Open Middle Math

Open Middle Math PDF

Author: Robert Kaplinsky

Publisher: Taylor & Francis

Published: 2023-10-10

Total Pages: 193

ISBN-13: 1003839886

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This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.

Open-Ended Maths Activities

Open-Ended Maths Activities PDF

Author: Peter Sullivan

Publisher:

Published: 2004

Total Pages: 112

ISBN-13: 9780195517682

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Open-ended Maths Activities Second Edition is the revised and expanded edition of the best-selling title by Peter Sullivan and Pat Lilburn. It discusses a type of open-ended, problem-solving question called a 'good' question. These questions enhance learning, teaching and assessment and are a useful addition to a teacher's strategies. It includes: practical advice on how to create your own 'good' questions to use within the classroom organised by subject area and levels (upper, middle and junior) the sixteen topics covered are included within Number, Measurement, Space and Chance and Data.

Values and Valuing in Mathematics Education

Values and Valuing in Mathematics Education PDF

Author: Philip Clarkson

Publisher: Springer

Published: 2019-04-24

Total Pages: 222

ISBN-13: 3030168921

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This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education systems. It also clearly shows that teaching mathematics involves not only reasoning and feelings, but also students’ interactions with their cultural setting and each other. The book brings together the work of world leaders and new thinkers in mathematics educational research to improve the learning and teaching of mathematics. Addressing themes such as discovering hidden cultural values, a multicultural society and methodological issues in the investigation of values in mathematics, it stimulates readers to consider these topics in cross-cultural ways, and offers suggestions for research and classroom practice. It is a valuable resource for scholars of mathematics education, from early childhood through to higher education and an inspiring read for all mathematics teachers.

Good Questions

Good Questions PDF

Author: Marian Small

Publisher: Teachers College Press

Published: 2012-01-01

Total Pages: 241

ISBN-13: 0807753130

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Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K–8 classroom. In this bestseller, math education expert Marian Small explains two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, Small also demonstrates more inclusive learning conversations that promote broader student participation and mathematical thinking required by CCSS. Specific strategies and examples for each grade band are organized around NCTM content strands: Number and Operations, Geometry, Measurement, Algebra, and Data Analysis and Probability.

More Good Questions

More Good Questions PDF

Author: Marian Small

Publisher: Teachers College Press

Published: 2010-05-15

Total Pages: 225

ISBN-13: 0807750883

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We know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, this book also demonstrates how to use more inclusive learning conversations to promote broader student participation. Strategies and examples are organized around Big Ideas within the National Council of Teachers of Mathematics (NCTM) content strands. With particular emphasis on Algebra, chapters also address Number and Operations, Geometry, Measurement, and Data Analysis and Probability, with examples included for Pre-Calculus. To help teachers differentiate math instruction with less difficulty and greater success, this resource: Underscores the rationale for differentiating secondary math instruction. Provides specific examples for secondary math content. Describes two easy-to-implement strategies designed to overcome the most common DI problems that teachers encounter. Offers almost 300 questions and tasks that teachers and coaches can adopt immediately, adapt, or use as models to create their own, along with scaffolding and consolidating questions. Includes Teaching Tips sidebars and an organizing template at the end of each chapter to help teachers build new tasks and open questions. Shows how to create a more inclusive classroom learning community with mathematical talk that engages participants from all levels. PROFESSIONAL DEVELOPMENT: Visit Marian Small’s website onetwoinfinity.ca for in-person and online professional development.

Mathematics Counts

Mathematics Counts PDF

Author: Great Britain. Committee of Inquiry into the Teaching of Mathematics in Schools

Publisher: Stationery Office Books (TSO)

Published: 1982

Total Pages: 332

ISBN-13:

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SUMMARY: Recommendations on the teaching of mathematics in primary & secondary schools in England & Wales, with particular regard to the mathematics required in further & higher education, employment & adult life generally.

The SAGE Encyclopedia of Communication Research Methods

The SAGE Encyclopedia of Communication Research Methods PDF

Author: Mike Allen

Publisher: SAGE Publications

Published: 2017-04-11

Total Pages: 2013

ISBN-13: 1483381420

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Communication research is evolving and changing in a world of online journals, open-access, and new ways of obtaining data and conducting experiments via the Internet. Although there are generic encyclopedias describing basic social science research methodologies in general, until now there has been no comprehensive A-to-Z reference work exploring methods specific to communication and media studies. Our entries, authored by key figures in the field, focus on special considerations when applied specifically to communication research, accompanied by engaging examples from the literature of communication, journalism, and media studies. Entries cover every step of the research process, from the creative development of research topics and questions to literature reviews, selection of best methods (whether quantitative, qualitative, or mixed) for analyzing research results and publishing research findings, whether in traditional media or via new media outlets. In addition to expected entries covering the basics of theories and methods traditionally used in communication research, other entries discuss important trends influencing the future of that research, including contemporary practical issues students will face in communication professions, the influences of globalization on research, use of new recording technologies in fieldwork, and the challenges and opportunities related to studying online multi-media environments. Email, texting, cellphone video, and blogging are shown not only as topics of research but also as means of collecting and analyzing data. Still other entries delve into considerations of accountability, copyright, confidentiality, data ownership and security, privacy, and other aspects of conducting an ethical research program. Features: 652 signed entries are contained in an authoritative work spanning four volumes available in choice of electronic or print formats. Although organized A-to-Z, front matter includes a Reader’s Guide grouping entries thematically to help students interested in a specific aspect of communication research to more easily locate directly related entries. Back matter includes a Chronology of the development of the field of communication research; a Resource Guide to classic books, journals, and associations; a Glossary introducing the terminology of the field; and a detailed Index. Entries conclude with References/Further Readings and Cross-References to related entries to guide students further in their research journeys. The Index, Reader’s Guide themes, and Cross-References combine to provide robust search-and-browse in the e-version.

Make Just One Change

Make Just One Change PDF

Author: Dan Rothstein

Publisher: Harvard Education Press

Published: 2011-09-01

Total Pages: 192

ISBN-13: 161250454X

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The authors of Make Just One Change argue that formulating one’s own questions is “the single most essential skill for learning”—and one that should be taught to all students. They also argue that it should be taught in the simplest way possible. Drawing on twenty years of experience, the authors present the Question Formulation Technique, a concise and powerful protocol that enables learners to produce their own questions, improve their questions, and strategize how to use them. Make Just One Change features the voices and experiences of teachers in classrooms across the country to illustrate the use of the Question Formulation Technique across grade levels and subject areas and with different kinds of learners.

Open Problems in Mathematics

Open Problems in Mathematics PDF

Author: John Forbes Nash, Jr.

Publisher: Springer

Published: 2016-07-05

Total Pages: 543

ISBN-13: 3319321625

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The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Essential Questions

Essential Questions PDF

Author: Jay McTighe

Publisher: ASCD

Published: 2013-03-27

Total Pages: 130

ISBN-13: 1416615709

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What are "essential questions," and how do they differ from other kinds of questions? What's so great about them? Why should you design and use essential questions in your classroom? Essential questions (EQs) help target standards as you organize curriculum content into coherent units that yield focused and thoughtful learning. In the classroom, EQs are used to stimulate students' discussions and promote a deeper understanding of the content. Whether you are an Understanding by Design (UbD) devotee or are searching for ways to address standards—local or Common Core State Standards—in an engaging way, Jay McTighe and Grant Wiggins provide practical guidance on how to design, initiate, and embed inquiry-based teaching and learning in your classroom. Offering dozens of examples, the authors explore the usefulness of EQs in all K-12 content areas, including skill-based areas such as math, PE, language instruction, and arts education. As an important element of their backward design approach to designing curriculum, instruction, and assessment, the authors *Give a comprehensive explanation of why EQs are so important; *Explore seven defining characteristics of EQs; *Distinguish between topical and overarching questions and their uses; *Outline the rationale for using EQs as the focal point in creating units of study; and *Show how to create effective EQs, working from sources including standards, desired understandings, and student misconceptions. Using essential questions can be challenging—for both teachers and students—and this book provides guidance through practical and proven processes, as well as suggested "response strategies" to encourage student engagement. Finally, you will learn how to create a culture of inquiry so that all members of the educational community—students, teachers, and administrators—benefit from the increased rigor and deepened understanding that emerge when essential questions become a guiding force for learners of all ages.

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