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.
Bringing Math Students Into The Formative Assessment Equation
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Author : Susan Janssen Creighton
language : en
Publisher: Corwin Press
Release Date : 2015-01-21
Bringing Math Students Into The Formative Assessment Equation written by Susan Janssen Creighton and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-21 with Education categories.
Make formative assessment work for you—and your math students! Finally, formative assessment that adds up! Bringing Math Students Into the Formative Assessment Equation is the ultimate resource for helping teachers implement formative assessment in the middle school mathematics classroom. And it’s much more than that. With this research-based, teacher-tested guide, you won’t just learn effective teaching strategies—you’ll turn your students into self-regulated learners. They’ll monitor and assess their own progress—and communicate to you about it! Features include: A clear and manageable six-aspect instructional model Detailed strategies for helping students own their successes Real-life examples from middle school mathematics teachers Useful resources and a companion website to help you implement formative assessment in your classroom Formative assessment isn’t just for teachers anymore. With the help of this essential resource, you’ll work together with your students toward a common goal of math success. "This book is outstanding. I would recommend it to any math educator. The depth of research integrated into practice is extensive and, as a result, it is the most practical book I have come across related to formative assessment and mathematics The self-regulation aspects, as well as the ownership and involvement emphasized in the book, went beyond the traditional cognitive strategies endorsed in most books." Marc Simmons, Principal Ilwaco Middle School, Ocean Beach School District, Long Beach, WA "The ideas in this book are brought to life with examples of teachers and students in the classroom. The teacher voices, comments, and quotes lend credibility and are a big component of the book’s strengths as well as the visuals and graphics." Rita Tellez, Math Coordinator Ysleta Independent School District, El Paso, TX
Open Middle Math
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Author : Robert Kaplinsky
language : en
Publisher: Taylor & Francis
Release Date : 2023-10-10
Open Middle Math written by Robert Kaplinsky and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Education categories.
This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.
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.
The Nature Of Mathematical Thinking
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Author : Robert J. Sternberg
language : en
Publisher: Routledge
Release Date : 2012-10-12
The Nature Of Mathematical Thinking written by Robert J. Sternberg and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-12 with Education categories.
Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.
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.