ESU5 Day 1

I am attending the ESU5 - the 5th European Summer University On The History And Epistemology In Mathematics Education. This goes on in Prague this week, and I will report on it in this blog. More than 220 participants will choose from the 128 activities by presenters from 28 countries.

The first plenary speaker was Luis Puig. His title was "Researching the history of algebraic ideas from an educational point of view." He compared three approaches to algebra: the Babylonian, as interpreted bz Jens Hoyrup, al-Khwarizmi´s and Jordanus de Nemore´s. Especially interesting to me was Nemore "De Numeris Datis", 1225, who assigned letters to all quantities, with no distinction between known and unknown. If a times a was needed, it would be assigned a letter, say b. Puig noted parallells with how some pupils treat letters in the beginning, before they see the point of the letters.

Then I joined Jan van Maanen´s workshop on "The work of Euler and the current discussion on skills". We were given copies of part of Euler´s 1770 algebra textbook, and studied parts of it. Euler goes to great length to define + and -, for instance, so it is clear that Euler saw a great need to improve the "basic skills" of his fellow men. However, he did so while relating algebra to the real world. In the copies were also Euler´s explanation of the algorithm for extracting square roots. As I have never learned that, I should do that as homework...
It is terribly hot in Prague now, but huge doses of refreshing mathematics and history helps!