Algebra And Algebraic Thinking In School Mathematics
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Algebra And Algebraic Thinking In School Mathematics
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Author : Carole E. Greenes
language : en
Publisher:
Release Date : 2008
Algebra And Algebraic Thinking In School Mathematics written by Carole E. Greenes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Education categories.
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.
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.
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
Algebra And Algebraic Thinking In School Mathematics
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Author : Carole E. Greenes
language : en
Publisher:
Release Date : 2008
Algebra And Algebraic Thinking In School Mathematics written by Carole E. Greenes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Education categories.
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.
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.
Developing Thinking In Algebra
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Author : John Mason
language : en
Publisher: Paul Chapman Educational Publishing
Release Date : 2005-04-23
Developing Thinking In Algebra written by John Mason and has been published by Paul Chapman Educational Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-23 with Education categories.
This book has been constructed in a way that will enable teachers and their support staff to experience and to teach algebraic thinking to pupils aged 7-16.
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.
And The Rest Is Just Algebra
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Author : Sepideh Stewart
language : en
Publisher: Springer
Release Date : 2018-04-22
And The Rest Is Just Algebra written by Sepideh Stewart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-22 with Education categories.
This book addresses college students' weak foundation in algebra, its causes, and potential solutions to improve their long-term success and understanding in mathematics as a whole. The authors, who are experts in a wide variety of fields, emphasize that these difficulties are more complex than just forgotten rules, and offer strategic approaches from a number of angles that will increase the chances of student understanding. Instructors who are frustrated with their students’ lack of skills and knowledge at college level will find this volume helpful, as the authors confront the deeper reasons why students have difficulties with Algebra and reveal how to remedy the issue.
Approaches To Algebra
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Author : N. Bednarz
language : en
Publisher: Springer
Release Date : 1996-06-30
Approaches To Algebra written by N. Bednarz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-30 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.