making sense of math

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Making Sense Of Math

Author : Cathy L. Seeley
ISBN : 9781416622451
Genre : Education
File Size : 83. 8 MB
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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.

Making Sense Of Mathematics For Teaching High School

Author : Edward C. Nolan
ISBN : 9781942496496
Genre : Education
File Size : 23. 70 MB
Format : PDF, Docs
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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 K 2

Author : Juli K. Dixon
ISBN : 1942496397
Genre : Education
File Size : 40. 6 MB
Format : PDF, Docs
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Develop a deep understanding of mathematics. This user-friendly resource presents grades K-2 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. Clarify math essentials with figures and tables that facilitate understanding through visualization. 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 Number Concepts and Place Value 2 Word Problem Structures 3 Addition and Subtraction Using Counting Strategies 4 Addition and Subtraction Using Grouping Strategies 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

Author : Melissa Boston
ISBN : 1947604090
Genre : Mathematics
File Size : 29. 85 MB
Format : PDF, Docs
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Discover a clear path for improving mathematics instructional strategies at any grade level. Designed for individuals or collaborative teams, this practical resource introduces a set of rubrics -- the Instructional Quality Assessment (IQA) Toolkit -- that readers can rely on to help guide reflections, conversations, feedback, and planning. Also included is a series of short videos that showcase how to use the book's math strategies and tools in classrooms. Ensure the instructional quality of your teaching strategies in mathematics: Utilize tasks, questions, and evidence (the TQE process) and the associated IQA rubrics as a road map for increasing instructional quality. Become familiar with the connection between efficient use of tasks and teacher questioning with increased student success. Learn how to gauge student response to tasks and lessons in order to understand student mastery of the material. Enhance your understanding of mathematics through hands-on activities. Access free online reproducibles for use in teaching mathematics in the classroom. Contents: About the Authors Introduction Part 1: Connecting to the T in TQE -- Tasks and Task Implementation Chapter 1: Potential of the Task Chapter 2: Implementation of the Task Part 2: Connecting to the Q in TQE -- Questions and Their Role as Discourse Actions Chapter 3: The Teacher's Questions Chapter 4: Teacher's Linking and Teacher's Press Part 3: Connecting to the E in TQE -- Evidence of Students' Mathematical Work and Thinking Chapter 5: Students' Linking and Students' Providing Chapter 6: The IQA Toolkit as a Tool to Assess and Improve Instructional Practice Epilogue: Next Steps Appendix A: The IQA Toolkit Appendix B: Suggested Answers for Activity 1.4 Appendix C: Suggested Answers for Activity 3.2 Appendix D: Additional Support for Rating Tasks Appendix E: List of Figures and Videos References and Resources Index

Making Sense Of Mathematics For Teaching Grades 6 8

Author : Edward C. Nolan
ISBN : 9781942496465
Genre : Education
File Size : 46. 80 MB
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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 Teacher Education

Author : Fou-Lai Lin
ISBN : 9789401008280
Genre : Education
File Size : 64. 75 MB
Format : PDF
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This is a research-based book that deals with a broad range of issues about mathematics teacher education. It examines teacher education programs from different societies and cultures as it develops an international perspective on mathematics teacher education. Practical situations that are associated with related theories are studied critically. It is intended for teacher educators, mathematics educators, graduate students in mathematics education, and mathematics teachers.

Making Sense Of Mathematics For Teaching Grades 3 5

Author : Juli K. Dixon
ISBN : 9781942496434
Genre : Education
File Size : 75. 80 MB
Format : PDF, Kindle
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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 Word Problems

Author : Eric de Corte
ISBN : 9026516282
Genre : Education
File Size : 68. 29 MB
Format : PDF, ePub
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Word problems have been a staple of mathematics instruction for centuries, yet the rationale for their use has remained largely unexamined. A range of findings have shown how students consistently answer them in ways that fail to take account of the reality of the situations described. This monograph reports on studies carried out to investigate this "suspension of sense-making" in answering word problems. In Part One, a wide range of examples documenting the strength of the phenomenon is reviewed. Initial surprise at the findings was replaced by a conviction that the explanation lies in the culture of the mathematics classroom, specifically the rules implicitly governing the nature and interpretation of the word problem genre. This theoretical shift is reflected in Part Two. A detailed analysis of the way in which word problems are currently taught in typical mathematical classrooms is followed by reviews of design experiments illustrating how, by immersing students in a fundamentally changed learning environment, they can acquire what the authors consider to be more appropriate conceptions about, and strategies for doing, word problems. Part Three turns to a wider discussion of theoretical issues, a further analysis of the features of the educational system considered responsible for outcomes detrimental to many students' understanding and conception of mathematics, and suggestions for rethinking the role of word problems within the curriculum.

Making Sense Of Mathematics For Teaching The Small Group

Author : Juli K. Dixon
ISBN : 194760404X
Genre : Group work in education
File Size : 60. 96 MB
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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 Chapter 4: How to Tie It All Together References Index

Making Sense Of Mathematics For Teaching Girls

Author : Thomasenia Lott Adams
ISBN : 1945349786
Genre : Academic achievement
File Size : 31. 55 MB
Format : PDF, ePub
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Close the gender gap in mathematics across K-5 classrooms. In Making Sense of Mathematics for Teaching Girls in Grades K-5, a team of acclaimed experts presents their research and recommendations for teaching math to girls in four succinct, results-focused chapters. Included are a variety of tools, tips, short exercises, and reflection questions, as well as videos demonstrating how real classroom teachers strengthen girls' experiences as learners of mathematics. Use this book to better understand gender biases related to mathematics and improve girls' education: Understand the environmental barriers and gender stereotypes that create gender differences in mathematics performance and prevent many girls from learning mathematics at high levels. Learn how to foster a safe learning environment that encourages girls to take risks when they learn math. Focus on the mathematics gender achievement gap through three lenses: (1) perceptions, (2) possibilities, and (3) priorities. Apply the tasks, questions, and evidence (TQE) process to successfully plan and implement inclusive lessons that engage all students. Watch short videos of girls engaging meaningfully in mathematics learning. Contents: About the Authors Introduction Chapter 1: Mathematics Gender Achievement Gap Chapter 2: Perceptions About Girls in Mathematics Chapter 3: Possibilities for Girls in Mathematics Chapter 4: Priorities for Teaching Girls Mathematics Epilogue: Encouragement for Girls in Mathematics References and Resources Index

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