Hi Pierre,
Just to throw a spanner in the works... I suspect we are of an age where the slide rule was very important, and as the SR-71 Blackbird was built using one, what a valuable tool it really was. But I am coming to the conclusion that much of what we needed, we thought of as important or what we think is important, is really not. I had one student tell me that "Nothing is really important, and if it was it probably would not matter anyway." Ha!
P.S. To answer calculated questions you need to know HOW to calculate the response,
Why do we need to know? We certainly need to know how to read and write and count, and I think we should be able to do mental arithmetic, but do we need to calculate manually? I am not so sure. If we understand how an equation works, and we have a calculator or a computer, or even a cell phone, do we need to do the actual calculations by hand? I am sot so sure.We have students who can do some whiz bang things in World of Warcraft, or whatever the latest game is, they manage entire armies, and build cities, they make incredible manouveres between levels in their games, but we ask them to sit down and eschew their computers, something they are good at, and use a pencil to calculate things? No wonder we cannot get students to take up maths.
We have to be able to work out, in our heads, that if I can buy a can of beans for $1, and yet can buy 3 cans for $2.50, there is a saving for me. That is not what we are teaching btw, I suggest we should, but somehow we consider it less important than it was. For some reason, it seems using our brains is given over to allowing the ubiquitous beige box to do it for us. It appears we do not need to remember things any more, we have the computer to do it for us.
Gutenberg developed his printing techniques and press in the 1430's, yet it was not until Erasmus, 70 years later, that the question of whether we were using it correctly was asked. It was another 150 odd years for Locke and, later, Bentham to propose that universal literacy was not an unachievable goal with the printed word. Yet it was nearly another century, and an Industrial Revolution, before people worked out that it was, indeed possible. We do not have this kind of time line with the computer, we need to make it work now. When TV was introduced, it was touted as an educational tool, but look how quickly I love Lucy took over. (I even remember the ABC here putting AJP Taylor, I think it was, on talking about history, nothing else, just talking, delivering a lecture if you like. It was fascinating, even if I had no idea what he was talking about.) Today, we do not use a lot of TV in the classroom, I don't anyway, just for some strongly visual elements, but now I am more likely to use a data projector.
I do not propose we drop computers from the education process, but I do suspect we need to target our use of them better, we certainly need better tools, and Moodle goes a long way towards that end. We should not dismiss the "old ways" because they are old, but because they are not valid. Rote learning is not practiced in our schools, but I wonder what the ratio of ADHD and Asperger suffers are in those countries that still use it compared to ours. We complain about kids not "knowing" their times tables - yet what do we do about that? Reintroduce mental arithmetic based on rote learning, no, not at all we seem to ignore it all and just continue on with practices that have demonstrable flaws.
As an aside, people throw words like "constructivism" around and they have this clear picture of what it is. Almost inevitably, they miss one vital component of the concept, that is it directs children's attention along particular lines. This is OK for training purposes, but for an education? I am not so sure. If you direct attention into particular channels, which is what we do do, are other channels then invalidated? Do we in fact, as Ken Robinson suggests, kill initiative and imagination by adopting these philosophies or pursuing these lines of education? I do not know, but I do know we need to do it better than we are.
So Itamar, what is it then that we are actually testing? Understanding or memory?