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 [...]
Archive for May, 2008
What is left after everything is forgotten
Posted in Uncategorized on May 28, 2008 | 1 Comment »
The benefits of being left alone
Posted in Uncategorized on May 26, 2008 | 3 Comments »
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 [...]
Calculus without limits
Posted in Uncategorized on May 26, 2008 | 3 Comments »
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 [...]
Why is arithmetic difficult, II
Posted in Uncategorized on May 26, 2008 | 1 Comment »
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 [...]
First tremors of a tectonic shift?
Posted in Uncategorized on May 25, 2008 | 12 Comments »
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 [...]
Fermat’s Last Theorem for Polynomials
Posted in Uncategorized on May 24, 2008 | 3 Comments »
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 [...]
Craft, Art, Science
Posted in Uncategorized on May 22, 2008 | Leave a Comment »
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. [...]
Gert Biesta
Posted in Uncategorized on May 22, 2008 | 4 Comments »
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 [...]
What is a minus sign anyway/
Posted in Uncategorized on May 17, 2008 | 31 Comments »
[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 [...]
Why is arithmetic difficult?
Posted in Uncategorized on May 14, 2008 | 12 Comments »
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 [...]