Category Archives: mathematics

The logician, the mathematician, the physicist, and the engineer

The logician, the mathematician, the physicist, and the engineer. “Look at this mathematician,” said the logician. “He observes that the first ninety-nine numbers are less than hundred and infers hence, by what he calls induction, that all numbers are less … Continue reading

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On mathematics

Mathematics is regarded as a demonstrative science. Yet this is only one of its aspects. Finished mathematics presented in a finished form appears as purely demonstrative, consisting of proofs only. Yet mathematics in the making resembles any other human knowledge … Continue reading

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Unreal and Useless Problems

We had previously talked about problem with contexts given in mathematics problems. This is not new, Thorndike in 1926 made similar observations. Unreal and Useless Problems In a previous chapter it was shown that about half of the verbal problems … Continue reading

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On not learning or con in the context

We will, we will, fail you by testing what you do not know… We live in a rather strange world. Or is it that we assume the world to be non-strange in a normative way, but the descriptive world has … Continue reading

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What is a mathematical proof?

A dialogue in The Mathematical Experience by Davis and Hersh 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

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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

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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 work  compares the teaching of mathematics … Continue reading

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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

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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

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