What is left after everything is forgotten

My comrade-in-arms muriel sent me this quote on education by the early 20th-century Canadian humorist (and economics professor), Stephen Leacock from his book, “Literary Lapses“:
Educations are divided into splendid educations, thorough
classical educations, and average educations. All very old men have splendid educations; all men who apparently know nothing else have thorough classical educations; nobody has [...]

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The benefits of being left alone

According to BBC, The Institute for Public Policy Research said (see their report) studies suggested pupils’ reading and maths abilities regressed because the summer break was too long.
Ms Sodha [leading author of the report]report told BBC Radio 5 Live that the current structure of the school year was a relic from the time when [...]

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Calculus without limits

I re-publish my old post from my old blog, with comments (some of them new) included in the body.
My post:
Thanks to Michael Livshits, I became aware of an alternative approach to calculus based on eliminating the concept of a limit and replacing it by uniform Lipschitz bounds. For example, definition of derivative becomes

I would love [...]

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Why is arithmetic difficult, II

I expand an earlier post with the same title.
My colleague EHK told me about a difficulty she experienced in her first encounter with arithmetic, aged 6. She could easily solve “put a number in the box” problems of the type
,
buy counting how many 1’s she had to add to 7 in order to get 12
but [...]

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First tremors of a tectonic shift?

This my post is unusually political, although I am not normally interested in politics. Depending on my readers’ comments, I reserve my right to say “oops!” and delete the post. But while it is online, please read it and comment on it.
In the last few weeks, I started to pick in the general white noise [...]

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Fermat’s Last Theorem for Polynomials

An old post by Nick Halloway at sci.math:
Someone mentioned to that an analog of FLT is true in as well, i.e. there are no relatively prime [non-constant] polynomials , and in with
for .
This is true. You can show it by adapting the false proof of FLT.
It’s only necessary to [...]

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Craft, Art, Science

misha asked me:
What’s the difference between art and science again?
To answer, I reuse my old post from “A Sentimental Journey”:
I prefer to use nomination (simple naming of things, or giving examples) rather than definitions. Therefore a possible answer is: Opera is art. Pottery is a craft. Physics is a science. [...]

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Gert Biesta

For reasons that require a separate and lengthy explanation, I developed a habit of attending conferences on education research. Nevertheless I got to a meeting The Teaching-Research Interface: Implications for Practice in HE and FE by mistake: I red the title literally, but the organisers meant the interface between teaching and research in teaching. I [...]

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What is a minus sign anyway/

[I transfer this post from my old blog.]
A paper under this name is placed on the Internet by John Baldwin. He asks a seemingly naive question: how do we justify, in school mathematics teaching, manipulations like
(40+20) – (12+5) = (40-12) + (20-5)?
John Baldwin writes:
The associative law can only work on two applications of [...]

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Why is arithmetic difficult?

My colleague EHK told me today about a difficulty she experienced in her first encounter with arithmetic, aged 6. She could easily solve “put a number in the box” problems of the type
,
buy counting how many 1’s she had to add to 7 in order to get 12
but struggled with
,
because she did not know where [...]

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