This is a nice little item which talks about the various things that “=” can mean.
Bayes’ theorem is so cool because it allows you to make predictions based on observations.
It is often taught, however, as a kind of alphabet soup of symbols and weird language (‘prior and posterior probabilities’) so that even very smart people fail to get it…and certainly can’t apply it for themselves.
In this diagram, the whole idea is explained as simply as possible (click on the image below for a bigger version):
I’m a big fan of technology…anything which can help me to do a given task more effectively.
This criterion isn’t usually met by the interactive whiteboard it seems…especially when in the hands of a rule-bound teacher.
Here is an article which discusses the rush to classroom technology -as if that can solve the problems in US schools.
The worst problems are to do with textbooks full of shallow, misleading examples and teachers who teach by rote (I have had recent personal experience of someone teaching chemistry with almost no real understanding..it was more like cookery than science. How do some of these people get a licence to educate chiuldren?)
Feynman would have a fit.
Publishers have often said that every equation in a book halves its readership (this shows that publishers don’t understand Limits, but we know what they mean).
It now appears that other people’s equations put off even professional scientists -who tend not to read papers which are filled with this notation.
So often, in science, the maths is portrayed as having driven or supported the research. In many cases, it’s really used as a kind of shorthand to render ‘respectable’ and summarise all the thinking that was actually done quite intuitively. The publishing process demands this, but few authors are allowed the space to provide much additional explanation. So, once again the very power of maths makes its power harder to learn about.
Lots of folk these days have trouble with long division. This makes perfect sense for two reasons:
- Everyone uses a calculator, so the laborious, paper-based approach is bypassed
- The method for long division has always been taught like cookery…ie ‘just do this’
It’s no wonder that it’s been shown that if you don’t get to grips with fractions and long division, then the rest of the subject remains a mystery.
Many of us just can’t follow the method without understanding why…somebody has to take the time to explain all of this stuff before solid progress can be made.
I’m certainly not in favour of ranks of young people chanting “we must get into college.”
This is partly because, having seen the inside of many (Western) universities, I’m not sure they do a particularly special job of educating our young people. This applies even to the big-name, high-prestige institutions where undergraduates no longer get much face-to-face access to Professors.
That said, this article about the aspirations of the Chinese people is interesting.
They really do seem to have the ambition to ensure that, through hard work, even people with less than stellar academic backgrounds can achieve real success.
“…anyone can create an education system where a few at the top succeed, the real challenge is to push through the entire cohort.
In China […] this means using the best teachers in the toughest schools. ”
Students seem to perform better in tests when they have had enough water to drink.
It seems that maths can be very frightening for many young people.
Here’s a little garden design project I tried, with an interesting mathematical basis.