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.


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.


The Math Pact, Middle School

The Math Pact, Middle School

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  • Author: Sarah B. Bush
  • Publisher: Corwin Press
  • ISBN: 1544399588
  • Category : Education
  • Languages : en
  • Pages : 165

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!


The Math Pact, Elementary

The Math Pact, Elementary

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  • Author: Karen S. Karp
  • Publisher: Corwin Press
  • ISBN: 1544399529
  • Category : Education
  • Languages : en
  • Pages : 167

A school-wide 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!


The Problem with Math Is English

The Problem with Math Is English

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  • Author: Concepcion Molina
  • Publisher: John Wiley & Sons
  • ISBN: 1118237021
  • Category : Education
  • Languages : en
  • Pages : 304

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.


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.


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.


Standards-based School Mathematics Curricula

Standards-based School Mathematics Curricula

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  • Author: Sharon L. Senk
  • Publisher: Routledge
  • ISBN: 1000149366
  • Category : Education
  • Languages : en
  • Pages : 512

The Curriculum and Evaluation Standards for School Mathematics published by the National Council of Teachers of Mathematics in 1989 set forth a broad vision of mathematical content and pedagogy for grades K-12 in the United States. These Standards prompted the development of Standards-based mathematics curricula. What features characterize Standards-based curricula? How well do such curricula work? To answer these questions, the editors invited researchers who had investigated the implementation of 12 different Standards-based mathematics curricula to describe the effects of these curricula on students' learning and achievement, and to provide evidence for any claims they made. In particular, authors were asked to identify content on which performance of students using Standards-based materials differed from that of students using more traditional materials, and content on which performance of these two groups of students was virtually identical. Additionally, four scholars not involved with the development of any of the materials were invited to write critical commentaries on the work reported in the other chapters. Section I of Standards-Based School Mathematics Curricula provides a historical background to place the current curriculum reform efforts in perspective, a summary of recent recommendations to reform school mathematics, and a discussion of issues that arise when conducting research on student outcomes. Sections II, III, and IV are devoted to research on mathematics curriculum projects for elementary, middle, and high schools, respectively. The final section is a commentary by Jeremy Kilpatrick, Regents Professor of Mathematics Education at the University of Georgia, on the research reported in this book. It provides a historical perspective on the use of research to guide mathematics curriculum reform in schools, and makes additional recommendations for further research. In addition to the references provided at the end of each chapter, other references about the Standards-based curriculum projects are provided at the end of the book. This volume is a valuable resource for all participants in discussions about school mathematics curricula--including professors and graduate students interested in mathematics education, curriculum development, program evaluation, or the history of education; educational policy makers; teachers; parents; principals and other school administrators. The editors hope that the large body of empirical evidence and the thoughtful discussion of educational values found in this book will enable readers to engage in informed civil discourse about the goals and methods of school mathematics curricula and related research.


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.


Teaching Mathematics in the Visible Learning Classroom, Grades 6-8

Teaching Mathematics in the Visible Learning Classroom, Grades 6-8

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  • Author: John Almarode
  • Publisher: Corwin Press
  • ISBN: 154433317X
  • Category : Education
  • Languages : en
  • Pages : 154

Select the right task, at the right time, for the right phase of learning It could happen in the morning during homework review. Or perhaps it happens when listening to students as they struggle through a challenging problem. Or maybe even after class, when planning a lesson. At some point, the question arises: How do I influence students′ learning—what’s going to generate that light bulb "aha" moment of understanding? In this sequel to the megawatt best seller Visible Learning for Mathematics, John Almarode, Douglas Fisher, Nancy Frey, John Hattie, and Kateri Thunder help you answer that question by showing how Visible Learning strategies look in action in the mathematics classroom. Walk in the shoes of middle school teachers as they engage in the 200 micro-decisions-per-minute needed to balance the strategies, tasks, and assessments seminal to high-impact mathematics instruction. Using grade-leveled examples and a decision-making matrix, you’ll learn to Articulate clear learning intentions and success criteria at surface, deep, and transfer levels Employ evidence to guide students along the path of becoming metacognitive and self-directed mathematics achievers Use formative assessments to track what students understand, what they don’t, and why Select the right task for the conceptual, procedural, or application emphasis you want, ensuring the task is for the right phase of learning Adjust the difficulty and complexity of any task to meet the needs of all learners It’s not only what works, but when. Exemplary lessons, video clips, and online resources help you leverage the most effective teaching practices at the most effective time to meet the surface, deep, and transfer learning needs of every student.