Download or read book Making Sense of Algebra written by Ernest Paul Goldenberg and published by Heinemann Educational Books. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book has much to offer teachers of middle and high school algebra who wish to implement the Common Core Standards for all of their students." -Hyman Bass, Samuel Eilenberg Distinguished University Professor of Mathematics & Mathematics Education, University of Michigan "One of the joys of Making Sense of Algebra is how clearly and practically the 'how' question is answered." -Steven Leinwand, American Institutes for Research, author of Accessible Mathematics "Paul Goldenberg and his colleagues have done a fantastic job of connecting mathematical ideas to teaching those ideas." -David Wees, New Visions for Public Schools, New York City Every teacher wants to help students make sense of mathematics; but what if you could guide your students to expect mathematics to make sense? What if you could help them develop a deep understanding of the reasons behind its facts and methods? In Making Sense of Algebra, the common misconception that algebra is simply a collection of rules to know and follow is debunked by delving into how we think about mathematics. This "habits of mind" approach is concerned not just with the results of mathematical thinking, but with how mathematically proficient students do that thinking. Making Sense of Algebra addresses developing this type of thinking in your students through: using well-chosen puzzles and investigations to promote perseverance and a willingness to explore seeking structure and looking for patterns that mathematicians anticipate finding-and using this to draw conclusions cultivating an approach to authentic problems that are rarely as tidy as what is found in textbooks allowing students to generate, validate, and critique their own and others' ideas without relying on an outside authority. Through teaching tips, classroom vignettes, and detailed examples, Making Sense of Algebra shows how to focus your instruction on building these key habits of mind, while inviting students to experience the clarity and meaning of mathematics-perhaps for the first time. Discover more math resources at Heinemann.com/Math
Download or read book Making Sense written by James Hiebert and published by Heinemann Educational Books. This book was released on 1997 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several key principles for teaching mathematics for understanding that you can use to reflect on your own teaching, make more informed decisions, and develop more effective systems of instruction.
Download or read book Making Sense of Mathematics for Teaching High School written by Edward C. Nolan and published by Solution Tree Press. This book was released on 2016-05-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Making Sense of Math written by Cathy L. Seeley and published by ASCD. This book was released on 2016-04-05 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Making Sense of Math, Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: * Making sense of math by fostering habits of mind that help students analyze, understand, and adapt to problems when they encounter them. * Addressing the mathematical building blocks necessary to include in effective math instruction. * Turning teaching “upside down” by shifting how we teach, focusing on discussion and analysis as much as we focus on correct answers. * Garnering support for the changes you want to make from colleagues and administrators. Learn how to make math meaningful for your students and prepare them for a lifetime of mathematical fluency and problem solving.
Download or read book Visual Math written by Jessika Sobanski and published by Learning Express (NY). This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Visual Math has been designed to allow learners to "see" why math makes sense. By combining logical math concepts with pictures, previously unclear images will fade and math will suddenly click for you. Pictures, graphs, and diagrams help you understand math questions in the areas of number concepts and properties, fractions and decimals, ratios and proportions, percents, algebra, geometry, and much more. Designed especially for students who have difficulty with conventional math rules, this book gives you step-by step instructions with pictures to help you solve math problems.
Download or read book Making Sense of Mathematics for Teaching Grades 3 5 written by Juli K. Dixon and published by Solution Tree Press. This book was released on 2016-04-11 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Math Makes Sense 7 written by Ray Appel and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spatial Sense Makes Math Sense written by Catheryne Draper and published by Rowman & Littlefield. This book was released on 2017-12-08 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial Sense Makes Math Sense: How Parents Can Help Their Children Learn Both brings the strengths of both algebra (arithmetic) and geometry into focus by showing how spatial relationships can make both make more sense. Parents will learn how to further develop and improve their child’s spatial sense using visual-spatial strategies of classifying, drawing diagrams, big idea concept building, visualizing, and more. As Sawyer encourages, “Even if the pictures are not good, the effort of making them will leave lasting traces in the mind and can cause the work to be remembered.” Whether you had a preference for geometry and endured algebra, loved algebra and never understood geometry, or were one of those people who never recognized a purpose for any of the math topics or, in truth, in any mathematics, this book will show parents how developing spatial sense can help visually explain both algebra and geometry relationships. You will read about Sophie Germain who believed that algebra and geometry worked hand-in-hand because, as she described them, algebra is written geometry and geometry is figured algebra.
Download or read book Making Sense of Mathematics for Teaching the Small Group written by Juli K. Dixon and published by Every Student Can Learn Mathem. This book was released on 2018-07-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When done right, small-group instruction is a powerful tool for facilitating student understanding in K-5 mathematics. Throughout the book, best practices for small-group math instruction are addressed in detail, from planning tasks that encourage deep understanding to asking effective questions to engaging learners in meaningful conversations. Readers will learn how teaching mathematics in small groups allows you to differentiate instruction for both remediation and enrichment. The included small-group instruction videos demonstrate the suggested strategies in a real-classroom setting, giving readers the opportunity to see best practice in action. Develop math-specific instruction strategies for teaching small groups in elementary school: Explore the benefits of small-group math activities and how these activities are unique compared to large-group instruction. Discover the teacher's and students' roles in small-group instruction and how teachers can help students develop the skills to fulfill their role. Learn how to apply the general tasks, questions, and evidence (TQE) process to small-group instruction in order to enhance student learning and improve your knowledge of teaching mathematics. View examples of small-group instruction, which provide both math intervention and math enrichment activities for different students. Contents: Acknowledgments Table of Contents About the Authors Introduction Chapter 1: Best Practices in Small-Group Instruction Chapter 2: The TQE Process in Small-Group Instruction Chapter 3: Discourse in Small-Group Instruction Epilogue: How to Tie It All Together References Index
Download or read book Math Makes Sense A Constructivist Approach To The Teaching And Learning Of Mathematics written by Ana Helvia Quintero and published by World Scientific. This book was released on 2016-03-02 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics.Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding.The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers.
Download or read book Challenging Problems in Algebra written by Alfred S. Posamentier and published by Courier Corporation. This book was released on 2012-05-04 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
Download or read book Thinking Mathematically written by Thomas P. Carpenter and published by Heinemann Educational Books. This book was released on 2003 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic
Download or read book Mathematical Mindsets written by Jo Boaler and published by John Wiley & Sons. This book was released on 2015-10-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Children s Mathematics written by Thomas P. Carpenter and published by Heinemann Educational Books. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.
Download or read book Powerful Problem Solving written by Max Ray and published by Heinemann Educational Books. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter.
Download or read book Reasoning and Sense Making in the Elementary Grades Prekindergarten Grade 2 written by Michael T. Battista and published by National Council of Teachers of English. This book was released on 2016 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library.
Download or read book Reasoning and Sense Making in the Mathematics Clasroom 3 5 written by Michael T. Battista and published by . This book was released on 2016-08-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
