Learn, combine, repeat (a thousand times)

Mathematics might not have the most sexy image in the world. Common wisdom tells us that being a nerd is cool these days. But it’s a package deal. You shouldn’t only look like a cool nerd and act like a cool nerd, but have the actual knowledge and interests a nerd has. Like for math.

My experience with math education are old – more than 35 years to be precise – but good. However, I remember two things. First of all that the transfer from high school to university was a shift from first to sixth gear. In my last two years a part of math wasn’t obligatory for university admission (mainly vector spaces). Entering university, students were told if necessary to get up to speed with a crash course. The same material that took me two years to complete were condensed in a twelve part course of six weeks.
The second aspect is something I realised when I started rehashing everything I learned from my old books from junior and senior high school as well as from university. It is the ssometimes scattered and piecemeal approach to teaching.

Especially the second aspect was a real problem. School kids learn what a logarithm is. Then some time later, they learn what e and its definition is. Then some time later they learn what a derivative is. In the mean time they learn about a plethora of other things, both in math and other disciplines. Then, after a few years of education, they need to calculate the derivative of the natural from scratch, and they have no idea. They must combine the definition of the derivative, the rules for logarithms and the definition of e. To combine it, they have to really understand all these concepts. That’s the moment when things often go wrong. Too little repetition, too much diverse stuff. …

(to be continued tomorrow)