DMCA. Copyrighted Work that you can Claim.

# ðŸ“™ History in Mathematics Education by John Fauvel, J. A. Van Maanen â€” download pdf

## Similar books results

**Philosophical Dimensions in Mathematics Education (Mathematics Education Library) free download by Karen Francois, Jean Paul Van Bendegem**

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives f...

**Alternative Theoretical Frameworks for Mathematics Education Research: Theory Meets Data epub download by Elizabeth de Freitas, Margaret Walshaw (auth.)**

This book explicates some of the fundamental philosophical tenets underpinning key theoretical frameworks, and demonstrates how these tenets inform particular kinds of research practice in mathematics education research. We believe that a deep understandi...

**Mathematics Education in Different Cultural Traditions- A Comparative Study of East Asia and the West pdf free by Frederick K.S. Leung, Klaus-D. Graf, Francis J. Lopez-Real**

The fundamental idea of the ICMI Study 13 is outlined as follows: Education in any social environment is influenced in many ways by the traditions of these environments. As a consequence the results of such education will naturally differ with different t...

**Mathematical Applications and Modelling: Yearbook 2010, Association of Mathematics Educators free epub by Berinderjeet Kaur, Berinderjeet Kaur, Jaguthsing Dindyal**

''Mathematical Applications and Modelling'' is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate...

**Mathematics Education and Language: Interpreting Hermeneutics and Post-Structuralism pdf free by Tony Brown**

`Contemporary thinking on philosophy and the social sciences has been dominated by analyses that emphasise the importance of language in understanding societies and individuals functioning within them; important developments which have been under-utili...

**Anthropology, History, and Education (The Cambridge Edition of the Works of Immanuel Kant in Translation) epub download by Immanuel Kant, Robert B. Louden ed., Gunter Zoller ed.**

Anthropology, History, and Education contains all of Kant's major writings on human nature. Some of these works, which were published over a thirty-nine year period between 1764 and 1803, have never before been translated into English. Kant's question 'Wh...

**New Directions for Situated Cognition in Mathematics Education (Mathematics Education Library) free pdf by Anne Watson, Peter Winbourne (Editors)**

This book draws together a range of papers by experienced writers in mathematics education who have used the concept of situated cognition in their research within recent years. No other books are available which take this view specifically in mathematics...

**Mapping Equity and Quality in Mathematics Education epub download by Anna Chronaki (auth.), Bill Atweh, Mellony Graven, Walter Secada, Paola Valero (eds.)**

The issues of equity and quality have been central to international debates on mathematics in research, policy, curriculum and teaching. This book covers a wide variety of topics in the research and practice of mathematics education, demonstrating how equ...

**Towards Gender Equity in Mathematics Education: An ICMI Study (New ICMI Study Series) free download by Gila Hanna (Editor)**

The present volume consists of original scholarly articles that develop further issues pertaining to gender equity in mathematics education. The premise - that there is no physical or intellectual barrier to the participation of women in mathematics, ...

**How Chinese Learn Mathematics: Perspectives From Insiders (Mathematics Education, 1) free epub by Fan Lianghuo**

The book has been written by an international group of very active researchers and scholars who have a passion for the study of Chinese mathematics education. It aims to provide readers with a comprehensive and updated picture of the teaching and learning...

**Estimation in regression models for longitudinal binary data with outcome-dependent follow-up download pdf by Fitzmaurice G.M., Lipsitz S.R., Ibrahim J.G.**

**Estimation with correlated censored survival data with missing covariates pdf free by Lipsitz S.R., Ibrahim J.G.**

**Etale Homotopy pdf free by Michael Artin, Barry Mazur**

**Estimates of analytic capacity pdf free by Kral J.**

**Estimation Problems in Hybrid Systems free download by David D. Sworder, John E. Boyd**

A guide to how diverse sensors can be integrated to create enhanced controllers and estimators in a variety of situations....

**Eternal people free pdf by David Milofsky**

Eternal People tells the story of Joseph Abrams, a Ukrainian Jew who finds his way to America at the end of the nineteenth-century. During a break from his studies in Russia, he returns to his shtetl in the Ukraine to find it is the target of a Cossack r...

**Estimation of Microbial Protein Supply in Ruminants Using Urinary Purine Derivatives pdf free by H. P. S. Makkar (auth.), Harinder P. S. Makkar, X. B. Chen (eds.)**

The Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture has a long history of coordinating isotope aided research projects for improving animal productivity in developing countries. These projects have focused on enhancing the efficiency...

**Estimating the Flammable Mass of a Vapor Cloud: A CCPS Concept Book epub download by John L. Woodward(auth.)**

This CCPS Concept book shows designers and operators of chemical facilities how to realistically estimate the flammable mass in a cloud of accidentally released material that is capable of igniting. It provides information on industry experience with flam...

**Estuarine Ecology, Second Edition download pdf by **

Estuaries are among the most biologically productive ecosystems on the planet--critical to the life cycles of fish, other aquatic animals, and the creatures which feed on them. Estuarine Ecology, Second Edition, covers the physical and chemical aspects of...

**Estuarine Water Quality Management: Monitoring, Modelling and Research free epub by **

About The ProductPublished by the American Geophysical Union as part of the Coastal and Estuarine Studies Series. The pollution of rivers, estuaries and the sea, the associated impact on these ecosystems and the effect on organisms, food-chains, water-sup...

The importance of the subject matter of this book is reasserted again and again throughout, but never with the force and eloquence of Beltrami's statement of 1873:
"Students should learn to study at an early stage the great works of the great masters instead of making their minds sterile through the everlasting exercises of college, which are of no use whatever, except to produce a new Arcadia where indolence is veiled under the form of useless activity." (Beltrami, quoted on p. 36).
Teachers who think that sterility of student minds is innate rather than their doing had better consider that when a student calls mathematics teaching stupid he is merely echoing the opinion of the greatest mathematicians who ever lived. When the teacher blames his student for being too unmathematical to grasp his teaching, the truth is rather that the student is too mathematical to accept the anti-mathematical junk that is being taught.
Let us concretise this in the case of complex numbers. Here the teacher tries to trick the student into believing that complex numbers are useful because they enable us to "solve" otherwise unsolvable equations such as x^2+1=0. What a load of rubbish. The supposed "solutions" are nothing but fictitious combinations of symbols which serve absolutely no purpose whatsoever except that if you write them down on exams then the teachers tells you that you are a good student. A mathematically inclined student is not one who plays along with the charade but rather one who calls the bluff.
If we look at the history of complex numbers we find first of all that the nonsense about "solving" equations with no real roots is nowhere to be found. Secondly, we find that complex numbers were first conceived as computational shorthands to produce *real* solutions of higher-degree equations from certain formulas. But the inventor of this technique, Cardano, immediately condemned it as "as refined as it is useless," noting "the mental tortures involved" (Cardano, quoted on p. 305). Cardano's condemnation was not reactionary but perfectly sound and justified, for blind manipulation of symbols leads to paradoxes such as -2 = Sqrt(-2)Sqrt(-2) = Sqrt((-2)(-2)) = Sqrt(4) = 2. (This example is from Euler, quoted on p. 307.) These paradoxes dissolve with a proper geometric understanding of complex numbers. Only after such an understanding had been reached in the 19th century did the mathematical community take complex numbers to their heart (cf. pp. 304-305).
From this outline of history we learn not only that students are right to call their teachers charlatans and corrupters of honest knowledge, but also that students are in fact much more receptive to and enthusiastic about mathematics than mathematicians themselves. This is made clear in an interesting experiment conducted by Bagni (pp. 264-265). High school students who did not know complex numbers were interviewed. First they were shown complex numbers in the bogus context of examples such as x^2+1=0; then they were shown Cardano-style examples of complex numbers acting as computational aids in obtaining real solutions to cubic equations. In the first case "only 2% accepted the solution"; in the second 54%. But if the examples were given in the reverse order then 18% accepted complex numbers as solutions to x^2+1=0. In other words, students echoed the judgement of the masters of the past, except that they were more enthusiastic, being somewhat impressed by an idea referred to by its inventor as useless mental torture. Teachers should recognise what privilege it is to work with such admirably critical yet receptive students. The teacher should nourish this clarity of judgement and independent thought "instead of making their minds sterile."

## About book:

## About file:

Security code:

- Author:
**John Fauvel, J. A. Van Maanen** - Year:
**2002** - Publisher:
**Kluwer Academic Publishers** - Language:
**English** - ISBN:
**9780306472206,9780792363996,9781402009426,079236399X,1402009429**

- File size:
**4 895 513** - Format:
**pdf**

Security code:

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives f...

This book explicates some of the fundamental philosophical tenets underpinning key theoretical frameworks, and demonstrates how these tenets inform particular kinds of research practice in mathematics education research. We believe that a deep understandi...

The fundamental idea of the ICMI Study 13 is outlined as follows: Education in any social environment is influenced in many ways by the traditions of these environments. As a consequence the results of such education will naturally differ with different t...

''Mathematical Applications and Modelling'' is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate...

`Contemporary thinking on philosophy and the social sciences has been dominated by analyses that emphasise the importance of language in understanding societies and individuals functioning within them; important developments which have been under-utili...

Anthropology, History, and Education contains all of Kant's major writings on human nature. Some of these works, which were published over a thirty-nine year period between 1764 and 1803, have never before been translated into English. Kant's question 'Wh...

This book draws together a range of papers by experienced writers in mathematics education who have used the concept of situated cognition in their research within recent years. No other books are available which take this view specifically in mathematics...

The issues of equity and quality have been central to international debates on mathematics in research, policy, curriculum and teaching. This book covers a wide variety of topics in the research and practice of mathematics education, demonstrating how equ...

The present volume consists of original scholarly articles that develop further issues pertaining to gender equity in mathematics education. The premise - that there is no physical or intellectual barrier to the participation of women in mathematics, ...

The book has been written by an international group of very active researchers and scholars who have a passion for the study of Chinese mathematics education. It aims to provide readers with a comprehensive and updated picture of the teaching and learning...

A guide to how diverse sensors can be integrated to create enhanced controllers and estimators in a variety of situations....

Eternal People tells the story of Joseph Abrams, a Ukrainian Jew who finds his way to America at the end of the nineteenth-century. During a break from his studies in Russia, he returns to his shtetl in the Ukraine to find it is the target of a Cossack r...

The Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture has a long history of coordinating isotope aided research projects for improving animal productivity in developing countries. These projects have focused on enhancing the efficiency...

This CCPS Concept book shows designers and operators of chemical facilities how to realistically estimate the flammable mass in a cloud of accidentally released material that is capable of igniting. It provides information on industry experience with flam...

Estuaries are among the most biologically productive ecosystems on the planet--critical to the life cycles of fish, other aquatic animals, and the creatures which feed on them. Estuarine Ecology, Second Edition, covers the physical and chemical aspects of...

About The ProductPublished by the American Geophysical Union as part of the Coastal and Estuarine Studies Series. The pollution of rivers, estuaries and the sea, the associated impact on these ecosystems and the effect on organisms, food-chains, water-sup...