
Download or read book Designing Professional Development for Teachers of Science and Mathematics written by Susan Loucks-Horsley and published by Corwin Press. This book was released on 2009-11-24 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classic guide for designing robust science and mathematics professional development programs! This expanded edition of one of the most widely cited resources in the field of professional development for mathematics and science educators demonstrates how to design professional development experiences for teachers that lead to improved student learning. Presenting an updated professional development (PD) planning framework, the third edition of the bestseller reflects recent research on PD design, underscores how beliefs and local factors can influence PD design, illustrates a wide range of PD strategies, and emphasizes the importance of: Continuous program monitoring Combining strategies to address diverse needs Building cultures that sustain learning
Book Synopsis Mathematics and Science for a Change by : Iris R. Weiss
Download or read book Mathematics and Science for a Change written by Iris R. Weiss and published by Heinemann Educational Books. This book was released on 2009 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Take advantage of what this volume offers. You will be in a better position to make well-informed decisions because you will be able to see the full sweep of what constitutes quality professional development for mathematics and science teachers. - Barbara Miller Education Development Center, Inc. You've decided it's time for something different. A new way to teach mathematics and science that supports higher achievement in all students. And that means rethinking how you provide teacher professional development. Sounds like a tough task, but you've got a guide to doing it right. Mathematics and Science for a Change collects the wisdom of successful initiatives into one concise guide to making successful change. Mathematics and Science for a Changedescribes the lessons learned by effective National Science Foundation - funded Local Systemic Change programs. Iris Weiss and Joan Pasley support your initiative with key practices drawn from a careful examination of more than ten years of case histories and data. With their observations, you'll: lay the groundwork for change by diagnosing your building or district needs and establishing a vision for high-quality mathematics and science instruction that is consistent with national standards design professional development that achieves your goals by deepening teacher content knowledge, modeling best-practice instruction, and encouraging more productive assessments launch and sustain your professional development model by identifying, preparing, and supporting PD providers then uncovering and nurturing leadership among your staff bolster your improvement effort by enlisting key school or district leaders, partnering with the mathematics and science community outside your system, and engaging the support of parents. Weiss and Pasley fill Mathematics and Science for a Change with on-the-ground advice and the specific strategies of top initiatives around the country. Everything in their book helps you smoothly meet the most important objective of any change program: helping every student learn mathematics and science better.
Book Synopsis Improving Mathematics Education by : National Research Council
Download or read book Improving Mathematics Education written by National Research Council and published by National Academies Press. This book was released on 2002-01-28 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improving Mathematics Education has been designed to help inform stakeholders about the decisions they face, to point to recent research findings, and to provide access to the most recent thinking of experts on issues of national concern in mathematics education. The essence of the report is that information is available to help those charged with improving student achievement in mathematics. The documents cited above can guide those who make decisions about content, learning, teaching, and assessment. The report is organized around five key questions: What should we teach, given what we know and value about mathematics and its roles? How should we teach so children learn, given what we know about students, mathematics, and how people learn mathematics? What preparation and support do teachers need? How do we know whether what we are doing is working? What must change? Each of the five main chapters in this report considers a key area of mathematics education and describes the core messages of current publication(s) in that area. To maintain the integrity of each report's recommendations, we used direct quotes and the terminology defined and used in that report. If the wording or terminology seems to need clarification, the committee refers the reader directly to the original document. Because these areas are interdependent, the documents often offer recommendations related to several different areas. While the individual documents are discussed under only one of the components in Improving Mathematics Education, the reader should recognize that each document may have a broader scope. In general, the references in this report should serve as a starting point for the interested reader, who can refer to the original documents for fuller discussions of the recommendations and, in some cases, suggestions for implementation. Improving Mathematics Education is designed to help educators build a critical knowledge base about mathematics education, recognizing that the future of the nation's students is integrally intertwined with the decisions we make (or fail to make) about the mathematics education they receive.
Book Synopsis University Science and Mathematics Education in Transition by : Ole Skovsmose
Download or read book University Science and Mathematics Education in Transition written by Ole Skovsmose and published by Springer Science & Business Media. This book was released on 2008-11-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than ever, our time is characterised by rapid changes in the organisation and the production of knowledge. This movement is deeply rooted in the evolution of the scientific endeavour, as well as in the transformation of the political, economic and cultural organisation of society. In other words, the production of scientific knowledge is changing both with regard to the internal development of science and technology, and with regard to the function and role science and technology fulfill in society. This general social context in which universities and knowledge production are placed has been given different names: the informational society, the knowledge society, the learning society, the post-industrial society, the risk society, or even the post-modern society. A common feature of different characterisations of this historic time is the fact that it is a period in construction. Parts of the world, not only of the First World but also chunks of the Developing World, are involved in these transformations. There is a movement from former social, political and cultural forms of organisation which impact knowledge production into new forms. These forms drive us into forms of organisation that are unknown and that, for their very same complexity, do not show a clear ending stage. Somehow the utopias that guided the ideas of development and progress in the past are not present anymore, and therefore the transitions in the knowledge society generate a new uncertain world. We find ourselves and our universities to be in a transitional period in time. In this context, it is difficult to avoid considering seriously the challenges that such a complex and uncertain social configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. It is clear that the transformation of knowledge outside universities has implied a change in the routes that research in mathematics, science and technology has taken in the last decades. It is also clear that in different parts of the world these changes have happened at different points in time. While universities in the "New World" (the American Continent, Africa, Asia and Oceania) have accommodated their operation to the challenges of the construction in the new world, in many European countries universities with a longer existence and tradition have moved more slowly into this time of transformation and have been responding at a less rapid pace to environmental challenges. The process of tuning universities, together with their forms of knowledge production and their provision of education in science and mathematics, with the demands of the informational society has been a complex process, as complex as the general transformation undergoing in society. Therefore an understanding of the current transitions in science and mathematics education has to consider different dimensions involved in such a change. Traditionally, educational studies in mathematics and science education have looked at changes in education from within the scientific disciplines and in the closed context of the classroom. Although educational change in the very end is implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network of educational, cultural, administrative and ideological views and practices that permeate and constitute science and mathematics education in universities today. This book contributes to understanding some of the multiple aspects and dimensions of the transition of science and mathematics education in the current informational society. Such an understanding is necessary for finding possibilities to improve science and mathematics education in universities all around the world. Such a broad approach to the transitions happening in these fields has not been addressed yet by existing books in the market.
Book Synopsis Reimagining the Mathematics Classroom by : Cathery Yeh
Download or read book Reimagining the Mathematics Classroom written by Cathery Yeh and published by National. This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a comprehensive systems approach to examining mathematics teaching. This volume synthesizes and illustrates current research on the essential elements of mathematics teaching and learning, unpacking each component. In addition, tips on using technology to assess and enhance learning are embedded throughout the book.
Book Synopsis Improving Indicators of the Quality of Science and Mathematics Education in Grades K-12 by : National Research Council
Download or read book Improving Indicators of the Quality of Science and Mathematics Education in Grades K-12 written by National Research Council and published by National Academies Press. This book was released on 1988-02-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a carefully developed monitoring system to track the progress of mathematics and science education, particularly the effects of ongoing efforts to improve students' scientific knowledge and mathematics competency. It describes an improved series of indicators to assess student learning, curriculum quality, teaching effectiveness, student behavior, and financial and leadership support for mathematics and science education. Of special interest is a critical review of current testing methods and their use in probing higher-order skills and evaluating educational quality.
Book Synopsis Improving Math and Science Teaching by : Kay McKinney
Download or read book Improving Math and Science Teaching written by Kay McKinney and published by Department of Education. This book was released on 1993 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 1992 conference on mathematics and science teaching focused on two specific topics: enhanced professional development for educators and better instructional materials for the classroom. Teachers, members of Congress, governors, teacher educators, professors, researchers, and policymakers shared what they believed was needed to be done to improve mathematics and science education in the United States. This booklet reports the views of the participants and the general consensus of the conference regarding changes needed in the education system. The concepts of systemic reform in education and the setting of national standards as exemplified by the National Council of Teachers of Mathematics are discussed in section 1. The second section discusses the necessity of providing all children with an opportunity to learn mathematics and science. The third section reports the participants' views emphasizing courses that teach mathematics and science for understanding. The fourth section discusses the necessity to prepare teachers of math and science to higher standards of skill and knowledge. Extensive professional development to help practicing teachers enhance their skills is suggested. The fifth section examines the need for the development of better instructional materials for the mathematics and science classroom. Finally, 20 recommendations in the following 4 themes are reported: (1) standards; (2) improving mathematics and science teaching; (3) instructional materials; and (4) systemic change. A list of presenters and demonstrators and a statement of principles on school reform in mathematics and science are provided. (MDH)
Book Synopsis Educating Teachers of Science, Mathematics, and Technology by : National Research Council
Download or read book Educating Teachers of Science, Mathematics, and Technology written by National Research Council and published by National Academies Press. This book was released on 2001-01-18 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each new headline about American students' poor performance in math and science leads to new calls for reform in teaching. Education Teachers of Science, Mathematics, and Technology puts the whole picture together by synthesizing what we know about the quality of math and science teaching, drawing conclusions about why teacher preparation needs reform, and then outlining recommendations for accomplishing the most important goals before us. As a framework for addressing the task, the book advocates partnerships among school districts, colleges, and universities, with contributions from scientists, mathematicians, teacher educators, and teachers. It then looks carefully at the status of the education reform movement and explores the motives for raising the bar for how well teachers teach and how well students learn. Also examined are important issues in teacher professionalism: what teachers should be taught about their subjects, the utility of in-service education, the challenge of program funding, and the merits of credentialing. Professional Development Schools are reviewed and vignettes presented that describe exemplary teacher development practices.
Author :National Academies of Sciences, Engineering, and Medicine Publisher :National Academies Press ISBN 13 :0309380189 Total Pages :257 pages Book Rating :4.3/5 (93 download)
Book Synopsis Science Teachers' Learning by : National Academies of Sciences, Engineering, and Medicine
Download or read book Science Teachers' Learning written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2016-01-15 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Currently, many states are adopting the Next Generation Science Standards (NGSS) or are revising their own state standards in ways that reflect the NGSS. For students and schools, the implementation of any science standards rests with teachers. For those teachers, an evolving understanding about how best to teach science represents a significant transition in the way science is currently taught in most classrooms and it will require most science teachers to change how they teach. That change will require learning opportunities for teachers that reinforce and expand their knowledge of the major ideas and concepts in science, their familiarity with a range of instructional strategies, and the skills to implement those strategies in the classroom. Providing these kinds of learning opportunities in turn will require profound changes to current approaches to supporting teachers' learning across their careers, from their initial training to continuing professional development. A teacher's capability to improve students' scientific understanding is heavily influenced by the school and district in which they work, the community in which the school is located, and the larger professional communities to which they belong. Science Teachers' Learning provides guidance for schools and districts on how best to support teachers' learning and how to implement successful programs for professional development. This report makes actionable recommendations for science teachers' learning that take a broad view of what is known about science education, how and when teachers learn, and education policies that directly and indirectly shape what teachers are able to learn and teach. The challenge of developing the expertise teachers need to implement the NGSS presents an opportunity to rethink professional learning for science teachers. Science Teachers' Learning will be a valuable resource for classrooms, departments, schools, districts, and professional organizations as they move to new ways to teach science.
Book Synopsis Science and Mathematics Education for 21st Century Citizens by : Laurinda Leite
Download or read book Science and Mathematics Education for 21st Century Citizens written by Laurinda Leite and published by Nova Science Publishers. This book was released on 2020 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book addresses the challenges that face science and mathematics education if it is to be relevant to 21st century citizens, as well as the ways that outstanding specialists from several countries around the world think it should deal with those challenges. Starting with the issue of science and mathematics teacher education in a changing world, it moves on to deal with innovative approaches to teaching science and mathematics. It then discusses contemporary issues related to the role played by technology in science and mathematics education, the challenges of the STEM agenda, and ways of making science and mathematics education more inclusive. Finally, it focuses on assessment issues, as the success of science and mathematics education depends at least in part on the purposes for which, and ways in which, students' learning is assessed. There is a worldwide trend towards providing meaningful science and mathematics education to all children for the sake of literacy and numeracy development and a need to produce enough science and technology specialists. This trend and need, coupled with the concern raised by students' disengagement in these two knowledge areas and the role that technology may play in countering it, put increasingly high demands on teachers. As shown in this book, science and mathematics education may offer a unique contribution in developing responsible citizens by fostering skills required in order to assume wider responsibilities and roles, focusing on personal, social and environmental dimensions. For instance, it offers unique insights into how teachers can build on students' complicated and interconnected real-worlds to help them learn authentic and relevant science and mathematics. Additionally, the book highlights potential positive relationships between science and mathematics, which are often envisaged as having a conflicting relationship in school curricula. By uncovering the similarities between them, and by providing evidence that both areas deal with issues that are relevant for citizens' daily lives, the book explores ways of linking and giving coherence to science and mathematics knowledge as components of everyday life settings. It also provides directions for future research on the educational potential of interconnecting science and mathematics at the different educational levels. Therefore, this is a worthwhile book for researchers, teacher educators and schoolteachers. It covers theoretical perspectives, research-based approaches and practical applications that may make a difference in education that is relevant and inclusive for citizens in the 21st century"--
Book Synopsis Designing Professional Development for Teachers of Science and Mathematics by : Susan Loucks-Horsley
Download or read book Designing Professional Development for Teachers of Science and Mathematics written by Susan Loucks-Horsley and published by Corwin Press. This book was released on 2003-02-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This New Edition collects and brings together in one place what has been learned from professional developers efforts across the country in order to make the framework, principles, and strategies of the first edition come to life. This edition deepens our understanding of professional development through further research and new resources. The original purpose of this book to put a competent and caring teacher in every classroom has yet to be fulfilled and is more urgent now than ever. The authors provide one-stop shopping for busy practitioners that incorporates the most up-to-date research gleaned from the broadest possible research base as well as robust and rich descriptions of effective professional development programmes. It incorporates the growing knowledge base about learning, teaching, the nature of science and mathematics, professional development, and change. The authors scanned the field of professional development in mathematics and science over the last five years, noting what has changed and what has not, dissected the original framework, updated examples, incorporate what authors have learned as well as advances in the field. This essential primer offers a framework that considers key inputs and combines strategies uniquely tailored to their environment and goals; summarizes key knowledge and best practices; provides guidance on assessing one′s context; describes strategies that go beyond most common workshops and institutes; provides real-life examples of how elements of the framework were used to create professional development initiatives; offers references and resources for further exploration and inquiry. Highlights of the Second Edition include: - New design framework that incorporates standards, student learning data, and evaluation techniques - More guidance for assessing context using data - More strategies for professional development, including lesson study, aligning and selecting curriculum, and demonstration lessons. - Stronger real-life examples, including new uses of technology and data-driven designs An essential resource for educators who design, conduct, and support professional development for teachers of mathematics and science, including staff developers, principals, teacher leaders, curriculum supervisors, and leadership teams. College and university faculty in education, science, and mathematics will also find this to be a useful compendium of ideas for improving mathematics and science education.
Download or read book Mindstorms written by Seymour A Papert and published by Basic Books. This book was released on 2020-10-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this revolutionary book, a renowned computer scientist explains the importance of teaching children the basics of computing and how it can prepare them to succeed in the ever-evolving tech world. Computers have completely changed the way we teach children. We have Mindstorms to thank for that. In this book, pioneering computer scientist Seymour Papert uses the invention of LOGO, the first child-friendly programming language, to make the case for the value of teaching children with computers. Papert argues that children are more than capable of mastering computers, and that teaching computational processes like de-bugging in the classroom can change the way we learn everything else. He also shows that schools saturated with technology can actually improve socialization and interaction among students and between students and teachers. Technology changes every day, but the basic ways that computers can help us learn remain. For thousands of teachers and parents who have sought creative ways to help children learn with computers, Mindstorms is their bible.
Author :National Science Resources Center of the National Academy of Sciences and the Smithsonian Institution Publisher :National Academies Press ISBN 13 :0309176298 Total Pages :240 pages Book Rating :4.3/5 (91 download)
Book Synopsis Science for All Children by : National Science Resources Center of the National Academy of Sciences and the Smithsonian Institution
Download or read book Science for All Children written by National Science Resources Center of the National Academy of Sciences and the Smithsonian Institution and published by National Academies Press. This book was released on 1997-01-08 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Remember the first time you planted a seed and watched it sprout? Or explored how a magnet attracted a nail? If these questions bring back memories of joy and wonder, then you understand the idea behind inquiry-based scienceâ€"an approach to science education that challenges children to ask questions, solve problems, and develop scientific skills as well as gain knowledge. Inquiry-based science is based on research and experience, both of which confirm that children learn science best when they engage in hands-on science activities rather than read from a textbook. The recent National Science Education Standards prepared by the National Research Council call for a revolution in science education. They stress that the science taught must be based on active inquiry and that science should become a core activity in every grade, starting in kindergarten. This easy-to-read and practical book shows how to bring about the changes recommended in the standards. It provides guidelines for planning and implementing an inquiry-based science program in any school district. The book is divided into three parts. "Building a Foundation for Change," presents a rationale for inquiry-based science and describes how teaching through inquiry supports the way children naturally learn. It concludes with basic guidelines for planning a program. School administrators, teachers, and parents will be especially interested in the second part, "The Nuts and Bolts of Change." This section describes the five building blocks of an elementary science program: Community and administrative support. A developmentally appropriate curriculum. Opportunities for professional development. Materials support. Appropriate assessment tools. Together, these five elements provide a working model of how to implement hands-on science. The third part, "Inquiry-Centered Science in Practice," presents profiles of the successful inquiry-based science programs in districts nationwide. These profiles show how the principles of hands-on science can be adapted to different school settings. If you want to improve the way science is taught in the elementary schools in your community, Science for All Children is an indispensable resource.
Book Synopsis Making the Connection by : Marilyn Paula Carlson
Download or read book Making the Connection written by Marilyn Paula Carlson and published by MAA. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.
Book Synopsis A Framework for K-12 Science Education by : National Research Council
Download or read book A Framework for K-12 Science Education written by National Research Council and published by National Academies Press. This book was released on 2012-02-28 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science, engineering, and technology permeate nearly every facet of modern life and hold the key to solving many of humanity's most pressing current and future challenges. The United States' position in the global economy is declining, in part because U.S. workers lack fundamental knowledge in these fields. To address the critical issues of U.S. competitiveness and to better prepare the workforce, A Framework for K-12 Science Education proposes a new approach to K-12 science education that will capture students' interest and provide them with the necessary foundational knowledge in the field. A Framework for K-12 Science Education outlines a broad set of expectations for students in science and engineering in grades K-12. These expectations will inform the development of new standards for K-12 science education and, subsequently, revisions to curriculum, instruction, assessment, and professional development for educators. This book identifies three dimensions that convey the core ideas and practices around which science and engineering education in these grades should be built. These three dimensions are: crosscutting concepts that unify the study of science through their common application across science and engineering; scientific and engineering practices; and disciplinary core ideas in the physical sciences, life sciences, and earth and space sciences and for engineering, technology, and the applications of science. The overarching goal is for all high school graduates to have sufficient knowledge of science and engineering to engage in public discussions on science-related issues, be careful consumers of scientific and technical information, and enter the careers of their choice. A Framework for K-12 Science Education is the first step in a process that can inform state-level decisions and achieve a research-grounded basis for improving science instruction and learning across the country. The book will guide standards developers, teachers, curriculum designers, assessment developers, state and district science administrators, and educators who teach science in informal environments.
Book Synopsis Mathematics as the Science of Patterns by : Patrick M. Jenlink
Download or read book Mathematics as the Science of Patterns written by Patrick M. Jenlink and published by IAP. This book was released on 2022-02-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.
