Making Sense of Mathematics for Teaching High School


Book Description

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




Making Sense of Mathematics for Teaching, Grades 3-5


Book Description

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




Making Sense of Mathematics for Teaching Grades 6-8


Book Description

Develop a deep understanding of mathematics. This user-friendly resource presents grades 6–8 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Make connections between elementary fraction-based content to fraction operations taught in the middle grades. 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 grow as both learners and teachers of mathematics. Gain clarity about the most productive progression of mathematical teaching and learning for grades 6–8. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Fraction Operations and Integer Concepts and Operations 2 Ratios and Proportional Relationships 3 Equations, Expressions, and Inequalities 4 Functions 5 Measurement and Geometry 6 Statistics and Probability Epilogue: Next Steps References and Resources Index




Making Sense of Mathematics for Teaching


Book Description

"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




Making Sense of Math


Book Description

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.




High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice


Book Description

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.




Number Talks


Book Description

"A multimedia professional learning resource"--Cover.




Making Sense of Algebra


Book Description

"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




Visible Learning for Mathematics, Grades K-12


Book Description

Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.




Culturally Responsive Teaching


Book Description

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.