2 October 2010


In his posting "a rant about fractions", Jason Rosenhouse makes some good points about the way fractions are taught in elementary and middle high school math classes. For example, he says that kids get taken points off if, when adding two fractions, they find a non-reduced result, like 10/24. Instead, teachers tell them they should have found 5/12 immediately. Read the posting for more information on silly things going on in the teaching of elementary mathematics. No wonder, says Jason, that most people end up being afraid or hating mathematics.

Here is something else, from my recent university experience. I taught for a while in a department of Statistics & Actuarial Mathematics (where some very funny things are happening in eduation, both for students and teachers alike) in the UK. In Spring 2009 I was asked to solve some exercises for an elementary probability class, for first or second year students. The students had taken calculus before. We had to compute a certain integral (related to a density function) and I asked the students to do this by themselves. I asked a student to tell me her answer and she, correctly, responded b-2b/3.
"So," I continued, "this is equal to what?"
"I don't know", replies the student (who had done the integra correctly), "I'm not good with fractions."
"What about the rest of the class?", I asked the handful of students who were present. 
Apparently nobody knew how to subtract two thirds from 1.

So, remembering my elementrary school days, I turned back to the blackboard, and drew a pie:

(Actual picture from the lecture)
"So, if I cut a pie into three pieces and take out two, how many pieces remain?, I ask.
"One", replies the student.
"Very good", I enourage.
"Oh, that was easy", says another, "even my daughter could have done this".
When Jason, correctly, expressed his frustration with the teaching of fractions, he referred to elementary and middle school education. I repeat that the example above is taken, from personal experience, from university education.

There seemed to be something very, very, wrong in this system. This is why I left.

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What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant