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# π Approaches to Algebra: Perspectives for Research and Teaching by Nadine Bednarz, Carolyn Kieran, Lesley Lee (auth.), Nadine Bernarz, Carolyn Kieran, Lesley Lee (eds.) β free download

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**Approaches to Algebra: Perspectives for Research and Teaching (Mathematics Education Library) pdf free by N. Bednarz, C. Kieran, L. Lee**

In the international research community, the teaching and learning of algebra have received a great deal of interest. The difficulties encountered by students in school algebra show the misunderstandings that arise in learning at different school level...

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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.

- Series:
**Mathematics Education Library 18** - Author:
**Nadine Bednarz, Carolyn Kieran, Lesley Lee (auth.), Nadine Bernarz, Carolyn Kieran, Lesley Lee (eds.)** - Year:
**1996** - Publisher:
**Springer Netherlands** - Language:
**English** - ISBN:
**978-0-7923-4168-0,978-94-009-1732-3**

- File size:
**18 698 896** - Format:
**pdf**

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In the international research community, the teaching and learning of algebra have received a great deal of interest. The difficulties encountered by students in school algebra show the misunderstandings that arise in learning at different school level...

This book aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. Four different perspectives, e...

A wide range of projects are described in the latest Biennial Report of the International Agency for Research on Cancer (IARC), the cancer research branch of the World Health Organization. Most of these projects involve collaborations with scientists in i...

When you have the right math teacher, learning math can be painless and even fun! Let Basic Math and Pre-Algebra Workbook For Dummies teach you how to overcome your fear of math and approach the subject correctly and directly. A lot of the topics that pro...

This book provides the teacher with an understanding of dyslexia and offers practical approaches that can be used for assessment, teaching and learning. The book aims to highlight how the needs of children with dyslexia can be met within the curriculum an...

A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students.The most popular treatment of control for nonlinear systems is from the viewpoint of differential geometry yet this approach proves not...

New Perspectives on Grammar Teaching in Second Language Classrooms brings together various approaches to the contextualized teaching of grammar and communicative skills as integrated components of second language instruction. Its purpose is to show from b...

Foreword to the first edition: "This book is an exceptional introduction to some difficult ideas. It is full of downright good advice for every academic who wants to do something practical to improve his or hers studentsβ learning." Paul Ramsden, Br...

An authoritative examination of the present and potential impact of nanoscale science and technology on modern life Because truly transformative technologies have far-reaching consequences, they always generate controversy. Establishing an effectiv...