Developing Deep Knowledge In Middle School Mathematics

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Developing Deep Knowledge in Middle School Mathematics

Sergei Abramovich,Michael L. Connell
Developing Deep Knowledge in Middle School Mathematics Book PDF

Author : Sergei Abramovich,Michael L. Connell
Publisher : Springer Nature
Page : 451 pages
File Size : 53,6 Mb
Release : 2021-05-10
Category : Education
ISBN : 9783030685645

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Developing Deep Knowledge in Middle School Mathematics by Sergei Abramovich,Michael L. Connell Pdf

This textbook is for prospective teachers of middle school mathematics. It reflects on the authors’ experience in offering various mathematics education courses to prospective teachers in the US and Canada. In particular, the content can support one or more of 24-semester-hour courses recommended by the Conference Board of the Mathematical Sciences (2012) for the mathematical preparation of middle school teachers. The textbook integrates grade-appropriate content on all major topics in the middle school mathematics curriculum with international recommendations for teaching the content, making it relevant for a global readership. The textbook emphasizes the inherent connections between mathematics and real life, since many mathematical concepts and procedures stem from common sense, something that schoolchildren intuitively possess. This focus on teaching formal mathematics with reference to real life and common sense is essential to its pedagogical approach. In addition, the textbook stresses the importance of being able to use technology as an exploratory tool, and being familiar with its strengths and weaknesses. In keeping with this emphasis on the use of technology, both physical (manipulatives) and digital (commonly available educational software), it also explores e.g. the use of computer graphing software for digital fabrication. In closing, the textbook addresses the issue of creativity as a crucial aspect of education in the digital age in general, and in mathematics education in particular.

Understanding Middle School Math

Arthur A. Hyde,Susan Friedlander,Cheryl Heck,Lynn Pittner
Understanding Middle School Math Book PDF

Author : Arthur A. Hyde,Susan Friedlander,Cheryl Heck,Lynn Pittner
Publisher : Heinemann Educational Books
Page : 288 pages
File Size : 51,6 Mb
Release : 2009
Category : Mathematics
ISBN : UCSD:31822037170750

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Understanding Middle School Math by Arthur A. Hyde,Susan Friedlander,Cheryl Heck,Lynn Pittner Pdf

Imagine handling students state-by-state data on the number of gallons of soft drinks sold per person in one year. Imagine using it to lead a vibrant problem-solving session in which students energetically pose and answer mathematical questions: Why does it say sold instead of consumed? What is a soft drink? Is it the same as a soda? Who would collect this kind of data? Why would they collect it? How was gallons per person calculated? What was the total amount of soda sold in our state? How many 12-ounce cans is that? 20-ounce bottles? How many of each per person? Understanding Middle School Math gathers 50 cool problems like this that lead to deep thinking. Problems such as the Renovation Problem, in which students uncover ideas about how perimeter, area, length, and cost affect a construction project. Or Chocolate Algebra, where they discover linear relationships among the pocket money available to buy two differently priced chocolate candies. Arthur Hyde combines the latest research and decades of classroom experience to braid language, cognition, and math. His approach can help any student, including underprepared ones, with the rigors of math in middle school and beyond. He has created and adapted problems that strongly connect math to the real world, to students lives, and to prior knowledge. Problems that scaffold content and processes, and give students multiple entry points into learning. Every problem has been extensively field tested and refined by classroom teachers. And for each cool problem practicing middle school teachers describe how they used it to differentiate over a wide range of students and extend learning. For fantastic problems your students won't soon forget and teaching solutions that are exciting, substantial, and transformative, turn to Art Hyde. Read and use Understanding Middle School Math and pass your love of math on as you meet your classroom goals.

Elementary and Middle School Mathematics

John A. Van de Walle
Elementary and Middle School Mathematics Book PDF

Author : John A. Van de Walle
Publisher : Allyn & Bacon
Page : 624 pages
File Size : 45,8 Mb
Release : 2007
Category : Education
ISBN : UOM:39015076110017

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Elementary and Middle School Mathematics by John A. Van de Walle Pdf

This leading K-8 math methods book has the most coverage of the NCTM standards, the strongest coverage of middle school mathematics, and the highest student approval of any math methods book currently available. Elementary and Middle School Mathematics provides an unparalleled depth of ideas and discussion to help readers develop a real understanding of the mathematics they teach. John Van de Walle, one of the foremost experts on how children learn mathematics, finds that 80 percent of the students who purchase this book keep it for reference when they begin their professional teaching careers. This book reflects the NCTM Principles and Standards and the benefits of constructivist-or student-centered-mathematics instruction. Improvements for the sixth edition include sections on planning for a diverse classroom and a completely new section addressing planning in a classroom where there are English language learners.

Teaching Middle School Mathematics

Douglas K. Brumbaugh
Teaching Middle School Mathematics Book PDF

Author : Douglas K. Brumbaugh
Publisher : Routledge
Page : 568 pages
File Size : 45,8 Mb
Release : 2013-05-13
Category : Education
ISBN : 9781136756214

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Teaching Middle School Mathematics by Douglas K. Brumbaugh Pdf

Middle school teaching and learning has a distinct pedagogy and curriculum that is grounded in the concept of developmentally appropriate education. This text is designed to meet the very specific professional development needs of future teachers of mathematics in middle school environments. Closely aligned with the NCTM Principles and Standards for School Mathematics, the reader-friendly, interactive format encourages readers to begin developing their own teaching style and making informed decisions about how to approach their future teaching career. A variety of examples establish a broad base of ideas intended to stimulate the formative development of concepts and models that can be employed in the classroom. Readers are encouraged and motivated to become teaching professionals who are lifelong learners. The text offers a wealth of technology-related information and activities; reflective, thought-provoking questions; mathematical challenges; student life-based applications; TAG (tricks-activities-games) sections; and group discussion prompts to stimulate each future teacher's thinking. "Your Turn" sections ask readers to work with middle school students directly in field experience settings. This core text for middle school mathematics methods courses is also appropriate for elementary and secondary mathematics methods courses that address teaching in the middle school grades and as an excellent in-service resource for aspiring or practicing teachers of middle school mathematics as they update their knowledge base. Topics covered in Teaching Middle School Mathematics: *NCTM Principles for School Mathematics; *Representation; *Connections; *Communication; *Reasoning and Proof; *Problem Solving; *Number and Operations; *Measurement; *Data Analysis and Probability; *Algebra in the Middle School Classroom; and *Geometry in the Middle School Classroom.

The Problem with Math Is English

Concepcion Molina
The Problem with Math Is English Book PDF

Author : Concepcion Molina
Publisher : John Wiley & Sons
Page : 304 pages
File Size : 43,9 Mb
Release : 2012-09-06
Category : Education
ISBN : 9781118237021

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The Problem with Math Is English by Concepcion Molina Pdf

Teaching K-12 math becomes an easier task when everyoneunderstands the language, symbolism, and representation of mathconcepts Published in partnership with SEDL, The Problem with Math IsEnglish illustrates how students often understand fundamentalmathematical concepts at a superficial level. Written to inspire?aha? moments, this book enables teachers to help students identifyand comprehend the nuances and true meaning of math concepts byexploring them through the lenses of language and symbolism,delving into such essential topics as multiplication, division,fractions, place value, proportional reasoning, graphs, slope,order of operations, and the distributive property. Offers a new way to approach teaching math content in a waythat will improve how all students, and especially English languagelearners, understand math Emphasizes major attributes of conceptual understanding inmathematics, including simple yet deep definitions of key terms,connections among key topics, and insightful interpretation This important new book fills a gap in math education byillustrating how a deeper knowledge of math concepts can bedeveloped in all students through a focus on language andsymbolism.

Teaching Elementary and Middle School Mathematics Using the MSA Approach

Shuhua An,Zhonghe Wu
Teaching Elementary and Middle School Mathematics Using the MSA Approach Book PDF

Author : Shuhua An,Zhonghe Wu
Publisher : Unknown
Page : 128 pages
File Size : 41,8 Mb
Release : 2017-08-01
Category : Electronic
ISBN : 0981996647

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Teaching Elementary and Middle School Mathematics Using the MSA Approach by Shuhua An,Zhonghe Wu Pdf

This book is designed for elementary and middle school mathematics methods courses and for K-8 mathematics teacher professional development programs. It describes a new cognitive mathematics teaching and learning method: Model-Strategy-Application (MSA) approach. The aim of this book is to help pre-service and in-service teachers develop deep pedagogical content knowledge in a structured and systematic manner, and supports them in teaching mathematics and assessing student thinking effectively. The book focuses on developing students' mathematics proficiency in the three components of conceptual understanding, procedural fluency, and competence in word problem solving through the MSA approach in every content area. To help students learn a mathematics concept with deep understanding, a variety of concrete or visual models are developed to address the mathematics concept; to build fluency in procedure and computation corresponding to the concept, various computational strategies including basic and specific techniques are developed; to learn how to apply the conceptual understanding and strategies to word problem solving, applications of different types and levels of word problems are introduced.

Minds on Mathematics

Wendy Ward Hoffer
Minds on Mathematics Book PDF

Author : Wendy Ward Hoffer
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 41,6 Mb
Release : 2012
Category : Education
ISBN : 0325044341

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Minds on Mathematics by Wendy Ward Hoffer Pdf

Minds-on Mathematics explains the core elements of math workshop and provides detailed strategies for implementing the workshop structure, including Lesson Openers that engage students,Minilessons that model thinking and problem solving.

Developing Mathematical Thinking

Jonathan D. Katz
Developing Mathematical Thinking Book PDF

Author : Jonathan D. Katz
Publisher : Rowman & Littlefield
Page : 145 pages
File Size : 47,9 Mb
Release : 2014-07-07
Category : Education
ISBN : 9781475810585

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Developing Mathematical Thinking by Jonathan D. Katz Pdf

In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

Making Sense of Mathematics for Teaching Grades 6-8

Edward C. Nolan,Juli K. Dixon
Making Sense of Mathematics for Teaching Grades 6 8 Book PDF

Author : Edward C. Nolan,Juli K. Dixon
Publisher : Solution Tree Press
Page : 248 pages
File Size : 49,5 Mb
Release : 2016-04-13
Category : Education
ISBN : 9781942496465

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Making Sense of Mathematics for Teaching Grades 6-8 by Edward C. Nolan,Juli K. Dixon Pdf

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

Mathematical Argumentation in Middle School-The What, Why, and How

Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nicole Shechtman
Mathematical Argumentation in Middle School The What Why and How Book PDF

Author : Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nicole Shechtman
Publisher : Corwin Press
Page : 192 pages
File Size : 40,8 Mb
Release : 2017-09-21
Category : Education
ISBN : 9781506394244

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Mathematical Argumentation in Middle School-The What, Why, and How by Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nicole Shechtman Pdf

Get them talking: Your formula for bringing math concepts to life! Want your middle schoolers to intelligently engage with mathematical ideas? Ready to help them construct and critique viable arguments that meet tough Standards for Mathematical Practice 3 standards? Look no further. This research-based gem will help you foster the critical reasoning and argumentation skills every student needs for intelligent discourse within our modern society. Learn how to bring mathematical argumentation alive in your classroom—all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding. Filled with content-focused and classroom-ready games, activities, vignettes, sample tasks, and links to online tools and a rich companion website, this innovative guide will help you Immediately engage students in fun, classroom-ready argumentation activities Plan lessons that foster lively, content-driven, viable argumentation Help students explore mathematical ideas and take ownership of their learning Facilitate deep mathematical understanding Promote students’ precise use of mathematical language to construct, justify, and critique mathematical ideas and mathematical statements or the arguments of others. Encourage logical, clear connections between abstract ideas for enhanced 21st century skills This guide delivers all the tools you need to get serious about mathematical argumentation and bring well-planned, well-constructed mathematical discourse to life in your classroom today!

Essential Math Skills

Bob Sornson
Essential Math Skills Book PDF

Author : Bob Sornson
Publisher : Teacher Created Materials
Page : 168 pages
File Size : 54,8 Mb
Release : 2014-04-01
Category : Education
ISBN : 9781425895877

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Essential Math Skills by Bob Sornson Pdf

Support and assess the learning of essential skills needed for students' mathematics success! Created to support College and Career Readiness and other state standards, this resource is a great tool for educators. This must-have professional book allows teachers to systematically monitor students' progress toward proficiency in every essential skill. The 250 activities provide a rich menu of math learning experiences, which includes the use of manipulatives, activities, exploration, inquiry, and play. Digital resources are also provided and include student activity pages and teacher resources.

Visible Learning for Mathematics, Grades K-12

John Hattie,Douglas Fisher,Nancy Frey,Linda M. Gojak,Sara Delano Moore,William Mellman
Visible Learning for Mathematics Grades K 12 Book PDF

Author : John Hattie,Douglas Fisher,Nancy Frey,Linda M. Gojak,Sara Delano Moore,William Mellman
Publisher : Corwin Press
Page : 209 pages
File Size : 48,6 Mb
Release : 2016-09-15
Category : Education
ISBN : 9781506362953

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Visible Learning for Mathematics, Grades K-12 by John Hattie,Douglas Fisher,Nancy Frey,Linda M. Gojak,Sara Delano Moore,William Mellman Pdf

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.

The Math Pact, Middle School

Sarah B. Bush,Karen S. Karp,Barbara J. Dougherty
The Math Pact Middle School Book PDF

Author : Sarah B. Bush,Karen S. Karp,Barbara J. Dougherty
Publisher : Corwin
Page : 209 pages
File Size : 41,9 Mb
Release : 2020-09-19
Category : Education
ISBN : 9781544399577

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The Math Pact, Middle School by Sarah B. Bush,Karen S. Karp,Barbara J. Dougherty Pdf

A schoolwide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · Practical templates and checklists · PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics!

Teaching to the Math Common Core State Standards

F. D. Rivera
Teaching to the Math Common Core State Standards Book PDF

Author : F. D. Rivera
Publisher : Springer
Page : 224 pages
File Size : 50,8 Mb
Release : 2015-06-17
Category : Education
ISBN : 9789462099623

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Teaching to the Math Common Core State Standards by F. D. Rivera Pdf

This is a methods book for preservice middle level majors and beginning middle school teachers. It takes a very practical approach to learning to teach middle school mathematics in an emerging Age of the Common Core State Standards. The Common Core State Standards in Mathematics (CCSSM) is not meant to be “the” official mathematics curriculum; it was purposefully developed primarily to provide clear learning expectations of mathematics content that are appropriate at every grade level and to help prepare all students to be ready for college and the workplace. A quick glance at the Table of Contents in this book indicates a serious engagement with the recommended mathematics underlying the Grade 5 through Grade 8 and (traditional pathway) Algebra I portions of the CCSSM first, with issues in content-practice assessment, learning, teaching, and classroom management pursued next and in that order. In this book we explore what it means to teach to the CCSSM within an alignment mindset involving content-practice learning, teaching, and assessment. The Common Core state content standards, which pertain to mathematical knowledge, skills, and applications, have been carefully crafted so that they are teachable, learnable, coherent, fewer, clearer, and higher. The practice standards, which refer to institutionally valued mathematical actions, processes, and habits, have been conceptualized in ways that will hopefully encourage all middle school students to engage with the content standards more deeply than merely acquiring mathematical knowledge by rote and imitation. Thus, in the CCSSM, proficiency in content alone is not sufficient, and so does practice without content, which is limited. Content and practice are both equally important and, thus, must come together in teaching, learning, and assessment in order to support authentic mathematical understanding. This blended multisourced text is a “getting smart” book. It prepares preservice middle level majors and beginning middle school teachers to work within the realities of accountable pedagogy and to develop a proactive disposition that is capable of supporting all middle school students in order for them to experience growth in mathematical understanding that is necessary for high school and beyond, including future careers.

Teaching Numeracy

Margie Pearse,K. M. Walton
Teaching Numeracy Book PDF

Author : Margie Pearse,K. M. Walton
Publisher : Corwin Press
Page : 241 pages
File Size : 49,6 Mb
Release : 2011-03-23
Category : Education
ISBN : 9781452224404

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Teaching Numeracy by Margie Pearse,K. M. Walton Pdf

Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.