How Students Think When Doing Algebra
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How Students Think When Doing Algebra
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Author : Steve Rhine
language : en
Publisher: IAP
Release Date : 2018-11-01
How Students Think When Doing Algebra written by Steve Rhine and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-01 with Education categories.
Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and students’ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematics’ (NCTM) call to better link research and practice by capturing what we have learned about students’ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on students’ algebraic thinking to capture what might be useful information for teachers to know—over 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic concepts—their misconceptions, ways of thinking, and when and how they are challenged to understand—and use that knowledge to anticipate students’ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naïve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachers’ “experience” with how students think when doing algebra in middle or high school as well as to supplement veteran teachers’ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a student’s struggles with particular algebraic ideas—to help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a “how to” book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, “how might my students struggle with this algebraic concept I am about to teach?” The primary audience for this book is early career mathematics teachers who don’t have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.
How To Think About Abstract Algebra
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Author : Lara Alcock
language : en
Publisher: Oxford University Press
Release Date : 2021-02-04
How To Think About Abstract Algebra written by Lara Alcock and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-04 with Science categories.
How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about. This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five topics: binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education. The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.
Classroom Ready Rich Algebra Tasks Grades 6 12
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Author : Barbara J. Dougherty
language : en
Publisher: Corwin Press
Release Date : 2023-03-15
Classroom Ready Rich Algebra Tasks Grades 6 12 written by Barbara J. Dougherty and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Education categories.
Stop algebra from being a mathematical gatekeeper. With rich math tasks, all students can succeed. Every teacher strives to make instruction effective and interesting, yet traditional methods of teaching algebra are not working for many students! That’s a problem. But the answer isn’t to supplement the curriculum with random tasks. Classroom Ready-Rich Math Tasks for Grades 6-12 equips you with a cohesive solution--50+ mathematical tasks that are rich, research-based, standards-aligned, and classroom-tested. The tasks: Are organized into learning progressions that help all students make the leap from arithmetic to algebra Offer students interesting mathematics problems to think about and solve so math is investigative, interactive, and engaging Provide opportunities for you to connect new content to prior knowledge or focus on an underdeveloped concept Engage students in conceptual understanding, procedural practice, and problem solving through critical thinking and application Come with downloadable planning tools, student resource pages, and extension questions Include additional support for students who may be struggling Every learner deserves opportunities to engage in meaningful, rigorous mathematics. And every teacher can develop mathematical thinking and reasoning abilities in students. Part of the bestselling series spanning elementary and middle school, Classroom-Ready Rich Algebra Tasks, Grades 6-12 is a powerful add-on to any core mathematics program at your school.
The Future Of The Teaching And Learning Of Algebra
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Author : Kaye Stacey
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-19
The Future Of The Teaching And Learning Of Algebra written by Kaye Stacey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-19 with Education categories.
This book presents a wide-ranging, international perspective on the state of the field of algebra from invited participants to the 12th ICMI Study Conference held in Melbourne, Australia in 2001. The authors are renowned academics from all around the world who have written individual chapters associated with the teaching and learning of algebra that relate to their particular areas of research and teaching expertise. The book includes information about different approaches to the teaching and learning of algebra - from early algebra to tertiary algebra, the impact of tools and technology (including Computer Algebra Systems), the role of symbols and language, teachers of algebra, and the history of algebra. The Future of the Teaching and Learning of Algebra: the 12th ICMI Study is of interest to researchers, curriculum developers, educational policy makers, teachers of mathematics, and trainee mathematics teachers.
Handbook Of Research On Teacher Education In The Digital Age
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Author : Niess, Margaret L.
language : en
Publisher: IGI Global
Release Date : 2015-08-03
Handbook Of Research On Teacher Education In The Digital Age written by Niess, Margaret L. and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-03 with Education categories.
Traditional classrooms are fast becoming a minority in the education field. As technologies continue to develop as a pervasive aspect of modern society, educators must be trained to meet the demands and opportunities afforded by this technology-rich landscape. The Handbook of Research on Teacher Education in the Digital Age focuses on the needs of teachers as they redesign their curricula and lessons to incorporate new technological tools. Including theoretical frameworks, empirical research, and best practices, this book serves as a guide for researchers, educators, and faculty and professional developers of distance learning tools.
Classroom Research On Mathematics And Language
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Author : Núria Planas
language : en
Publisher: Taylor & Francis
Release Date : 2021-03-22
Classroom Research On Mathematics And Language written by Núria Planas and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-22 with Education categories.
This book offers an international perspective on the current and future state of the research, focusing, in particular, on the role and use of language in mathematics school teaching and learning. It focuses on the development of a unified view of the languages of the learners, of the teachers and of mathematics by considering the role of language in the learning, teaching and doing of mathematics in the classroom, and the current richness and plurality of language and culture. The contributions in this volume combine to show how views of language and of language research in mathematics education have changed significantly in recent decades, and how they will continue to change and become even more complex and challenging in the era of diversity. All of these contributions by leading scholars are grouped into two sections for emphasis on issues of: • Theorising the complexity of language in mathematics teaching and learning • Opening spaces of learning with mathematics classroom research on language This book will be of great interest to mathematics teachers, teacher educators, curriculum developers and mathematics education researchers who deal with the study and implementation of pedagogies of mathematics teaching and learning, specifically in regions of the world which are culturally and sociolinguistically diverse.
Doing Math In Morning Meeting
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Author : Andy Dousis
language : en
Publisher: Center for Responsive Schools, Inc.
Release Date : 2010
Doing Math In Morning Meeting written by Andy Dousis and has been published by Center for Responsive Schools, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Education categories.
Bring joy and energy to math learning without adding to your already-packed schedule! Here are 150 fun and engaging math activities suitable for kindergartners to 5th graders, with math-themed ideas for all four Morning Meeting components: greeting, group activity, sharing, and morning message. Use these games, songs, chants, hands-on experiments, and more to inspire students' interest in math and help them practice skills. Each activity includes easy how-to steps; relevant NCTM content and process standards; specific math skills addressed; materials needed (all require few or no materials); tips on preparing students for success; math vocabulary to emphasize; and variations and extensions.
Traditional Math An Effective Strategy That Teachers Feel Guilty Using
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Author : Barry Garelick
language : en
Publisher: Hachette UK
Release Date : 2022-11-04
Traditional Math An Effective Strategy That Teachers Feel Guilty Using written by Barry Garelick and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-04 with Education categories.
"Despite experiencing our teaching in different times, we are both oriented to traditional math teaching. It wasn't because we were both taught that way, as some may believe, but because that method worked for us and we have seen it work for our students. It is efficient, effective, non-confusing and helped our students develop mathematical reasoning, understanding, and confidence. Most importantly it helped them to be successful." So begins the book on traditional math, which provides a glimpse of what explicit instruction looks like in the classroom for grades K through 8. Barry Garelick and J.R. Wilson are retired math teachers who describe the methods of traditionally taught math that they used in their teaching. Their descriptions serve two purposes: 1) It provides assurance to teachers who may already practice these methods that they are not alone, and 2) For others, it may provide some new ideas.
Special Education Design And Development Tools For School Rehabilitation Professionals
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Author : Singh, Ajay
language : en
Publisher: IGI Global
Release Date : 2019-12-13
Special Education Design And Development Tools For School Rehabilitation Professionals written by Singh, Ajay and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-13 with Education categories.
Educators who work with students with disabilities have the unique challenge of providing comprehensive and quality educational experiences for students who have a wide range of abilities and levels of focus. Pedagogies and educational strategies can be applied across a student population, though they tend to have varied success. Developing adaptive teaching methods that provide quality experiences for students with varied disabilities are necessary to promote success for as many of these students as possible. Special Education Design and Development Tools for School Rehabilitation Professionals is a comprehensive research publication that examines special education practices and provides in-depth evaluations of pedagogical practices for improved educational experiences for students with disabilities. Highlighting a range of topics such as bilingual education, psychometrics, and physical education, this book is ideal for special education teachers, instructors, rehabilitation professionals, academicians, school administrators, instructional designers, curriculum developers, principals, educational software developers, researchers, and students.
The Nature And Role Of Algebra In The K 14 Curriculum
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 1998-09-23
The Nature And Role Of Algebra In The K 14 Curriculum written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-23 with Education categories.
With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.