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# Category Archives: mathematics

## What is a mathematical proof?

A dialogue in The Mathematical Experience by Davis and HershÂ on what is mathematical proof and who decides what a proof is? Let’s see how our ideal mathematician (IM) made out with a student who came to him with a strange … Continue reading

Posted in education, mathematics, mathematics education
Tagged mathematical ideas, mathematics, norms, proof, teaching
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## Mathematical Literacy Goals for Students

National Council of Teachers for Mathematics NCTM proposed these five goals to cover the idea of mathematical literacy for students: Learning to value mathematics: Understanding its evolution and its role in society and the sciences. Becoming confident of one’s own … Continue reading

## Reflections on Liping Ma’s Work

Liping Ma’s book Knowing and teaching elementary mathematics has been very influential in Mathematics Education circles. This is a short summary of the book and my reflections on it. Introduction Liping Ma in her workÂ compares the teaching of mathematics … Continue reading

Posted in education, mathematics, mathematics education, politics
Tagged american, book, chinese, education, elementary, liping ma, mathematics education, pufm, review, teachers
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## Topological Art

ILLUSTRATIONS FOR TOPOLOGY From the book Introduction to Topology by Yu. Borisovich, N. Bliznyakov, Ya. Izrailevich, T. Fomenko. The book was published by Mir Publishers in 1985. ILLUSTRATION TO CHAPTER I The central part of the picture presents the standard … Continue reading

Posted in art, books, mathematics
Tagged art, illustrations, mathematical, maths, topology
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## On Division of Education

‘Consider how we design our educational programs. We take the major subjects apart and reduce them to a number of main sub-sections. Then we subdivide the sub-sections. We continue until we have a large collection of little pieces that we … Continue reading

Posted in aims of education, books, constructionism, ebooks, education, mathematics, mathematics education, papert, philosophy, science, science education, teacehrs, turtle art
Tagged logo, turtle
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## Rousseau on education…

There are, indeed, professors. . . for whom I have the greatest love and esteem, and think them very capable of instructing youth were they not tied down by established customs. . . . Perhaps an attempt may be made … Continue reading

Posted in education, mathematics, philosophy, science education
Tagged morris kline, undergraduate education
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## A parable on…

A Parable Once upon a time, in a far away country, there was a community that had a wonderful machine. The machine had been built by most inventive of their people … generation after generation of men and women toiling … Continue reading

Posted in aims of education, children, control, education, logic, mathematics, mathematics education, papert, science, sociology, sophie
Tagged history, knowledge, parable
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## Gel’fand’s Quote

This is taken from The Method of Coordinates by I. M. Gel’fandE.G. Glagoleva A.A. Kirillov Of course, it was not our intention that aIl thesestudents who studied from these books or evencompleted the School should choose mathematics astheir future career. … Continue reading

Posted in education, gelfand, mathematics, quotes
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## Heaven and Hell

Circle Limit IV Heaven and Hell by M C Escher Yesterday I have put up Escher’s Circle Limit IV – Heaven and Hell on my new desk. The Circle Limit series of drawings was drawn by Escher are essentially what … Continue reading

Posted in escher, evil, heaven hell, images, mathematics
Tagged art, circle limit 4, cosmology, escher, h s m coxeter, heaven hell, orosz
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## Zero

For a proper understanding of the evolution and the need for the concept of zero we need to understand how our current number system has evolved from its ancestors. The very need for the concept of zero did not arise … Continue reading