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| big 5 pedagogy math: The Five Practices in Practice [Elementary] Margaret (Peg) Smith, Victoria Bill, Miriam Gamoran Sherin, 2019-08-14 Take a deep dive into the five practices for facilitating productive mathematical discussions Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. • Video excerpts vividly illustrate the five practices in action in real elementary classrooms • Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion • Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks. |
| big 5 pedagogy math: Answers to Your Biggest Questions About Teaching Elementary Math John J. SanGiovanni, Susie Katt, Latrenda D. Knighten, Georgina Rivera, 2021-08-31 Your guide to grow and learn as a math teacher! Let’s face it, teaching elementary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Today, we recognize placing the student at the center of their learning increases engagement, motivation, and academic achievement soars. Teaching math in a student-centered way changes the role of the teacher from one who traditionally “delivers knowledge” to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching elementary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your elementary math classroom: 1. How do I build a positive math community? 2. How do I structure, organize, and manage my math class? 3. How do I engage my students in math? 4. How do I help my students talk about math? 5. How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey? |
| big 5 pedagogy math: Five Practices for Orchestrating Productive Mathematics Discussions Margaret Schwan Smith, Mary Kay Stein, 2011 Describes five practices for productive mathematics discussions, including anticipating, monitoring, selecting, sequencing, and connecting. |
| big 5 pedagogy math: 5 Principles of the Modern Mathematics Classroom Gerald Aungst, 2015-10-09 Students pursue problems they’re curious about, not problems they’re told to solve. Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration. Aungst shows you how to Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment. Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended! Cindy Johanson, Executive Director, Edutopia George Lucas Educational Foundation Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today. Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces |
| big 5 pedagogy math: Culturally Responsive Teaching Geneva Gay, 2010 The achievement of students of color continues to be disproportionately low at all levels of education. More than ever, Geneva Gay's foundational book on culturally responsive teaching is essential reading in addressing the needs of today's diverse student population. Combining insights from multicultural education theory and research with real-life classroom stories, Gay demonstrates that all students will perform better on multiple measures of achievement when teaching is filtered through their own cultural experiences. This bestselling text has been extensively revised to include expanded coverage of student ethnic groups: African and Latino Americans as well as Asian and Native Americans as well as new material on culturally diverse communication, addressing common myths about language diversity and the effects of English Plus instruction. |
| big 5 pedagogy math: The On-Your-Feet Guide to Orchestrating Mathematics Discussions Margaret (Peg) Smith, Miriam Gamoran Sherin, 2019-04-15 This laminated, tri-fold (6 page) On-Your-Feed Guide is based on the best-selling 5 Practices for Orchestrating Productive Mathematics Discussions and provides: A brief look at each of the five practices for orchestrating productive mathematics discussions Key questions, tools, and challenges for each practice to consider as you plan and carry out your mathematics lesson Special considerations and helpful hints to think about as you troubleshoot your lessons and assess your implementation of the practices A focus on supporting equity and identity Brief videos with commentary from authors and teachers about each of the five practices |
| big 5 pedagogy math: Building Thinking Classrooms in Mathematics, Grades K-12 Peter Liljedahl, 2020-09-28 A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling non-thinking student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before. |
| big 5 pedagogy math: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| big 5 pedagogy math: High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice Robert Q. Berry III, Basil M. Conway IV, Brian R. Lawler, John W. Staley, 2020-03-09 Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future. |
| big 5 pedagogy math: Windows on Teaching Math Katherine Klippert Merseth, 2003-01-01 Cases, while always interesting to read, are more effective when discussed under the guidance of a skillful leader. Because many educators are new to the case method of instruction, particularly in the subject area of secondary mathematics, this facilitator's guide is an essential companion to Windows on Teaching Math: Cases of Middle and Secondary Classrooms. In this guide, Katherine Merseth provides specific teaching notes that correspond to each case, helping educators to successfully use Windows on Teaching Math in a teacher education course or professional development workshop. |
| big 5 pedagogy math: Mathematical Mindsets Jo Boaler, 2015-10-12 Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age. |
| big 5 pedagogy math: Teaching Math With Examples Michael Pershan, 2021-02-23 Some teachers think that there’s little to say about teaching with examples – after all, everyone uses them. But here are just some of the questions you might have about teaching with worked examples: How do we introduce an example? What do we ask students to do when studying a solution? Should a solution be presented all at once or revealed step-by-step? After we study an example, what comes next? Does it matter if the solution is presented as if from a fictional student, a real student in class, or from the teacher? How do we help students move from understanding someone else’s ideas towards using it on their own to solve problems? How do we write a solution in a clear way, that students can learn from? When is a good time to offer a worked example? When is it better to let students try a problem? Are worked examples more useful for some mathematical content than others? This book will answer all of these questions. In some cases, research offers answers. Other questions represent gaps in the research literature and the book offers solutions arrived at through experience and trial-and-error and the author’s own process of classroom problem solving. Welcome to the world of teaching with examples! |
| big 5 pedagogy math: Knowing and Teaching Elementary Mathematics Liping Ma, 2010-03-26 Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work. |
| big 5 pedagogy math: Making Sense of Mathematics for Teaching High School Edward C. Nolan, Juli K. Dixon, Farhsid Safi, Erhan Selcuk Haciomeroglu, 2016-05-19 Develop a deep understanding of mathematics by grasping the context and purpose behind various strategies. This user-friendly resource presents high school teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Combine student understanding of functions and algebraic concepts so that they can better decipher the world. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, or modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Gain clarity about the most productive progression of mathematical teaching and learning for high school. Watch short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction Equations and Functions Structure of Equations Geometry Types of Functions Function Modeling Statistics and Probability Epilogue: Next Steps Appendix: Weight Loss Study Data References Index |
| big 5 pedagogy math: Mine the Gap for Mathematical Understanding, Grades K-2 John SanGiovanni, 2016-10-31 Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct gap commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see. |
| big 5 pedagogy math: Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8 Nathalie Sinclair, David Pimm, Melanie Skelin, 2012-01 Why are there so many formulas for area and volume, and why do some of them look alike? Why does one quadrilateral have no special name while another has several, like square, rectangle, rhombus, and parallelogram—and why are all these names useful? How much do you know … and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. |
| big 5 pedagogy math: About Teaching Mathematics Marilyn Burns, 2007 A compendium of more than 240 classroom-tested lessons, this essential resource helps teachers build student understanding and skills and understand how children best learn math. In this third edition, Marilyn Burns has completely revised the first section to reflect what she has learned over the years from her classroom experience with students and her professional development experience with teachers. This section has also been expanded to address these important topics: teaching math vocabulary, incorporating writing into math instruction, linking assessment and instruction, and using children¿s literature to teach key math concepts. In an entirely new section, Marilyn addresses a wide range of questions she has received over the years from elementary and middle school teachers regarding classroom management and instructional issues. |
| big 5 pedagogy math: Inventing the Mathematician Sara N. Hottinger, 2016-03-01 Considers how our ideas about mathematics shape our individual and cultural relationship to the field. Where and how do we, as a culture, get our ideas about mathematics and about who can engage with mathematical knowledge? Sara N. Hottinger uses a cultural studies approach to address how our ideas about mathematics shape our individual and cultural relationship to the field. She considers four locations in which representations of mathematics contribute to our cultural understanding of mathematics: mathematics textbooks, the history of mathematics, portraits of mathematicians, and the field of ethnomathematics. Hottinger examines how these discourses shape mathematical subjectivity by limiting the way some groupsincluding women and people of colorare able to see themselves as practitioners of math. Inventing the Mathematician provides a blueprint for how to engage in a deconstructive project, revealing the limited and problematic nature of the normative construction of mathematical subjectivity. |
| big 5 pedagogy math: Understanding by Design Grant P. Wiggins, Jay McTighe, 2005 What is understanding and how does it differ from knowledge? How can we determine the big ideas worth understanding? Why is understanding an important teaching goal, and how do we know when students have attained it? How can we create a rigorous and engaging curriculum that focuses on understanding and leads to improved student performance in today's high-stakes, standards-based environment? Authors Grant Wiggins and Jay McTighe answer these and many other questions in this second edition of Understanding by Design. Drawing on feedback from thousands of educators around the world who have used the UbD framework since its introduction in 1998, the authors have greatly revised and expanded their original work to guide educators across the K-16 spectrum in the design of curriculum, assessment, and instruction. With an improved UbD Template at its core, the book explains the rationale of backward design and explores in greater depth the meaning of such key ideas as essential questions and transfer tasks. Readers will learn why the familiar coverage- and activity-based approaches to curriculum design fall short, and how a focus on the six facets of understanding can enrich student learning. With an expanded array of practical strategies, tools, and examples from all subject areas, the book demonstrates how the research-based principles of Understanding by Design apply to district frameworks as well as to individual units of curriculum. Combining provocative ideas, thoughtful analysis, and tested approaches, this new edition of Understanding by Design offers teacher-designers a clear path to the creation of curriculum that ensures better learning and a more stimulating experience for students and teachers alike. |
| big 5 pedagogy math: Making Sense of Mathematics for Teaching, Grades 3-5 Juli K. Dixon, Edward C. Nolan, 2016-04-11 Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals |
| big 5 pedagogy math: Mine the Gap for Mathematical Understanding, Grades 3-5 John SanGiovanni, 2016-09-16 Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct gap commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see. |
| big 5 pedagogy math: Effective Pedagogy in Mathematics/pāngarau Glenda Anthony, Margaret Walshaw, New Zealand. Ministry of Education, 2007 |
| big 5 pedagogy math: Quack and Count Keith Baker, 2004 Seven ducklings take a rhyming look at addition. |
| big 5 pedagogy math: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| big 5 pedagogy math: How People Learn National Research Council, Division of Behavioral and Social Sciences and Education, Board on Behavioral, Cognitive, and Sensory Sciences, Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice, 2000-08-11 First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methodsâ€to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education. |
| big 5 pedagogy math: Teaching Mathematics in Early Childhood Sally Moomaw, 2011 Includes bibliographical references (p. ) and index. |
| big 5 pedagogy math: Making Math Workshop Work Middle School Math Man, Alex O'Connor, 2018-12-31 Are you looking to find a way to reach all of your students every day? Teacher and education blogger, Alex O'Connor, shares his practical, classroom-tested strategies to implement math workshop in the classroom. This book includes everything you need to get math workshop started in your classroom. |
| big 5 pedagogy math: Knowing and Learning Mathematics for Teaching National Research Council, Mathematical Sciences Education Board, Center for Education, Mathematics Teacher Preparation Content Workshop Program Steering Committee, 2001-02-25 There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place. |
| big 5 pedagogy math: Eyes on Math Marian Small, 2012-12-30 This new book is an exciting follow-up to the authors bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K–8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students and teachers look more deeply and see the math behind the math! |
| big 5 pedagogy math: Teacher Quality, Instructional Quality and Student Outcomes Trude Nilsen, Jan-Eric Gustafsson, 2016-09-19 This volume offers insights from modeling relations between teacher quality, instructional quality and student outcomes in mathematics across countries. The relations explored take the educational context, such as school climate, into account. The International Association for the Evaluation of Educational Achievement’s Trends in Mathematics and Science Study (TIMSS) is the only international large-scale study possessing a design framework that enables investigation of relations between teachers, their teaching, and student outcomes in mathematics. TIMSS provides both student achievement data and contextual background data from schools, teachers, students and parents, for over 60 countries. This book makes a major contribution to the field of educational effectiveness, especially teaching effectiveness, where cross-cultural comparisons are scarce. For readers interested in teacher quality, instructional quality, and student achievement and motivation in mathematics, the comparisons across cultures, grades, and time are insightful and thought-provoking. For readers interested in methodology, the advanced analytical methods, combined with application of methods new to educational research, illustrate interesting novel directions in methodology and the secondary analysis of international large-scale assessment (ILSA). |
| big 5 pedagogy math: Curriculum and Evaluation Standards for School Mathematics National Council of Teachers of Mathematics. Commission on Standards for School Mathematics, 1989 Curriculum standards for mathematics for grades K-4, 5-8, and 9-12 are presented which suggest areas of instructional emphasis for specific student outcomes. Also discusses evaluation standards for both the curriculum and student achievement. K-12. |
| big 5 pedagogy math: Concept-Based Mathematics Jennifer T.H. Wathall, 2016-01-14 Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind! — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students. — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant |
| big 5 pedagogy math: Making Sense of Mathematics for Teaching Juli K. Dixon, Edward C. Nolan, Thomasenia Lott Adams, Lisa A. Brooks, Tashana D. Howse, 2016 With Making sense of mathematics for teaching grades K-2: the TQE process, participants have the opportunity to engage in mathematics as learners. This unscripted video program addresses three specific goals: (1) to explore meaningful tasks as learners of mathematics for teaching, (2) to make sense of the TQE process (tasks, questioning, and evidence), and (3) to create a shared vision of classrooms where teachers are supporting the TQE process and students are engaged in meaningful mathematics learning experiences. The program accomplishes these goals through the use of challenging tasks for teachers, effective questions related to classroom content, and classroom video showing tasks modeled during instruction.--Container |
| big 5 pedagogy math: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| big 5 pedagogy math: Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 Nathalie Sinclair, David Pimm, Melanie Skelin, 2012 Why does it matter whether we state definitions carefully when we all know what particular geometric figures look like? What does it mean to say that a reflection is a transformation—a function? How does the study of transformations and matrices in high school connect with later work with vector spaces in linear algebra? How much do you know… and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don’t get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers’ reflection. |
| big 5 pedagogy math: Open Middle Math Robert Kaplinsky, 2023-10-10 This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking. |
| big 5 pedagogy math: Beyond Good Teaching Sylvia Celedon-Pattichis, Nora G. Ramirez, 2012 English language learners share a basic need—to engage, and be engaged, in meaningful mathematics. Through guiding principles and instructional tools, together with classroom vignettes and video clips, this book shows how to go beyond good teaching to support ELLs in learning challenging mathematics while developing language skill. Position your students to share the valuable knowledge that they bring to the classroom as they actively build and communicate their understanding. The design of this book is interactive and requires the reader to move back and forth between the chapters and online resources at www.nctm.org/more4u. Occasionally, the reader is asked to stop and reflect before reading further in a chapter. At other times, the reader is asked to view video clips of teaching practices for ELLs or to refer to graphic organizers, observation and analysis protocols, links to resources, and other supplementary materials. The authors encourage the reader to use this resource in professional development. |
| big 5 pedagogy math: Elementary and Middle School Mathematics John A. Van de Walle, Karen S. Karp, Jennifer M. Bay-Williams, 2013 Elementary and Middle School Mathematics: Teaching Developmentally provides an unparalleled depth of ideas and discussion to help teachers develop a real understanding of the mathematics they will teach and the most effective methods of teaching the various mathematics topics. This text reflects the NCTM and Common Core State Standards and the benefits of problem-based mathematics instruction. It is structured for maximum flexibility, offering 23 chapters that may be mixed and matched to fit any course or teaching approach. This comprehensive, practical text offers readers a strong theoretical perspective reflecting the most current research on how students learn mathematics, ways to best teach it, and many problem-based activities to engage students. An important reference to consult throughout a teaching career, Van de Walle, Karp and Bay-William's book helps teachers and their preK-8 students find the excitement that happens when mathematics makes sense. |
| big 5 pedagogy math: EDthoughts John Sutton, Alice Krueger, 2009 |
| big 5 pedagogy math: Every Math Learner, Grades K-5 Nanci N. Smith, 2017-02-01 Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy K-5 mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom; and Adjust current instructional materials to better meet students' needs Includes classroom videos and a companion website. |
BIG | Bjarke Ingels Group
BIG has grown organically over the last two decades from a founder, to a family, to a force of 700. Our latest transformation is the BIG LEAP: Bjarke Ingels Group of Landscape, Engineering, …
Bjarke Ingels Group - BIG
Since BIG inception in 2006, David Zahle has been responsible for delivering imaginative and pioneering designs for buildings such as Copenhill, a waste-to energy plant with a ski slope on …
Athletics Las Vegas Ballpark | BIG | Bjarke Ingels Group
The project builds on a longstanding collaboration between BIG and the Athletics dating back to a different ballpark design in Oakland, California in 2018. The new ballpark’s roof is accentuated …
Jinji Lake Pavilion | BIG | Bjarke Ingels Group
Our latest transformation is the BIG LEAP: Bjarke Ingels Group of Landscape, Engineering, Architecture, Planning and Products. A plethora of in-house perspectives allows us to see …
Gowanus 175 Third Street | BIG | Bjarke Ingels Group
Catalyzed by the major Gowanus rezoning in 2021 – one of the most significant rezonings in New York City in recent years – 175 Third Street builds on years of BIG’s prior study and design …
Sankt Lukas Hospice and Lukashuset | BIG | Bjarke Ingels Group
A small step for each of us becomes a BIG LEAP for all of us. BIG has grown organically over the last two decades from a founder, to a family, to a force of 700. Our latest transformation is the …
Google Bay View | BIG | Bjarke Ingels Group
Leon Rost — Partner, BIG The campus includes 17.3 acres of high-value natural areas – including wet meadows, woodlands, and marsh – that contribute to Google’s broader efforts to …
Gelephu International Airport | BIG | Bjarke Ingels Group
As Bhutan’s second international airport, the project is a collaboration with aviation engineering firm NACO and an integral part of the Gelephu Mindfulness City (GMC) masterplan designed …
Opera and Ballet Theatre of Kosovo | BIG | Bjarke Ingels Group
BIG proposes a simple and prag matic arrangement of the performance venues draped in a soft, undulating exterior skin of photovoltaic tiles. The theatre ’s form is reminiscent of the free …
Freedom Plaza | BIG | Bjarke Ingels Group
Freedom Plaza will extend BIG’s contribution to New York City’s waterfront, alongside adjacent coastal projects that include the East Side Coastal Resiliency project, the Battery Park City …
BIG | Bjarke Ingels Group
BIG has grown organically over the last two decades from a founder, to a family, to a force of 700. Our latest transformation is the BIG LEAP: Bjarke Ingels Group of Landscape, Engineering, …
Bjarke Ingels Group - BIG
Since BIG inception in 2006, David Zahle has been responsible for delivering imaginative and pioneering designs for buildings such as Copenhill, a waste-to energy plant with a ski slope on …
Athletics Las Vegas Ballpark | BIG | Bjarke Ingels Group
The project builds on a longstanding collaboration between BIG and the Athletics dating back to a different ballpark design in Oakland, California in 2018. The new ballpark’s roof is accentuated …
Jinji Lake Pavilion | BIG | Bjarke Ingels Group
Our latest transformation is the BIG LEAP: Bjarke Ingels Group of Landscape, Engineering, Architecture, Planning and Products. A plethora of in-house perspectives allows us to see what …
Gowanus 175 Third Street | BIG | Bjarke Ingels Group
Catalyzed by the major Gowanus rezoning in 2021 – one of the most significant rezonings in New York City in recent years – 175 Third Street builds on years of BIG’s prior study and design …
Sankt Lukas Hospice and Lukashuset | BIG | Bjarke Ingels Group
A small step for each of us becomes a BIG LEAP for all of us. BIG has grown organically over the last two decades from a founder, to a family, to a force of 700. Our latest transformation is the …
Google Bay View | BIG | Bjarke Ingels Group
Leon Rost — Partner, BIG The campus includes 17.3 acres of high-value natural areas – including wet meadows, woodlands, and marsh – that contribute to Google’s broader efforts to …
Gelephu International Airport | BIG | Bjarke Ingels Group
As Bhutan’s second international airport, the project is a collaboration with aviation engineering firm NACO and an integral part of the Gelephu Mindfulness City (GMC) masterplan designed …
Opera and Ballet Theatre of Kosovo | BIG | Bjarke Ingels Group
BIG proposes a simple and prag matic arrangement of the performance venues draped in a soft, undulating exterior skin of photovoltaic tiles. The theatre ’s form is reminiscent of the free …
Freedom Plaza | BIG | Bjarke Ingels Group
Freedom Plaza will extend BIG’s contribution to New York City’s waterfront, alongside adjacent coastal projects that include the East Side Coastal Resiliency project, the Battery Park City …
