What Mathematics Do Students Know And How Is That Knowledge Changing

Author : Peter Kloosterman
Publisher : IAP
ISBN 13 : 1681232022
Total Pages : 385 pages
Book Rating : 4.27/5 ( download)

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Download or read book What Mathematics Do Students Know and How is that Knowledge Changing? written by Peter Kloosterman and published by IAP. This book was released on 2015-09-01 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended for researchers, curriculum developers, policy makers, and classroom teachers who want comprehensive information on what students at grades 4, 8, and 12 (the grades assessed by NAEP) can and cannot do in mathematics. After two introductory chapters on the design of NAEP, the volume contains a chapter on the challenges in analyzing NAEP data at the item level followed by five chapters that report 2005 through 2013 student performance on specific assessment items. These chapters are organized by content area and then by topic (e.g., understanding of place value, knowledge of transformations, ability to use metric and U.S. systems of measurement) and thus provide baseline data on the proportion of students who are able to complete the mathematics tasks currently used in the upper elementary, middle, and high?school mathematics curriculum. Additional chapters focus on student reasoning, U.S. performance on international assessments, and using construct analysis rather than percent correct on clusters of items to understand student knowledge on specific mathematics topics. Several themes emerge from the volume. One is that while the rate of improvement in mathematics learning in grades 4 and 8 has slowed in recent years, it has slowed more on some topics than others. Another is that relatively minor changes in wording can have significant effects on student performance and thus it is difficult to be specific about what students can do without knowing exactly what questions they were asked. A third theme is that changes in performance over time can sometimes but not always be understood in terms of what students are taught. For example, there were substantial gains on several grade 4 items requiring understanding of fractions and that is probably because the amount of instruction on fractions in grades 3 and 4 has been increasing. In contrast, while relatively few twelfth?grade students have ever been good at factoring trinomials, performance on this skill seems to be decreasing. This suggests that while more students are completing advanced mathematics courses in high school, these courses are not helping in the area of factoring trinomials. Finally, there are limitations to using NAEP as a measure of student performance on the Common Core State Standards. To the extent that NAEP can be used, however, the NAEP data show a substantial gap between expectations and performance.

Author : Jo Boaler
Publisher : Penguin
ISBN 13 : 9780670019526
Total Pages : 296 pages
Book Rating : 4.26/5 ( download)

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Download or read book What's Math Got to Do with It? written by Jo Boaler and published by Penguin. This book was released on 2008 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses how to make mathematics for children enjoyable and why it is important for American children to succeed in mathematics and choose math-based career paths in the future.

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 52 pages
Book Rating : 4.88/5 ( download)

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Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we’re teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre--kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Author : Dylan Wiliam
Publisher : Solution Tree Press
ISBN 13 : 1936765012
Total Pages : 200 pages
Book Rating : 4.10/5 ( download)

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Download or read book Embedded Formative Assessment written by Dylan Wiliam and published by Solution Tree Press. This book was released on 2011-11-01 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formative assessment plays an important role in increasing teacher quality and student learning when it’s viewed as a process rather than a tool. Emphasizing the instructional side of formative assessment, this book explores in depth the use of classroom questioning, learning intentions and success criteria, feedback, collaborative and cooperative learning, and self-regulated learning to engineer effective learning environments for students.

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309089506
Total Pages : 265 pages
Book Rating : 4.00/5 ( download)

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Download or read book How Students Learn written by National Research Council and published by National Academies Press. This book was released on 2005-01-28 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: How Students Learn: Science in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in science at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. This book discusses how to build straightforward science experiments into true understanding of scientific principles. It also features illustrated suggestions for classroom activities.

Author : Beth McCord Kobett
Publisher : Corwin
ISBN 13 : 1544374909
Total Pages : 273 pages
Book Rating : 4.01/5 ( download)

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Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin. This book was released on 2020-02-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Author : John Hattie
Publisher : Corwin Press
ISBN 13 : 1506362958
Total Pages : 209 pages
Book Rating : 4.53/5 ( download)

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Download or read book Visible Learning for Mathematics, Grades K-12 written by John Hattie and published by Corwin Press. This book was released on 2016-09-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Patrick M. Jenlink
Publisher : IAP
ISBN 13 : 1648027466
Total Pages : 265 pages
Book Rating : 4.68/5 ( download)

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Download or read book Mathematics as the Science of Patterns written by Patrick M. Jenlink and published by IAP. This book was released on 2022-02-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Author : John Sutton
Publisher :
ISBN 13 : 9781741700435
Total Pages : 109 pages
Book Rating : 4.34/5 ( download)

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Download or read book EDthoughts written by John Sutton and published by . This book was released on 2009 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Judy Willis
Publisher : ASCD
ISBN 13 : 1416612289
Total Pages : 270 pages
Book Rating : 4.85/5 ( download)

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Download or read book Learning to Love Math written by Judy Willis and published by ASCD. This book was released on 2010-09-09 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a way to get students to love math? Dr. Judy Willis responds with an emphatic yes in this informative guide to getting better results in math class. Tapping into abundant research on how the brain works, Willis presents a practical approach for how we can improve academic results by demonstrating certain behaviors and teaching students in a way that minimizes negativity. With a straightforward and accessible style, Willis shares the knowledge and experience she has gained through her dual careers as a math teacher and a neurologist. In addition to learning basic brain anatomy and function, readers will learn how to * Improve deep-seated negative attitudes toward math. * Plan lessons with the goal of "achievable challenge" in mind. * Reduce mistake anxiety with techniques such as errorless math and estimation. * Teach to different individual learning strengths and skill levels. * Spark motivation. * Relate math to students' personal interests and goals. * Support students in setting short-term and long-term goals. * Convince students that they can change their intelligence. With dozens of strategies teachers can use right now, Learning to Love Math puts the power of research directly into the hands of educators. A Brain Owner's Manual, which dives deeper into the structure and function of the brain, is also included—providing a clear explanation of how memories are formed and how skills are learned. With informed teachers guiding them, students will discover that they can build a better brain . . . and learn to love math!