Sergei Yakovenko's blog: on Math and Teaching

Saturday, January 2, 2021

Excellent reading

Filed under: books,Rothschild course "Geometry" — Sergei Yakovenko @ 4:01
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Alexandre Borovik, working in England, in his recent post touched upon a most serious problem which already caused an immense harm to Israeli students, both in high school and in the colleges/universities.

❝Mathematics education is poisoned by centrally set written examinations. They require a new set of exam question every year, new — but somehow familiar to students; this means creation of exceptionally boring problems which differ one from another only by values of numerical parameters. Real mathematics is built around iconic, unique, eternal problems which cannot be used in written exams and for that reason never mentioned to students in England — and in most other counties.❞

Where can you get these iconic problems? Well, this is a folklore. Several people attempted to put this folklore down in writing, necessarily covering only a part of the vast area.

The book by Alexandre Borovik and Tony Gardiner (free e-copy is available) is one such brilliant attempt. It provides quite a number of problems that you need to solve only once in your lifetime, which you cannot “recycle” many times from one class to another, but which you better try to solve (first yourself, next with your students) if you really want to understand Mathematics.

In particular, there are large sections of problems on Geometry and “Infinity” (which is a code word for “Mathematical Analysis”). Enjoy!

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