Developing Thinking In Algebra
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Developing Thinking In Algebra
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Author : John Mason
language : en
Publisher: SAGE
Release Date : 2005-04-23
Developing Thinking In Algebra written by John Mason and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-23 with Mathematics categories.
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.
Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds
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Author : Carolyn Kieran
language : en
Publisher: Springer
Release Date : 2018-09-01
Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds written by Carolyn Kieran and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-01 with Education categories.
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.
Early Algebra
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Author : Carolyn Kieran
language : en
Publisher: Springer
Release Date : 2016-07-11
Early Algebra written by Carolyn Kieran and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Education categories.
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.
Thinking Mathematically
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Author : Thomas P. Carpenter
language : en
Publisher: Heinemann Educational Books
Release Date : 2003
Thinking Mathematically written by Thomas P. Carpenter and has been published by Heinemann Educational Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Education categories.
In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic
Developing Thinking In Geometry
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Author : Sue Johnston-Wilder
language : en
Publisher: SAGE
Release Date : 2005-09-14
Developing Thinking In Geometry written by Sue Johnston-Wilder and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-14 with Education categories.
This text and interactive CD-ROM help teachers extend their instructional practices through innovative approaches for teaching geometry as developed by the Open University's Centre for Mathematics Education.
Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5
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Author : Maria L. Blanton
language : en
Publisher:
Release Date : 2011
Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5 written by Maria L. Blanton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Algebra categories.
Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.
Early Algebraization
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Author : Jinfa Cai
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-24
Early Algebraization written by Jinfa Cai 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 2011-02-24 with Education categories.
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.
Algebra In The Early Grades
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Author : James J. Kaput
language : en
Publisher: Routledge
Release Date : 2017-09-25
Algebra In The Early Grades written by James J. Kaput and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Education categories.
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.
Fostering Algebraic Thinking
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Author : Mark J. Driscoll
language : en
Publisher: Heinemann Educational Books
Release Date : 1999
Fostering Algebraic Thinking written by Mark J. Driscoll and has been published by Heinemann Educational Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Education categories.
Fostering Algebraic Thinking is a timely and welcome resource for middle and high school teachers hoping to ease their students' transition to algebra.
Approaches To Algebra
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Author : N. Bednarz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approaches To Algebra written by N. Bednarz 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 2012-12-06 with Education categories.
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.