Algebra Structure Sense Development Amongst Diverse Learners

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Algebra Structure Sense Development amongst Diverse Learners

Author : Teresa Rojano
Publisher : Taylor & Francis
ISBN 13 : 1000591530
Total Pages : 210 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Algebra Structure Sense Development amongst Diverse Learners by : Teresa Rojano

Download or read book Algebra Structure Sense Development amongst Diverse Learners written by Teresa Rojano and published by Taylor & Francis. This book was released on 2022-06-07 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels. Positing algebra structure sense as fundamental to developing students’ broader mathematical maturity and advanced thinking, this text reviews conceptual, historical, cognitive, and semiotic factors, which influence the acquisition of algebra structure sense. It provides empirical evidence to demonstrate the feasibility of linking algebra structure sense to technological tools and promoting it amongst diverse learners. Didactic approaches include the use of adaptive digital environments, gamification, diagnostic and monitoring tools, as well as exercises and algebraic sequences of varied complexity. Advocating for a focus on both intuitive and formal knowledge, this volume will be of interest to students, scholars, and researchers with an interest in educational research, as well as mathematics education and numeracy.

The Role of the History of Mathematics in the Teaching/Learning Process

Author : Sixto Romero Sanchez
Publisher : Springer Nature
ISBN 13 : 3031299000
Total Pages : 464 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis The Role of the History of Mathematics in the Teaching/Learning Process by : Sixto Romero Sanchez

Download or read book The Role of the History of Mathematics in the Teaching/Learning Process written by Sixto Romero Sanchez and published by Springer Nature. This book was released on 2023-06-15 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents multiple perspectives on the uses of the history of mathematics for teaching and learning, including the value of historical topics in challenging mathematics tasks, for provoking teachers’ reflection on the nature of mathematics, curriculum development questions that mirror earlier pedagogical choices in the history of mathematics education, and the history of technological innovations in the teaching and learning of mathematics. An ethnomathematical perspective on the history of mathematics challenges readers to appreciate the role of mathematics in perpetuating consequences of colonialism. Histories of the textbook and its uses offer interesting insights into how technology has changed the fundamental role of curriculum materials and classroom pedagogies. History is explored as a source for the training of teachers, for good puzzles and problems, and for a broad understanding of mathematics education policy. Third in a series of sourcebooks from the International Commission for the Study and Improvement of Mathematics Teaching, this collection of cutting-edge research, stories from the field, and policy implications is a contemporary and global perspective on current possibilities for the history of mathematics for mathematics education. This latest volume integrates discussions regarding history of mathematics, history of mathematics education and history of technology for education that have taken place at the Commission's recent annual conferences.

Number Sense and Algebraic Thinking

Author : Carla McNeil
Publisher :
ISBN 13 : 9780790307138
Total Pages : 24 pages
Book Rating : 4.3/5 (71 download)

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Book Synopsis Number Sense and Algebraic Thinking by : Carla McNeil

Download or read book Number Sense and Algebraic Thinking written by Carla McNeil and published by . This book was released on 2005-01-01 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides exercises, activities, and games to help understand the concepts of numeracy and algebraic thinking. Designed to support Mathematics in the New Zealand curriculum. Suggested level: primary, intermediate.

Algebra in the Early Grades

Author : James J. Kaput
Publisher : Routledge
ISBN 13 : 1351577093
Total Pages : 552 pages
Book Rating : 4.3/5 (515 download)

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Book Synopsis Algebra in the Early Grades by : James J. Kaput

Download or read book Algebra in the Early Grades written by James J. Kaput and published by Routledge. This book was released on 2017-09-25 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.

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

Author : Carolyn Kieran
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.

Bridging the Gap Between Arithmetic & Algebra

Author : Bradley S. Witzel
Publisher : Council For Exceptional Children
ISBN 13 : 0865865086
Total Pages : 200 pages
Book Rating : 4.8/5 (658 download)

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Book Synopsis Bridging the Gap Between Arithmetic & Algebra by : Bradley S. Witzel

Download or read book Bridging the Gap Between Arithmetic & Algebra written by Bradley S. Witzel and published by Council For Exceptional Children. This book was released on 2015-11-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although two federal panels have concluded that all students can learn mathematics and most can succeed through Algebra 2, the abstractness of algebra and missing precursor understandings may be overwhelming to many students … and their teachers. Bridging the Gap Between Arithmetic & Algebra responds to this need for instruction and interventions that go beyond typical math lesson plans. Providing a review of evidence-based practices, the book is an essential reference for mathematics teachers and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra. Audiences: General education (mathematics) teachers, special education teachers, administrators, teacher educators.

The Impact on Algebra Vs. Geometry of a Learner's Ability to Develop Reasoning Skills

Author : Lisa a. Johnson Q. M. E.
Publisher :
ISBN 13 : 9781480912021
Total Pages : 54 pages
Book Rating : 4.9/5 (12 download)

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Book Synopsis The Impact on Algebra Vs. Geometry of a Learner's Ability to Develop Reasoning Skills by : Lisa a. Johnson Q. M. E.

Download or read book The Impact on Algebra Vs. Geometry of a Learner's Ability to Develop Reasoning Skills written by Lisa a. Johnson Q. M. E. and published by . This book was released on 2014-10-30 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this master's thesis, Dr. Lisa A. Johnson Q.M.E. examines the impact of three reasoning skills-number sense, structure sense, and abstract reasoning-on algebra and geometry. The study concentrates its efforts on data compiled from more than twenty researchers in this area, an extensive annotated bibliography, and work done at fictisciously named Union High School, real school classes consisting of 48 math students and eight math teachers. Through the efforts of this study, Dr. Johnson determined that algebra relies on abstract reasoning and structure sense, while geometry does not. Moreover, Dr. Johnson observed that further instruction needs to be given to teachers on communicating the three reasoning skills, as the teachers studied were not sufficiently knowledgeable in these areas. With teacher improvements, students in non-sufficient school systems could better excel in mathematics. About the Author Dr. Johnson holds two bachelors in sciences; three master's degrees, one of which is in Math Education Curriculum, and a doctorate degree. She attributes her success to her parents and sisters. This is her second publication.

Early Algebraization

Author : Jinfa Cai
Publisher : Springer Science & Business Media
ISBN 13 : 3642177352
Total Pages : 624 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Early Algebraization by : Jinfa Cai

Download or read book Early Algebraization written by Jinfa Cai and published by Springer Science & Business Media. This book was released on 2011-02-24 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.

Early Algebra

Author : Carolyn Kieran
Publisher : Springer
ISBN 13 : 3319322583
Total Pages : 48 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Early Algebra by : Carolyn Kieran

Download or read book Early Algebra written by Carolyn Kieran and published by Springer. This book was released on 2016-07-11 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.

Diversity, Equity, and Mathematical Learning

Author : Na¡lah Suad Nasir
Publisher : Routledge
ISBN 13 : 9781410608475
Total Pages : 288 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Diversity, Equity, and Mathematical Learning by : Na¡lah Suad Nasir

Download or read book Diversity, Equity, and Mathematical Learning written by Na¡lah Suad Nasir and published by Routledge. This book was released on 2002-09-12 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles developed for this special issue of Mathematical Thinking and Learning grew out of a series of two meetings held at Vanderbilt University in November 1999 and Northwestern University in September 2000. As a group, the six articles in this special issue have the potential to help us reframe issues of equity in mathematics education and to enrich understandings of the process by which "diverse" learners experience mathematics education. Some of these articles are theoretical in orientation and offer insights to how the sociocultural approach to equity in math education might be developed. Other papers rely on close analyses of mathematical learning in and out of the classroom to understand the construction of "equity" at the micro-level of social interactions. In sum, the articles that make up this special issue take the social and cultural worlds in which mathematics is learned to be central to the understandings of the dynamics of equity. The editors hope that the understandings of equity, diversity and mathematical learning continue to evolve and that this special issue will serve to spark thought, controversy, debate, and further research on this critically important topic.

Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown

Author : Paul Drijvers
Publisher : Springer Science & Business Media
ISBN 13 : 9460913342
Total Pages : 229 pages
Book Rating : 4.4/5 (69 download)

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Book Synopsis Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown by : Paul Drijvers

Download or read book Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown written by Paul Drijvers and published by Springer Science & Business Media. This book was released on 2011-10-19 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart of debates among teachers, educators, researchers and decision makers. What should the teaching of algebra in secondary school mathematics look like? Should it focus on procedural skills or on algebraic insight? Should it stress practice or integrate technology? Do we require formal proofs and notations, or do informal representations suffice? Is algebra in school an abstract subject, or does it take its relevance from application in (daily life) contexts? What should secondary school algebra education that prepares for higher education and professional practice in the twenty-first century look like? This book addresses these questions, and aims to inform in-service and future teachers, mathematics educators and researchers on recent insights in the domain, and on specific topics and themes such as the historical development of algebra, the role of productive practice, and algebra in science and engineering in particular. The authors, all affiliated with the Freudenthal Institute for Science and Mathematics Education in the Netherlands, share a common philosophy, which acts as a ? sometimes nearly invisible ? backbone for the overall view on algebra education: the theory of realistic mathematics education. From this point of departure, different perspectives are chosen to describe the opportunities and pitfalls of today’s and tomorrow’s algebra education. Inspiring examples and reflections illustrate current practice and explore the unknown future of algebra education to appropriately meet students’ needs.

Making Sense of Algebra

Author : Ernest Paul Goldenberg
Publisher : Heinemann Educational Books
ISBN 13 : 9780325053011
Total Pages : 0 pages
Book Rating : 4.0/5 (53 download)

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Book Synopsis Making Sense of Algebra by : Ernest Paul Goldenberg

Download or read book Making Sense of Algebra written by Ernest Paul Goldenberg and published by Heinemann Educational Books. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book has much to offer teachers of middle and high school algebra who wish to implement the Common Core Standards for all of their students." -Hyman Bass, Samuel Eilenberg Distinguished University Professor of Mathematics & Mathematics Education, University of Michigan "One of the joys of Making Sense of Algebra is how clearly and practically the 'how' question is answered." -Steven Leinwand, American Institutes for Research, author of Accessible Mathematics "Paul Goldenberg and his colleagues have done a fantastic job of connecting mathematical ideas to teaching those ideas." -David Wees, New Visions for Public Schools, New York City Every teacher wants to help students make sense of mathematics; but what if you could guide your students to expect mathematics to make sense? What if you could help them develop a deep understanding of the reasons behind its facts and methods? In Making Sense of Algebra, the common misconception that algebra is simply a collection of rules to know and follow is debunked by delving into how we think about mathematics. This "habits of mind" approach is concerned not just with the results of mathematical thinking, but with how mathematically proficient students do that thinking. Making Sense of Algebra addresses developing this type of thinking in your students through: using well-chosen puzzles and investigations to promote perseverance and a willingness to explore seeking structure and looking for patterns that mathematicians anticipate finding-and using this to draw conclusions cultivating an approach to authentic problems that are rarely as tidy as what is found in textbooks allowing students to generate, validate, and critique their own and others' ideas without relying on an outside authority. Through teaching tips, classroom vignettes, and detailed examples, Making Sense of Algebra shows how to focus your instruction on building these key habits of mind, while inviting students to experience the clarity and meaning of mathematics-perhaps for the first time. Discover more math resources at Heinemann.com/Math

Mathematics and Cognition

Author : Pearla Nesher
Publisher : CUP Archive
ISBN 13 : 9780521367875
Total Pages : 234 pages
Book Rating : 4.3/5 (678 download)

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Book Synopsis Mathematics and Cognition by : Pearla Nesher

Download or read book Mathematics and Cognition written by Pearla Nesher and published by CUP Archive. This book was released on 1990-02-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.

Teaching to the Math Common Core State Standards

Author : F. D. Rivera
Publisher : Springer
ISBN 13 : 9462099626
Total Pages : 224 pages
Book Rating : 4.4/5 (62 download)

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Book Synopsis Teaching to the Math Common Core State Standards by : F. D. Rivera

Download or read book Teaching to the Math Common Core State Standards written by F. D. Rivera and published by Springer. This book was released on 2015-06-17 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a methods book for preservice middle level majors and beginning middle school teachers. It takes a very practical approach to learning to teach middle school mathematics in an emerging Age of the Common Core State Standards. The Common Core State Standards in Mathematics (CCSSM) is not meant to be “the” official mathematics curriculum; it was purposefully developed primarily to provide clear learning expectations of mathematics content that are appropriate at every grade level and to help prepare all students to be ready for college and the workplace. A quick glance at the Table of Contents in this book indicates a serious engagement with the recommended mathematics underlying the Grade 5 through Grade 8 and (traditional pathway) Algebra I portions of the CCSSM first, with issues in content-practice assessment, learning, teaching, and classroom management pursued next and in that order. In this book we explore what it means to teach to the CCSSM within an alignment mindset involving content-practice learning, teaching, and assessment. The Common Core state content standards, which pertain to mathematical knowledge, skills, and applications, have been carefully crafted so that they are teachable, learnable, coherent, fewer, clearer, and higher. The practice standards, which refer to institutionally valued mathematical actions, processes, and habits, have been conceptualized in ways that will hopefully encourage all middle school students to engage with the content standards more deeply than merely acquiring mathematical knowledge by rote and imitation. Thus, in the CCSSM, proficiency in content alone is not sufficient, and so does practice without content, which is limited. Content and practice are both equally important and, thus, must come together in teaching, learning, and assessment in order to support authentic mathematical understanding. This blended multisourced text is a “getting smart” book. It prepares preservice middle level majors and beginning middle school teachers to work within the realities of accountable pedagogy and to develop a proactive disposition that is capable of supporting all middle school students in order for them to experience growth in mathematical understanding that is necessary for high school and beyond, including future careers.

Research agenda for mathematics education

Author : Sigrid Wagner
Publisher :
ISBN 13 : 9780873532686
Total Pages : pages
Book Rating : 4.5/5 (326 download)

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Book Synopsis Research agenda for mathematics education by : Sigrid Wagner

Download or read book Research agenda for mathematics education written by Sigrid Wagner and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Developing Thinking in Algebra

Author : John Mason
Publisher : SAGE
ISBN 13 : 9781412911719
Total Pages : 340 pages
Book Rating : 4.9/5 (117 download)

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Book Synopsis Developing Thinking in Algebra by : John Mason

Download or read book Developing Thinking in Algebra written by John Mason and published by SAGE. This book was released on 2005-04-23 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: By integrating pedagogy and subject knowledge through experiencing a variety of tasks for learners, this book makes it possible for all learners to succeed in thinking algebraically.

The Nature and Role of Algebra in the K-14 Curriculum

Author : Center for Science, Mathematics, and Engineering Education
Publisher : National Academies Press
ISBN 13 : 0309522455
Total Pages : 187 pages
Book Rating : 4.3/5 (95 download)

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Book Synopsis The Nature and Role of Algebra in the K-14 Curriculum by : Center for Science, Mathematics, and Engineering Education

Download or read book The Nature and Role of Algebra in the K-14 Curriculum written by Center for Science, Mathematics, and Engineering Education and published by National Academies Press. This book was released on 1998-10-07 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.