Developing Deep Knowledge in Middle School Mathematics

Developing Deep Knowledge in Middle School Mathematics

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  • Author: Sergei Abramovich
  • Publisher: Springer Nature
  • ISBN: 3030685640
  • Category : Education
  • Languages : en
  • Pages : 451

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.


Minds on Mathematics

Minds on Mathematics

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  • Author: Wendy Ward Hoffer
  • Publisher: Heinemann Educational Books
  • ISBN: 9780325044347
  • Category : Education
  • Languages : en
  • Pages : 0

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.


Principles to Actions

Principles to Actions

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  • Author: National Council of Teachers of Mathematics
  • Publisher: National Council of Teachers of Mathematics, Incorporated
  • ISBN: 9780873537742
  • Category : Curriculum planning
  • Languages : en
  • Pages : 139

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.


Elementary and Middle School Mathematics

Elementary and Middle School Mathematics

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  • Author: John A. Van de Walle
  • Publisher: Allyn & Bacon
  • ISBN:
  • Category : Education
  • Languages : en
  • Pages : 624

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.


Understanding Middle School Math

Understanding Middle School Math

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  • Author: Arthur A. Hyde
  • Publisher: Heinemann Educational Books
  • ISBN:
  • Category : Mathematics
  • Languages : en
  • Pages : 288

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.


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

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

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  • Author: Jennifer Knudsen
  • Publisher: Corwin Press
  • ISBN: 150639423X
  • Category : Education
  • Languages : en
  • Pages : 185

This research-based book brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive - all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.


Visible Learning for Mathematics, Grades K-12

Visible Learning for Mathematics, Grades K-12

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  • Author: John Hattie
  • Publisher: Corwin Press
  • ISBN: 1506362958
  • Category : Education
  • Languages : en
  • Pages : 209

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.


Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

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  • Author: Jennifer M. Bay-Williams
  • Publisher: Corwin
  • ISBN: 1071818430
  • Category : Education
  • Languages : en
  • Pages : 265

Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.


Teaching Elementary and Middle School Mathematics Using the MSA Approach

Teaching Elementary and Middle School Mathematics Using the MSA Approach

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  • Author: Shuhua An
  • Publisher:
  • ISBN: 9780981996646
  • Category :
  • Languages : en
  • Pages :

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.


Learning and Understanding

Learning and Understanding

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  • Author: National Research Council
  • Publisher: National Academies Press
  • ISBN: 030917080X
  • Category : Education
  • Languages : en
  • Pages : 588

This book takes a fresh look at programs for advanced studies for high school students in the United States, with a particular focus on the Advanced Placement and the International Baccalaureate programs, and asks how advanced studies can be significantly improved in general. It also examines two of the core issues surrounding these programs: they can have a profound impact on other components of the education system and participation in the programs has become key to admission at selective institutions of higher education. By looking at what could enhance the quality of high school advanced study programs as well as what precedes and comes after these programs, this report provides teachers, parents, curriculum developers, administrators, college science and mathematics faculty, and the educational research community with a detailed assessment that can be used to guide change within advanced study programs.