Concept-rich Mathematics Instruction

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Publisher : ASCD
ISBN 13 : 141660359X
Total Pages : 162 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Concept-rich Mathematics Instruction by : Meir Ben-Hur

Download or read book Concept-rich Mathematics Instruction written by Meir Ben-Hur and published by ASCD. This book was released on 2006 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an instructional approach that helps students in every grade level understand math concepts so they can apply them on assessments, across the curriculum, and outside of school. Provides teaching practices and lesson ideas that give students a stronger foundation for reasoning and problem solving.

Key Concepts in Mathematics

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Publisher : Corwin Press
ISBN 13 : 1412938422
Total Pages : 265 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Key Concepts in Mathematics by : Timothy J. McNamara

Download or read book Key Concepts in Mathematics written by Timothy J. McNamara and published by Corwin Press. This book was released on 2007 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Includes a large number of user-friendly examples that integrate mathematics content and process standards. The step-by-step guidance and explanations in each chapter are beneficial."-Melissa Miller, TeacherRandall G. Lynch Middle School, Farmington, AR "Great activities that are exploratory in nature. A valuable resource."-Carol Amos, Teacher Leader and Mathematics CoordinatorTwinfield Union School, Plainfield, VT Increase students' mathematics achievement with rich problem-solving lessons and activities that are aligned with NCTM standards! Helping teachers envision how math standards can be integrated into the secondary classroom, Key Concepts in Mathematics, Second Edition presents engaging activities and ready-to-use lessons aligned with NCTM content and process standards. This user-friendly book by mathematics educator Timothy J. McNamara is filled with a generous collection of lessons for each of the ten NCTM standards, with many activities that address multiple standards, and numerous practical suggestions for extending the lessons beyond the curriculum. In addition, this updated resource combines standards-based mathematics and technology by incorporating TI-73 Explorer(tm) and TI-83 Plus graphing calculator applications and programs. Each chapter offers: Ready-to-use lessons, hands-on activities, practical suggestions, and an abundance of "good problems" Suggestions for integrating multiple topics and concepts in each lesson Strategies to strengthen student engagement, understanding, and retention by building connections among mathematics topics This exciting guide delivers exactly what is needed for today's standards-based math classroom!

Concept-Based Mathematics

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Publisher : Corwin Press
ISBN 13 : 150633265X
Total Pages : 307 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Concept-Based Mathematics by : Jennifer T.H. Wathall

Download or read book Concept-Based Mathematics written by Jennifer T.H. Wathall and published by Corwin Press. This book was released on 2016-01-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant

Literacy Strategies for Improving Mathematics Instruction

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Author :
Publisher : ASCD
ISBN 13 : 1416603204
Total Pages : 122 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Literacy Strategies for Improving Mathematics Instruction by : Joan M. Kenney

Download or read book Literacy Strategies for Improving Mathematics Instruction written by Joan M. Kenney and published by ASCD. This book was released on 2005 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: An eyeopening look at how teachers can use literacy strategies to help students better understand mathematics.

Teacher Learning of Ambitious and Equitable Mathematics Instruction

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Author :
Publisher : Routledge
ISBN 13 : 1000556387
Total Pages : 284 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Teacher Learning of Ambitious and Equitable Mathematics Instruction by : Ilana Horn

Download or read book Teacher Learning of Ambitious and Equitable Mathematics Instruction written by Ilana Horn and published by Routledge. This book was released on 2022-03-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on sociocultural learning theory, this book offers a groundbreaking theory of secondary mathematics teacher learning in schools, focusing on the transformation of instruction as a conceptual change project to achieve ambitious and equitable mathematics teaching. Despite decades of research showing the importance of ambitious and equitable teaching, few inroads have been made in most U.S. classrooms, and teacher learning in general remains undertheorized in most educational research. Illustrating their theory through closely documented case studies of secondary mathematics teachers’ learning and instructional practices, authors Horn and Garner explore the key conceptual issues teachers are required to work through in order to more fully realize ambitious and equitable teaching in their classrooms. By theorizing teacher learning from a sociocultural perspective and focusing on instructional practice, the authors make a unique contribution to the field of teacher learning. This book offers researchers, scholars, and teacher educators new theoretical and methodological tools for the elusive phenomenon of teacher learning, and provides instructional leaders and coaches with practical examples of how teachers shift their thinking and practice.

Math Instruction for Students with Learning Problems

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Author :
Publisher : Routledge
ISBN 13 : 1317409329
Total Pages : 837 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Math Instruction for Students with Learning Problems by : Susan Perry Gurganus

Download or read book Math Instruction for Students with Learning Problems written by Susan Perry Gurganus and published by Routledge. This book was released on 2017-02-24 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math Instruction for Students with Learning Problems, Second Edition provides a research-based approach to mathematics instruction designed to build confidence and competence in pre- and in-service PreK–12 teachers. This core textbook addresses teacher and student attitudes toward mathematics, as well as language issues, specific mathematics disabilities, prior experiences, and cognitive and metacognitive factors. The material is rich with opportunities for class activities and field extensions, and the second edition has been fully updated to reference both NCTM and CCSSM standards throughout the text and includes an entirely new chapter on measurement and data analysis.

Guided Math: A Framework for Mathematics Instruction Second Edition

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Author :
Publisher : Teacher Created Materials
ISBN 13 : 1642903787
Total Pages : 264 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Guided Math: A Framework for Mathematics Instruction Second Edition by : Laney Sammons

Download or read book Guided Math: A Framework for Mathematics Instruction Second Edition written by Laney Sammons and published by Teacher Created Materials. This book was released on 2019-03-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This instructional math framework provides an environment for mathematics that fosters mathematical thinking and understanding while meeting the needs of all students. This updated math resource takes an innovative approach to mathematics instruction and uses the same teaching philosophies for guided reading. Educators will learn how to effectively utilize small-group and whole-group instruction, manipulatives, math warm-ups, and Math Workshop to engage K-12 students in connecting mathematics to their own lives. Maximize the impact of your instruction with ideas for using ongoing assessment and differentiation strategies. This 2nd edition guided math resource provides practical guidance and sample lessons for grade level bands K-2, 3-5, 6-8, and 9-12. Promote a classroom environment of numeracy and mathematical discourse with this essential professional resource for K-12 math teachers!

Transforming Mathematics Instruction

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Author :
Publisher : Springer
ISBN 13 : 3319049933
Total Pages : 586 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Transforming Mathematics Instruction by : Yeping Li

Download or read book Transforming Mathematics Instruction written by Yeping Li and published by Springer. This book was released on 2014-07-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys and examines different approaches and practices that contribute to the changes in mathematics instruction, including (1) innovative approaches that bring direct changes in classroom instructional practices, (2) curriculum reforms that introduce changes in content and requirements in classroom instruction, and (3) approaches in mathematics teacher education that aim to improve teachers’ expertise and practices. It also surveys relevant theory and methodology development in studying and assessing mathematics instruction. Classroom instruction is commonly seen as one of the key factors contributing to students’ learning of mathematics, but much remains to be understood about teachers’ instructional practices that lead to the development and enactment of effective classroom instruction, and approaches and practices developed and used to transform classroom instruction in different education systems. Transforming Mathematics Instruction is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including: - Identifying what is important in mathematics for teaching and learning emphasized in different approaches; - Exploring how students’ learning is considered and facilitated through different approaches and practices; - Understanding the nature of various approaches that are valued in different systems and cultural contexts; - Probing culturally valued approaches in identifying and evaluating effective instructional practices. The book brings new research and insights into multiple approaches and practices for transforming mathematics instruction to the international community of mathematics education, with 25 chapters and four section prefaces contributed by 56 scholars from 10 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, teacher educators, curriculum developers, and graduate students interested in learning about different instructional practices, approaches for instructional transformation, and research in different education systems. It will help readers to reflect on approaches and practices that are useful for instructional changes in their own education systems, and also inspire them to identify and further explore new areas of research and program development in improving mathematics teaching and learning.

Rethinking Mathematics

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Publisher : Rethinking Schools
ISBN 13 : 0942961544
Total Pages : 192 pages
Book Rating : 4.9/5 (429 download)

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Book Synopsis Rethinking Mathematics by : Eric Gutstein

Download or read book Rethinking Mathematics written by Eric Gutstein and published by Rethinking Schools. This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this unique collection, more than 30 articles show how to weave social justice issues throughout the mathematics curriculum, as well as how to integrate mathematics into other curricular areas. Rethinking Mathematics offers teaching ideas, lesson plans, and reflections by practitioners and mathematics educators. This is real-world math-math that helps students analyze problems as they gain essential academic skills. This book offers hope and guidance for teachers to enliven and strengthen their math teaching. It will deepen students' understanding of society and help prepare them to be critical, active participants in a democracy. Blending theory and practice, this is the only resource of its kind.

Implementing Problem-Based Instruction in Secondary Mathematics Classrooms

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Author :
Publisher : Teachers College Press
ISBN 13 : 0807782181
Total Pages : 177 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis Implementing Problem-Based Instruction in Secondary Mathematics Classrooms by : Sarah Ferguson

Download or read book Implementing Problem-Based Instruction in Secondary Mathematics Classrooms written by Sarah Ferguson and published by Teachers College Press. This book was released on 2024-03-22 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problem-based instruction (PBI) is a research-based, student-centered instructional strategy that uses rich mathematical tasks to connect students’ previously acquired math knowledge to new mathematical concepts. Unlike traditional teaching and learning strategies, PBI facilitates learning by making connections between mathematical concepts and real-world applications rather than through noncontextual, rote learning of skills, steps, and equations. This practical resource is an informative instructional tool for secondary mathematics teachers and teacher educators seeking to deepen their students’ understanding of, and engagement with, mathematical learning. Highlighting both teacher and student perspectives, the text provides an overview of the PBI instructional strategy that includes best practices, guidance for implementation, and 50 downloadable resources. In addition, readers will find 12 teacher-created sample lessons with prepared resources and detailed instructional guides. While written for novice PBI users, this book will enhance the instruction of teachers at all levels. Book Features: Provides 12 ready-to-use sample lesson plans aligned to the most common secondary mathematics topics. Focuses on the practical implementation of problem-based instruction specifically for middle and high school mathematics instruction. Includes a template to guide readers step-by-step through creating their own problem-based lessons. Contains links to more than 50 editable, online resources for easy classroom implementation.

Mastering Math Manipulatives, Grades 4-8

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Publisher : Corwin Press
ISBN 13 : 1071816063
Total Pages : 289 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Mastering Math Manipulatives, Grades 4-8 by : Sara Delano Moore

Download or read book Mastering Math Manipulatives, Grades 4-8 written by Sara Delano Moore and published by Corwin Press. This book was released on 2021-10-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Put math manipulatives to work in your classroom and make teaching and learning math both meaningful and productive. Mastering Math Manipulatives includes everything you need to integrate math manipulatives—both concrete and virtual—into math learning. Each chapter of this richly illustrated, easy-to-use guide focuses on a different powerful tool, such as base ten blocks, fraction manipulatives, unit squares and cubes, Cuisenaire Rods, Algebra tiles and two-color counters, geometric strips and solids, geoboards, and others, and includes a set of activities that demonstrate the many ways teachers can leverage manipulatives to model and reinforce math concepts for all learners. It features: · Classroom strategies for introducing math manipulatives, including commercial, virtual, and hand-made manipulatives, into formal math instruction. · Step-by-step instructions for over 70 activities that work with any curriculum, including four-color photos, printable work mats, and demonstration videos. · Handy charts that sort activities by manipulative type, math topic, domains aligned with standards, and grade-level appropriateness.

Fostering Children's Mathematical Power

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Publisher : Routledge
ISBN 13 : 1135674043
Total Pages : 1096 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Fostering Children's Mathematical Power by : Arthur J. Baroody

Download or read book Fostering Children's Mathematical Power written by Arthur J. Baroody and published by Routledge. This book was released on 1998-09-01 with total page 1096 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.

Making Sense of Mathematics for Teaching, Grades 3-5

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Publisher : Solution Tree Press
ISBN 13 : 1942496435
Total Pages : 386 pages
Book Rating : 4.9/5 (424 download)

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Book Synopsis Making Sense of Mathematics for Teaching, Grades 3-5 by : Juli K. Dixon

Download or read book Making Sense of Mathematics for Teaching, Grades 3-5 written by Juli K. Dixon and published by Solution Tree Press. This book was released on 2016-04-11 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Eyes on Math

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Publisher : Teachers College Press
ISBN 13 : 0807772364
Total Pages : 241 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis Eyes on Math by : Marian Small

Download or read book Eyes on Math written by Marian Small and published by Teachers College Press. This book was released on 2015-04-25 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book is an exciting follow-up to the authors’ bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K–8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students and teachers look more deeply and see the math behind the math! For each of more than 120 visuals, the text identifies the key math concept and the Common Core State Standard being addressed and then provides teachers with: Mathematical background and context.Questions to use with students to lead the instructional conversation.Expected answers and explanations of why each question is important.Follow-up extensions to solidify and assess student understanding. This book will be useful to a broad range of teachers who will find new ways to clarify concepts that students find difficult. It can be used as a resource to prepare teachers for the higher mathematical thinking requirements of the CCSS Mathematical Practices. It will also be an invaluable resource for teachers working with students with low reading ability, including English language learners and special education students. “This book provides a way for both teachers and students to get used to talking about mathematics in nonthreatening, open-ended ways. The author’s friendly explanations of the mathematical ideas the pictures are intended to surface give teachers who are less confident about the conceptual aspects of mathematics the support they need to facilitate less-scripted mathematical discourse with their students.” —Lucy West, education consultant Praise for Good Questions and More Good Questions! “A must for any educator who is serious about reaching more students more often and achieving more positive results.” —Resources for the Mathematics Educator “A valuable book for mathematics teachers, teacher educators, and faculty involved in differentiated instruction.” —Choice “A great resource.” —Mathematics Teaching in the Middle School “I highly recommend this user-friendly resource for all mathematics teachers.” —Teaching Children Mathematics

Creating a Language-Rich Math Class

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Publisher : Routledge
ISBN 13 : 9780367759957
Total Pages : 184 pages
Book Rating : 4.7/5 (599 download)

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Book Synopsis Creating a Language-Rich Math Class by : SANDRA L. ATKINS

Download or read book Creating a Language-Rich Math Class written by SANDRA L. ATKINS and published by Routledge. This book was released on 2021-10-19 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: What meanings do your students have for key mathematics concepts? What meanings do you wish them to have? Creating a Language-Rich Math Class offers practical approaches for developing conceptual understandings by connecting concrete, pictorial, verbal, and symbolic representations. The focus is on making mathematics memorable instead of on memorizing. You'll learn strategies for introducing students to math language that gives meaning to the terms and symbols they use every day; for building flexibility and precision in students' use of math language; and for structuring activities to make them more language-rich. This second edition also provides strategies for helping students to at times be quiet and listen to their peers; for purposefully using language to introduce students to more complex mathematical symbolism and algebraic properties; and for using writing prompts to zoom in on the meanings that individual students have given to the language-rich experiences. Appropriate for elementary teachers and instructional coaches, the book also includes features such as Investigations to Try and Questions for Reflection to help you incorporate these ideas into your practice. In addition, there are Blackline masters of game cards and puzzles, which can also be found on our website for free download at http: //www.routledge.com/9780367759957.

Problem Solving in Mathematics Education

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Author :
Publisher : WTM-Verlag Münster
ISBN 13 : 3959870132
Total Pages : 250 pages
Book Rating : 4.9/5 (598 download)

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Book Synopsis Problem Solving in Mathematics Education by : Torsten Fritzlar

Download or read book Problem Solving in Mathematics Education written by Torsten Fritzlar and published by WTM-Verlag Münster. This book was released on 2016-06-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: From 3rd to 5th of September 2015 the 17th international ProMath conference (Problem Solving in Mathematics Education) took place at the Faculty of Education of the Martin Luther University Halle-Wittenberg (Germany). For the first time, it was combined with the annual meeting of the working group “Problem Solving” of the Society of Didactics of Mathematics. This book contains 20 peer reviewed articles of researchers from five European countries. The topics of the papers evolved around different areas of learning and problem solving. There are some theoretical papers on problem oriented mathematics instruction and specific aspects of problem solving and creativity as well as reports on detailed studies of problem solving processes of pupils and preservice teachers. Authors also present experiences with “real” problem solving instruction in different countries, considerations and teaching experiments on didactic concepts to foster pupils’ problem solving abilities, and they describe mathematically rich problem fields and their potentials for mathematical investigations in class. ProMath is a group of experienced and early career researchers in the field of mathematics education who are interested in investigating and fostering mathematical problem solving and problem oriented mathematics teaching.

Mathematical Reasoning for Elementary School Teachers, Global Edition

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Publisher :
ISBN 13 : 9781292062365
Total Pages : 872 pages
Book Rating : 4.0/5 (623 download)

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Book Synopsis Mathematical Reasoning for Elementary School Teachers, Global Edition by : Calvin T. Long

Download or read book Mathematical Reasoning for Elementary School Teachers, Global Edition written by Calvin T. Long and published by . This book was released on 2014-07-22 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long/DeTemple/Millman's Mathematical Reasoning for Elementary Teachers presents the mathematical content needed for teaching within the context of the elementary classroom, giving future teachers the motivation they need while also showing them the bigger picture of when they will use and teach the concepts. The program also endeavors to answer the frequently-asked Why are we learning this? by going beyond skill explanations and showing the ways that these concepts are implemented in the future classroom and what types of questions children may ask. Now updated to include the Common Core State Standards for Mathematics, the text imparts mathematical reasoning skills, a deep conceptual understanding, and a positive attitude to those who aspire to be elementary or middle school teachers. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. Here's how: *Personalized learning with MyMathLab: MyMathLab delivers proven results in helping students succeed and provides engaging experiences that personalize learning.*Features for the future classroom demonstrate the relevance of the concepts students are learning, the ways in which the mathematical concepts will be employed in the classroom, provide perspective on the importance of learning the material, and engage students to learn by doing. *Strong pedagogical tools help students to understand and retain the essential principals.