Encountering Algebra

Encountering Algebra,. A Algebra conceptions of, 5, 10, 141–143, 163,235, 243, 244 curriculum, 2, 4, 31, 73, 74, 100, 103, 108 discourse, 165, 175–180, 182, ...


Author: Cecilia Kilhamn

Publisher: Springer

ISBN: 9783030175771

Category: Education

Page: 263

View: 939

The book reports a comparative research project about algebra teaching and learning in four countries. Algebra is a central topic of learning across the world, and it is well-known that it represents a hurdle for many students. The book presents analyses built on extensive video-recordings of classrooms documenting the first introduction to symbolic algebra (students aged 12 to 14). While the content addressed in all classrooms is variables, expressions and equations, the teaching approaches are diverse. The chapters bring the reader into different algebra classrooms, discussing issues such as mathematization and social norms, the role of mediating tools and designed examples, and teacher beliefs. By comparing classrooms, new insights are generated about how students understand the algebraic content, how teachers instruct, and how both parties deal with difficulties in learning elementary algebra. The book also describes a research methodology using video in search of taken-for-granted aspects of algebra lessons.

Planting the Seeds of Algebra PreK 2

To be more specific, I have written this book for teachers in the early grades, whose students are years away from encountering Algebra as a formal course, ...


Author: Monica Neagoy

Publisher: Corwin Press

ISBN: 9781452279701

Category: Education

Page: 208

View: 617

Help young minds explore algebraic concepts This book shows teachers how to create a strong foundation in algebra for very young children. Using in-depth math “explorations,” the author unpacks—step by step—the hidden connections to higher algebra. Each exploration contains an elegantly simple grade-banded lesson (on addition, subtraction, patterns, and odd and even numbers), followed by a discussion of the lesson's algebra connections, as well as suggestions for additional problems to explore. Throughout, readers will find: Clear explanations of algebraic connections Specific strategies for teaching the key ideas of algebra Lesson modifications for older or younger students An array of age-appropriate problems and games

Developing Thinking in Algebra

School algebra is generalised arithmetic not because letters are used in place ... the roots of algebra are found in expressing generality: encountering the ...


Author: John Mason

Publisher: SAGE

ISBN: 9781847878281

Category: Education

Page: 336

View: 809

'This is an incredibly interesting and thought provoking book. Intended for anyone interested in developing their own mathematical thinking, or of the students they teach, whether at a primary level or right through to FE. The book is a delightful blend of theory and practice - encouraging the reader to participate, to solve problems and to develop their own thinking' - Peter Hall, Imberhorne School, East Grinstead‘ Mason, Graham, and Johnston-Wilder have admirably succeeded in casting most of school algebra in terms of generalisation activity? not just the typical numerical and geometric pattern-based work, but also solving quadratics and simultaneous equations, graphing equations, and factoring. The authors raise our awareness of the scope of generalization and of the power of using this as a lens not just for algebra but for all of mathematics!’ - Professor Carolyn Kieran, Departement de Mathematiques, Universite du Quebec a Montreal Algebra has always been a watershed for pupils learning mathematics. This book will enable you to think about yourself as a learner of algebra in a new way, and thus to teach algebra more successfully, overcoming difficulties and building upon skills that all learners have. This book is based on teaching principles developed by the team at The Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning algebra. Written for teachers working with pupils aged 7-16, it includes numerous tasks ready for adaption for your teaching and discusses principles that teachers have found useful in preparing and conducting lessons. This is a 'must have' resource for all teachers of mathematics, primary or secondary, and their support staff. Anyone who wishes to create an understanding and enthusiasm for algebra, based upon firm research and effective practice, will enjoy this book. This book is the course reader for The Open University Course ME625 Developing Algebraic Thinking

Mathematical Encounters

Date: 24 November 2000: Hello everyone, I was wondering if anyone could help me with a math problem Iam having. I am wanting to know if there is any way ...


Author: Paul Chika Emekwulu

Publisher: Xlibris Corporation

ISBN: 9781453551035

Category: Mathematics

Page: 356

View: 969

Norman Author Pens Innovative Math Book "Mathematical Encounters for the Inquisitive Mind" a new work by Paul Chika Emekwulu of Norman takes an original approach to math. Emekwulu, an award-winning author and motivational speaker, hopes his works has something for everyone. The work is not strictly in line with any traditional curriculum. Sample Chapters include: A Student ́s Logic Under Trial: Verifying a summation strategy for first n Fibonacci numbers From Murder Scene to Building and Transforming Word Problems into Simple Equations Using Your Intuition for Self-Empowerment Mathematics Behind Bars: My Experience with U.S. Immigration (Courtesy of The Norman Transcript)

Introduction to Abstract Algebra Third Edition

Preface The first and second editions of Introduction to Abstract Algebra have proved very helpful to many students encountering abstract algebra for the ...


Author: T.A. Whitelaw

Publisher: CRC Press

ISBN: 0751401471

Category: Mathematics

Page: 256

View: 320

The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.



Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 9781475718607

Category: Mathematics

Page: 138

View: 217

Dynamics Of Complex And Irregular Systems Bielefeld Encounters In Mathematics And Physics Viii

Let us consider the associative algebra C of 2x2 matrices ( 0 1 _ (0 0 \ w, - _ ( 1 0 generated by Q+ = (. ...) and Q_ = ( }) We call I = Q10_ = ( }) and Y ...


Author: Blanchard P H

Publisher: World Scientific

ISBN: 9789814552325


Page: 372

View: 923

This volume includes papers by leading mathematicians in the fields of stochastic analysis, white noise theory and quantum information, together with their applications. The papers selected were presented at the International Conference on Stochastic Analysis: Classical and Quantum held at Meijo University, Nagoya, Japan from 1 to 5 November 2004. The large range of subjects covers the latest research in probability theory.

Differentiated Pathways of the Brain

Consider a chunk from Dr. Dweck's discussion of two students encountering algebra: Finally, students in the fixed mind-set don't recover well from setbacks.


Author: Dr. Linda Karges-Bone

Publisher: Lorenz Educational Press

ISBN: 9780787780265

Category: Education

Page: 144

View: 363

Which colors can stimulate creative thinking? What scents might help to calm a child who has anxiety? Why do certain classroom groupings facilitate learning, while others create tension? How can boys harness their boundless energy to attack language arts or girls draw on their strong verbal skills to make the most of a mathematics problem? Using current brain research, this book discusses sensory-rich learning techniques and gender-specific teaching methods used to stimulate the minds of your students. Based on Dr. Karges-Bone?s successful books Beyond Hands-On and More Than Pink and Blue, this resource is a must-read for all teachers exploring differentiated pathways of the brain!

A Treatise on Algebra Arithmetical algebra

a result which indicates that the final operation , to which the application of the rule conducts us , is impossible : we are perpetually encountering , in ...


Author: George Peacock


ISBN: HARVARD:32044050776194

Category: Algebra


View: 414

Encountering the World of Islam

Al-Khwarazmi is also the author of the first book on algebra. This science was developed by Muslims on the basis of earlier Greek and Indian works of a ...


Author: Keith E. Swartley

Publisher: InterVarsity Press

ISBN: 9780830856442

Category: Religion

Page: 574

View: 294

This comprehensive, evangelistic resource collects articles from eighty authors who have lived throughout the Muslim world. You will gain a positive, biblical perspective on the history of Islam, the current political landscape and much more.

Introduction to Noncommutative Algebra

Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings.


Author: Matej Brešar

Publisher: Springer

ISBN: 9783319086934

Category: Mathematics

Page: 199

View: 889

Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

Deleuze and Education

But it is at these levels that the standard, abstract math-image is ... even those of a middle-school student encountering algebra for the first time or a ...


Author: Inna Semetsky

Publisher: Edinburgh University Press

ISBN: 9780748669455

Category: Philosophy

Page: 288

View: 492

These 13 essays address the broad territory of educational theory and philosophy of education. Moving from the formal to post-formal mode of education, the contributors explore education as an experimental and experiential process of becoming grounded in life that represents the becoming-Other of Deleuze's thought.

Causality in a Social World

... one may hypothesize that a student is unlikely to learn algebra well in ... of inferior treatments such as encountering an incompetent math teacher who ...


Author: Guanglei Hong

Publisher: John Wiley & Sons

ISBN: 9781118332566

Category: Mathematics

Page: 425

View: 598

Causality in a Social World introduces innovative new statistical research and strategies for investigating moderated intervention effects, mediated intervention effects, and spill-over effects using experimental or quasi-experimental data. The book uses potential outcomes to define causal effects, explains and evaluates identification assumptions using application examples, and compares innovative statistical strategies with conventional analysis methods. Whilst highlighting the crucial role of good research design and the evaluation of assumptions required for identifying causal effects in the context of each application, the author demonstrates that improved statistical procedures will greatly enhance the empirical study of causal relationship theory. Applications focus on interventions designed to improve outcomes for participants who are embedded in social settings, including families, classrooms, schools, neighbourhoods, and workplaces.

Algebra Geometry

In fact, the first surprise on encountering university mathematics is that algebra is not singular but plural. Different algebras are governed by different ...


Author: Mark V. Lawson

Publisher: CRC Press

ISBN: 9781482246490

Category: Mathematics

Page: 384

View: 349

Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra

Encountering Education in the Global

One does not always discover the algebraic formula first and then calculate ... school children would need to learn algebra before they did number series.


Author: Fazal Rizvi

Publisher: Routledge

ISBN: 9781317932758

Category: Education

Page: 222

View: 308

In the World Library of Educationalists, international experts compile career-long collections of what they judge to be their finest pieces – extracts from books, key articles, salient research findings, major theoretical and practical contributions – so the world can read them in a single manageable volume. Readers will be able to follow the themes and strands and see how their work contributes to the development of the field. This volume brings together the selected works of Fazal Rizvi. Born in India, Fazal Rizvi has lived and worked in a number of countries, including Australia, England and the United States. Most of his educational encounters have been 'in the global'. He has developed a keen sense of the multiple and conflicting ways in which transnational ties and interactions are transforming the spaces in which identities and cultures are forged and performed, and in which education takes place. Much of his research has sought to examine how educational systems around the world have interpreted and responded to the challenges and opportunities of globalization. In this collection of his papers, written over a period of more than two decades, Fazal Rizvi seeks to understand the shifting discourses and practices of globalization and education, critically examining the ways in which these are: reshaping our sense of identity and citizenship, and our communities creating transnational systems of ties, networks and exchange taken into account in the development of policies and programs of educational reform producing uneven social effects that benefit some communities more than others. Fazal Rizvi's analysis shows how recent global transformations have mostly been interpreted through the conceptual prism of a neo-liberal imaginary that have undermined education's democratic and cosmopolitan possibilities.

Algebra and Algebraic Thinking in School Mathematics

... Rather than ( re- ) encountering algebraic manipulation as syntax devoid of meaning , teachers here learn to use algebraic notation to represent ideas .


Author: Carole E. Greenes


ISBN: STANFORD:36105130532364

Category: Algebra

Page: 311

View: 619

Examines the status of algebra in our schools and the changes that the curriculum has undergone over the past several years. Includes successful classroom practises for developing algebraic reasoning abilities and improving overall understanding.

Connecting Abstract Algebra to Secondary Mathematics for Secondary Mathematics Teachers

In School Algebra, students are introduced to the concept of inverse in many different settings. They encounter additive inverses, multiplicative inverses, ...


Author: Nicholas H. Wasserman

Publisher: Springer

ISBN: 9783319992143

Category: Education

Page: 461

View: 816

Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.

Encounters with Euclid

Descartes had applied algebraic methods to geometry, describing curved lines ... In several of his algebra books he left marginal annotations and notes, ...


Author: Benjamin Wardhaugh

Publisher: Princeton University Press

ISBN: 9780691211695

Category: Mathematics

Page: 416

View: 388

A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.

Encounters of a Mathematician

outstanding events in the history of algebra was the publication of van der Waerden's book Moderne Algebra, which brought about a strong tendency towards ...


Author: Walter Ledermann

Publisher: Lulu.com

ISBN: 9781409282679

Category: Biography & Autobiography

Page: 142

View: 676

Professor Walter Ledermann is one of the great algebraists of the twentieth century. His memoirs begin with life in pre-war Germany, the murder of several members of his family, and of the joy he found in mathematics and music. As the story of his remarkable life unfolds, we are entranced by tales of Scotland during the war and of academic life in Manchester and Sussex. His memoirs contain numerous entertaining, and often hilarious anecdotes of his encounters with famous mathematicians and physicists, such as Issai Schur, Heinz Hopf, Max Plank, Erwin Schroedinger, Edmund Whittaker, Alec Aitkin, Max Born and Alan Turing.