In the current issue of the European Mathematical Society newsletter, there is an article by Günter Ziegler entitled “Mathematics School Education Provides Answers – To Which Questions?” It is worth reading, in my opinion, and I urge you to take a look.
Ziegler’s thesis is that there is not just one “school mathematics”, but three, roughly speaking
- learning basic life skills (a rapidly changing area as a result of technological advances);
- appreciating mathematics as part of our culture, with a very great impact on our life at present;
- studying mathematics with a view to university or vocational studies in a numerate area or in mathematics itself.
He discusses four complaints about the way mathematics is currently taught, as seen from the perspective of a university professor: the students who come to university have insufficient knowledge of mathematics, an inadequate idea of their own state of knowledge, insufficient knowledge of what mathematics is, and insufficient knowledge of what it means to do mathematics.
Needless to say, he has no simple answers to the points he raises, but I think they are well worth considering.
Let me append two small comments to this.
Yesterday, one of our graduating students, who had just been awarded a first-class degree and is going to be a high-school teacher, came to see me and three others, to thank us for our methods of teaching, from which he had learned valuable lessons. It is very heartwarming to realise that one has made a difference; I am also very pleased that good students are going into teaching as a first-choice career (it used to be the last resort). Maybe things can change for the better.
Also, the following gem from later in the EMS newsletter:
There are 26 sheep and 10 goats on the boat. How old is the captain?
This question was given to 97 primary-school students in Grenoble. 76 of them did a calculation based on the data provided and gave an answer. (The article is about reciprocal expectations between teacher and students.)