Perspectives On School Algebra
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Perspectives On School Algebra
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Author : Rosamund Sutherland
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Perspectives On School Algebra written by Rosamund Sutherland 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 2006-04-11 with Education categories.
This book confronts the issue of how young people can find a way into the world of algebra. It represents multiple perspectives which include an analysis of situations in which algebra is an efficient problem-solving tool, the use of computer-based technologies, and a consideration of the historical evolution of algebra. The book emphasizes the situated nature of algebraic activity as opposed to being concerned with identifying students' conceptions in isolation from problem-solving activity.
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.
Mathematics For High School Teachers
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Author : Zalman Usiskin
language : en
Publisher: Prentice Hall
Release Date : 2003
Mathematics For High School Teachers written by Zalman Usiskin and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Education categories.
For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.
New Perspectives In Algebra Topology And Categories
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Author : Maria Manuel Clementino
language : en
Publisher: Springer Nature
Release Date : 2021-10-16
New Perspectives In Algebra Topology And Categories written by Maria Manuel Clementino and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-16 with Mathematics categories.
This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of « roadmap » and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a particular result for their own research and do not want to go through several research papers in order to understand a single proof. Although the chapters can be read as « self-contained » chapters, the authors have tried to coordinate the texts in order to make them complementary. The seven chapters of this volume correspond to the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the frame of the project Fonds d’Appui à l’Internationalisation of the Université catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.
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 Algebraization
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Author : Jinfa Cai
language : en
Publisher: Springer
Release Date : 2011-03-03
Early Algebraization written by Jinfa Cai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-03 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.
Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds
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Author : Carolyn Kieran
language : en
Publisher: Springer
Release Date : 2017-12-04
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 2017-12-04 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.
International Perspectives On The Teaching And Learning Of Geometry In Secondary Schools
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Author : Patricio Herbst
language : en
Publisher: Springer
Release Date : 2018-04-27
International Perspectives On The Teaching And Learning Of Geometry In Secondary Schools written by Patricio Herbst and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Education categories.
This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.
Educational Algebra
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Author : Eugenio Filloy
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-12
Educational Algebra written by Eugenio Filloy 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 2007-10-12 with Education categories.
This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning". These approaches and others of similar nature lead to a focus on competence rather than a user’s activity with mathematical language.
Secondary Algebra Education Revisiting Topics And Themes And Exploring The Unknown
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Author : Paul Drijvers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-19
Secondary Algebra Education Revisiting Topics And Themes And Exploring The Unknown written by Paul Drijvers 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 2011-10-19 with Education categories.
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.