Standard Grade, Foundation Mathematics 2008-2012

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Author :
Publisher : Bright Red
ISBN 13 : 9781849482523
Total Pages : 168 pages
Book Rating : 4.4/5 (825 download)

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Book Synopsis Standard Grade, Foundation Mathematics 2008-2012 by : Sqa

Download or read book Standard Grade, Foundation Mathematics 2008-2012 written by Sqa and published by Bright Red. This book was released on 2012-09-01 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Official SQA Past Papers' provide perfect exam preparation. As well as delivering at least three years of actual past papers - including the 2012 exam - all papers are accompanied by examiner-approved answers to show students how to write the best responses for the most marks.

Planting the Seeds of Algebra, PreK–2

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Author :
Publisher : Corwin Press
ISBN 13 : 1412996600
Total Pages : 210 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Planting the Seeds of Algebra, PreK–2 by : Monica Neagoy

Download or read book Planting the Seeds of Algebra, PreK–2 written by Monica Neagoy and published by Corwin Press. This book was released on 2012-04-20 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of algebra has always been important in American secondary mathematics education. However, algebra at the elementary level has been garnering increasing attention and importance over the past 15 years. There is consequently a dire need for ideas, suggestions and models for how best to achieve pre-algebraic instruction in the elementary grades. Planting the Seeds of Algebra will empower teachers with theoretical and practical knowledge about both the content and pedagogy of such instruction, and show them the different faces of algebra as it appears in the early grades. The book will walk teachers of young children through many examples of K-6 math lessons and unpack, step by step, the hidden connections to higher algebra. After reading this book, teachers will be better equipped ...

The Common Core Mathematics Companion: The Standards Decoded, Grades 6-8

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Author :
Publisher : Corwin Press
ISBN 13 : 1506341632
Total Pages : 305 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis The Common Core Mathematics Companion: The Standards Decoded, Grades 6-8 by : Ruth Harbin Miles

Download or read book The Common Core Mathematics Companion: The Standards Decoded, Grades 6-8 written by Ruth Harbin Miles and published by Corwin Press. This book was released on 2016-02-18 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Common Core Mathematics Companion 6-8 offers a practical guide for implementing the CCSS Math Standards. Teachers will appreciate the misconception alerts and ideas for differentiation." — Jay McTighe, Author and Consultant When it comes to math, standards-aligned is achievement-aligned... In the short time since The Common Core Mathematics Companions, Grades K-2 and 3-5 burst on the scene, they have been lauded as the best resources for making critical math ideas easy to teach. With this brand-new 6-8 volume, middle school math success is at your fingertips. Page by page, the authors lay out the pieces to a cutting-edge curriculum, helping you to: Get the inside scoop on which standards connect, what key vocabulary means, and time-saving tables showing where to focus instruction for each grade Write curriculum for: ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics & probability Use the What to Teach pages to deliver powerful standards-based lessons Learn effective techniques to create an environment where all students can experience math break-throughs Incorporate the Standards for Mathematical Practice to improve students’ ability to problem solve, construct viable arguments, use tools strategically, attend to precision, and more The Common Core Mathematics Companion, Grades 6–8 has what every middle school needs to provide students with the foundation for the concepts and skills they will be expected to know in grade 9–12. Ruth Harbin Miles is a mathematics coach, with special expertise in developing teachers’ content knowledge and strategies for engaging students to achieve high mathematics standards. A serving member on the Board of Directors for the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, Ruth is a co-author with Linda Gojak of The Common Core Mathematics Companions, K–2 and 3–5 (Corwin). Lois Williams, Ed.D., who taught mathematics in grades K–8 for 20 years, is currently an adjunct professor at Mary Baldwin College and an International Fellow with the Charles A. Dana Center, training teachers in the College and Career Readiness Standards She has been honored with a Fulbright Teacher Exchange and the Virginia Middle School Mathematics Teacher of the Year award.

Standards for K-12 Engineering Education?

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Author :
Publisher : National Academies Press
ISBN 13 : 0309160154
Total Pages : 160 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Standards for K-12 Engineering Education? by : National Research Council

Download or read book Standards for K-12 Engineering Education? written by National Research Council and published by National Academies Press. This book was released on 2010-10-28 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this study was to assess the value and feasibility of developing and implementing content standards for engineering education at the K-12 level. Content standards have been developed for three disciplines in STEM education-science, technology, and mathematic-but not for engineering. To date, a small but growing number of K-12 students are being exposed to engineering-related materials, and limited but intriguing evidence suggests that engineering education can stimulate interest and improve learning in mathematics and science as well as improve understanding of engineering and technology. Given this background, a reasonable question is whether standards would improve the quality and increase the amount of teaching and learning of engineering in K-12 education. The book concludes that, although it is theoretically possible to develop standards for K-12 engineering education, it would be extremely difficult to ensure their usefulness and effective implementation. This conclusion is supported by the following findings: (1) there is relatively limited experience with K-12 engineering education in U.S. elementary and secondary schools, (2) there is not at present a critical mass of teachers qualified to deliver engineering instruction, (3) evidence regarding the impact of standards-based educational reforms on student learning in other subjects, such as mathematics and science, is inconclusive, and (4) there are significant barriers to introducing stand-alone standards for an entirely new content area in a curriculum already burdened with learning goals in more established domains of study.

Common Standards for K-12 Education?

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Author :
Publisher : National Academies Press
ISBN 13 : 0309178398
Total Pages : 104 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Common Standards for K-12 Education? by : National Research Council

Download or read book Common Standards for K-12 Education? written by National Research Council and published by National Academies Press. This book was released on 2008-08-26 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standards-based accountability has become a central feature of the public education system in each state and is a theme of national discussions about how achievement for all students can be improved and achievement gaps narrowed. Questions remain, however, about the implementation of standards and accountability systems and about whether their potential benefits have been fully realized. Each of the 50 states has adopted its own set of standards, and though there is overlap among them, there is also wide variation in the ways states have devised and implemented their systems. This variety may have both advantages and disadvantages, but it nevertheless raises a fundamental question: Is the establishment of common K-12 academic standards, which states could voluntarily adopt, the logical next step for standards-based reform? The goal of this book is not to answer the policy question of whether or not common standards would be a good idea. Rather, the book provides an objective look at the available evidence regarding the ways in which standards are currently functioning, the strategies that might be used to pursue common standards, and the issues that doing so might present.

Mathematics Worksheets Don't Grow Dendrites

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Author :
Publisher : Corwin Press
ISBN 13 : 1452207240
Total Pages : 201 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Mathematics Worksheets Don't Grow Dendrites by : Marcia L. Tate

Download or read book Mathematics Worksheets Don't Grow Dendrites written by Marcia L. Tate and published by Corwin Press. This book was released on 2008-08-21 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engage students in effective, meaningful experiences in mathematics! Following the format of Marcia L. Tate’s previous bestsellers, this user-friendly guide offers math teachers 20 powerful, brain-based teaching strategies that incorporate visual, auditory, kinesthetic, and tactile modalities to promote student engagement and achievement. The book focuses on the NCTM focal points and includes a bibliography of math and literature resources and a lesson planning guide. The chapters offer: A what, why, and how for each strategy Specific brain-compatible mathematics activities and lessons from real teachers across the country Space for teachers to reflect on and apply individual strategies in their lessons

Mathematics Education

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Author :
Publisher : Springer
ISBN 13 : 3319449508
Total Pages : 382 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Mathematics Education by : Jacqueline Dewar

Download or read book Mathematics Education written by Jacqueline Dewar and published by Springer. This book was released on 2016-11-26 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

Mathematics Learning in Early Childhood

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Author :
Publisher : National Academies Press
ISBN 13 : 0309147433
Total Pages : 399 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematics Learning in Early Childhood by : National Research Council

Download or read book Mathematics Learning in Early Childhood written by National Research Council and published by National Academies Press. This book was released on 2009-11-13 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

Common Core Standards for Elementary Grades K–2 Math & English Language Arts

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Author :
Publisher : ASCD
ISBN 13 : 1416614656
Total Pages : 267 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Common Core Standards for Elementary Grades K–2 Math & English Language Arts by : Amber Evenson

Download or read book Common Core Standards for Elementary Grades K–2 Math & English Language Arts written by Amber Evenson and published by ASCD. This book was released on 2013-05-20 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smart implementation of the Common Core State Standards requires both an overall understanding of the standards and a grasp of their implications for planning, teaching, and learning. This Quick-Start Guide provides a succinct, all-in-one look at * The content, structure, terminology, and emphases of the Common Core standards for mathematics and English language arts and literacy in the lower elementary grades. * The meaning of the individual standards within each of the four ELA/literacy strands and five math domains, with an emphasis on areas that represent the most significant changes to business as usual. * How the standards connect across and within strands, domains, and grade levels to develop the foundational language arts, literacy, and mathematics understanding that will support a lifetime of successful learning. Here, teachers of grades K–2 and elementary school leaders will find information they need to begin adapting their practices to help all students master the new and challenging material contained in the standards. A practical lesson planning process to use with the Common Core, based on Classroom Instruction That Works, 2nd Ed., is included, along with six sample lessons. LEARN THE ESSENTIALS OF THE COMMON CORE The grade-level and subject-specific Quick-Start Guides in the Understanding the Common Core Standards series, edited by John Kendall, are designed to help school leaders and school staffs turn Common Core standards into coherent, content-rich curriculum and effective, classroom-level lessons.

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

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Author :
Publisher : Springer
ISBN 13 : 3319683519
Total Pages : 443 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by : Carolyn Kieran

Download or read book Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds written by Carolyn Kieran and published by Springer. This book was released on 2017-12-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.

Standards for Preparing Teachers of Mathematics

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Author :
Publisher : IAP
ISBN 13 : 1641139986
Total Pages : 199 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis Standards for Preparing Teachers of Mathematics by : Association of Mathematics Teacher Educators (AMTE)

Download or read book Standards for Preparing Teachers of Mathematics written by Association of Mathematics Teacher Educators (AMTE) and published by IAP. This book was released on 2020-02-01 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Also available in a black + white version AMTE, in the Standards for Preparing Teachers of Mathematics (SPTM), puts forward a national vision of initial preparation for all Pre-K–12 teachers who teach mathematics. SPTM contains critical messages for all who teach mathematics, including elementary school teachers teaching all disciplines, middle and high school mathematics teachers who may teach mathematics exclusively, special education teachers, teachers of emergent multilingual students, and other teaching professionals and administrators who have responsibility for students’ mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated. SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform assessment practices for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning teacher of mathematics who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles. Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.

Elementary Mathematics Specialists

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Author :
Publisher : IAP
ISBN 13 : 1681238241
Total Pages : 253 pages
Book Rating : 4.6/5 (812 download)

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Book Synopsis Elementary Mathematics Specialists by : Maggie B. McGatha

Download or read book Elementary Mathematics Specialists written by Maggie B. McGatha and published by IAP. This book was released on 2017-02-01 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary mathematics specialists are teacher leaders who are responsible for supporting effective PK–6 mathematics instruction and student learning. The Association of Mathematics Teacher Educators (AMTE), the Association of State Supervisors of Mathematics, the National Council of Supervisors of Mathematics, and the National Council of Teachers of Mathematics, in a 2010 joint position paper on Elementary Mathematics Specialists (EMSs), all advocate for the use of EMSs to support the teaching and learning of mathematics. The specific roles and expectations of EMSs will vary according to the needs of each setting, “but their expertise and successful experience at the elementary level is critical” (p 1). Elementary Mathematics Specialists: Developing, Refining, and Examining Programs that Support Mathematics Teaching and Learning is AMTE’s latest resource supporting the important work of EMSs. It has five sections related to the preparation and professional development of EMSs: (a) Overview and Current State of Affairs; (b) Models of EMS Program Development & Delivery; (c) Supporting EMSs in the Field; (d) The Mathematics Specialist Research; and (e) Future Directions. The book provides support to EMS practitioners, program providers/developers, and researchers seeking to answer important questions about how to prepare Mathematics Specialists, support them in the field, and research their effectiveness.

Debates in Mathematics Education

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Author :
Publisher : Routledge
ISBN 13 : 1134483724
Total Pages : 280 pages
Book Rating : 4.1/5 (344 download)

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Book Synopsis Debates in Mathematics Education by : Dawn Leslie

Download or read book Debates in Mathematics Education written by Dawn Leslie and published by Routledge. This book was released on 2013-10-01 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. It engages with established and contemporary debates, promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Written by experts in the field of mathematics education, it investigates and offers fresh insight into topics of central importance, including: Gender, social inequality and mathematics Mathematics, politics and climate change The history and culture of mathematics Using popular culture in the mathematics classroom The concept of ‘ability’ and its impact on learning What we mean by ‘teaching for understanding’ Choosing and using examples in teaching The fitness of formal examinations. Designed to stimulate discussion and support you in your own research, writing and practice, Debates in Mathematics Education will be a valuable resource for any student or practising teacher engaged in initial teacher training, continuing professional development or Masters level study. It also has much to offer to those leading initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.

Handbook of Research on Teaching

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Author :
Publisher :
ISBN 13 : 0935302484
Total Pages : 1553 pages
Book Rating : 4.9/5 (353 download)

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Book Synopsis Handbook of Research on Teaching by : Drew Gitomer

Download or read book Handbook of Research on Teaching written by Drew Gitomer and published by . This book was released on 2016-05-19 with total page 1553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifth Edition of the Handbook of Research on Teachingis an essential resource for students and scholars dedicated to the study of teaching and learning. This volume offers a vast array of topics ranging from the history of teaching to technological and literacy issues. In each authoritative chapter, the authors summarize the state of the field while providing conceptual overviews of critical topics related to research on teaching. Each of the volume's 23 chapters is a canonical piece that will serve as a reference tool for the field. The Handbook provides readers with an unaparalleled view of the current state of research on teaching across its multiple facets and related fields.

Teaching Mathematics in Grades 6 - 12

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Author :
Publisher : SAGE
ISBN 13 : 141299568X
Total Pages : 513 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Teaching Mathematics in Grades 6 - 12 by : Randall E. Groth

Download or read book Teaching Mathematics in Grades 6 - 12 written by Randall E. Groth and published by SAGE. This book was released on 2012-08-10 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: A journey into the vibrant and intriguing world of mathematics education Teaching Mathematics in Grades 6 - 12 explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows secondary mathematics teachers the value of being a researcher in the classroom by constantly experimenting with methods for developing students′ mathematical thinking and then connecting this research to practices that enhance students′ understanding of the material.The chapters in Part I introduce secondary teachers to the field of mathematics education with cross-cutting issues that apply to teaching and learning in all mathematics content areas. The chapters in Part II are devoted to specific mathematics content strands and describe how students think about mathematical concepts. The goal of the text is to have secondary math teachers gain a deeper understanding of the types of mathematical knowledge their students bring to grade 6 - 12 classrooms, and how students′ thinking may develop in response to different teaching strategies.

In Common No More

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Author :
Publisher : Bloomsbury Publishing USA
ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.2/5 (161 download)

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Book Synopsis In Common No More by : Arnold F. Shober

Download or read book In Common No More written by Arnold F. Shober and published by Bloomsbury Publishing USA. This book was released on 2016-06-13 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: When did the Common Core evolve from pet project to pariah among educators and parents? This book examines the rise and fall of our national education standards from their inception to the present day. Parents, teachers, and political groups have waged debates over the Common Core since the standards' adoption in 2010. This timely examination explores the shifting political alliances related to the Common Core State Standards Initiative, explains why initial national support has faded, and considers the major debates running through the Common Core controversy. The book is organized around four themes of political conflict: federal versus state control, minorities versus majorities, experts versus professionals, and elites versus local preferences. The work reviews the politics of state and national standards, evaluating the political arguments for and against the Common Core: federal overreach, lack of evidence for effectiveness, lack of parental control, lack of teacher input, improper adaptive testing, overtesting, and connections to private education-reform funders and foundations. The work includes a short primer on the Common Core State Standards Initiative as well as on the Partnership for Assessment of Readiness for College and Careers (PARCC) and Smarter Balance, two state-level organizations that have worked on the standards. An informative appendix presents brief descriptions of major interest groups and think tanks involved with the standards initiative along with a timeline of American educational standards reforms and the Common Core.

Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5

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Author :
Publisher : Corwin Press
ISBN 13 : 1483340198
Total Pages : 355 pages
Book Rating : 4.4/5 (833 download)

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Book Synopsis Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5 by : Cheryl Rose Tobey

Download or read book Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5 written by Cheryl Rose Tobey and published by Corwin Press. This book was released on 2013-11-27 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Take the guesswork out of grades 3-5 math assessment! Expertly pinpoint and reverse your students’ common math difficulties with this must-have resource from best-selling authors Cheryl Tobey and Carolyn Arline. You’ll find 25 research-based assessment probes designed specifically for Grades 3-5 and the new Common Core Standards for Mathematics. Learn to ask the right questions to uncover just where your students get confused, and apply practical strategies to get them quickly back on track – while learning is already underway. It’s all here in this detailed and time-saving guide. Organized by strand, the probes will enable you to: Quickly and objectively identify and correct students’ difficulties Systematically address conceptual misunderstandings and procedural mistakes-- before they become long-term problems Plan targeted instruction and remediation in multiplication and division, problem solving, the four operations, factorization, and beyond Master the essential CCSM mathematical processes and proficiencies for Grades 3-5 With the help of sample student responses, extensive Teacher Notes, reproducibles, and research-based tips and resources, you’ll quickly eliminate the guesswork and join thousands of busy teachers who’ve used these easy-to-implement probes to foster solid math proficiency!