131–140 of 257 posts
Earlier quoted context omitted.
The UK uses their own screwy imperial units for some measures
Not really. You still go to the shops and buy things in litres and kilograms, and their entire construction industry is in metric. The only commercial product that isn't in metric, funnily enough, is beer and cider. I guess getting pissed people to change proved harder than everything else.
Earlier quoted context omitted.
> I've always heard this explained as a sort of "selection bias". Since immigration to the US (particularly for university education) is often seen as desirable, the people who manage to pull it off tend to be above the mean. I think this is an explanation that could only be come up with by the descendants of those who have emigrated. Thinking here in Scotland, the people who emigrated were not necessarily the most a…
It's not clear that capability was that much of a factor. As the scion of Scots emigrants from the 19th Century, at least the 20h century version of my family was made up of bright capable people but hardly brilliant.
"Collective emigration is, therefore, the removal of a diseased and damaged part of our population. It is a relief to the rest of the population to be rid of this part."
Earlier quoted context omitted.
OTOH, the terrible truth is that it was necessary to order thousands of soldiers to their almost-certain deaths in order to win the war, and without a disciplined army this would not be possible. This says something about the value of discipline (in war or maths!) even when it's not obviously in your personal interest.
World War I was a stupid war over stupid pride-issues between imperialist powers.
The key to math education is practice. Even drilling, maybe. Other fields deal with concepts more or less mapped to the real world. Physics is about real world, more or less (right until you get to quants, then the level of abstraction rises dramatically). Same goes for biology, and even computer science in general. There, you can rely on words, which usually convey meaning. In math, you can't rely on words. You'll n…
Earlier quoted context omitted.
Spot on. The US education system is fairly elitist. It supports the top 5% and neglects the lower scoring pupils. That way (and with imported brains), the US can maintain a high level at academia while at the same time affording a fairly bad average education level of the total population in comparison to some other industrialized countries. The university system is also very elitist through student fees, Ivy League…
>the majority of US citizens must be mentally retarded and suffers from chronic lead poisoning. You probably think we only pay attention to news from the US but the Brexit vote is merely the most recent example to show that Europeans can be just as manipulable and unintelligent as Americans.
Earlier quoted context omitted.
OTOH, the terrible truth is that it was necessary to order thousands of soldiers to their almost-certain deaths in order to win the war, and without a disciplined army this would not be possible. This says something about the value of discipline (in war or maths!) even when it's not obviously in your personal interest.
Is that true? I mean: is it true that the actions where it was necessary to "order thousands of soldiers to their almost-certain deaths" were significant causes of the final outcome?
The final assault on the remains of the entrenched opposition were without exception extremely bloody and the side that would take the others trench never did so without significant losses.
The key to math education is practice. Even drilling, maybe. Other fields deal with concepts more or less mapped to the real world. Physics is about real world, more or less (right until you get to quants, then the level of abstraction rises dramatically). Same goes for biology, and even computer science in general. There, you can rely on words, which usually convey meaning. In math, you can't rely on words. You'll n…
They might try something that looks similar with word problems, but that is a far cry from the majesty of investigating the world with simple arithmetic. The problems they come up are contrived and students are no fools. Problems must come from within, not be handed to people.
Drilling vs understanding is not an either..or. Most learning starts with messing around, trying to figure something out. It is slow and will be painful if the interest is not there. At some point, understanding is sufficient with a foundation in place and then drilling comes in to get a mastery, but what "drilling" is and needs to be will vary from person to person. Too little, and the speed fails to materialize inhibiting understanding of higher level concepts. Too much and it gets boring shutting off critical interest.
All of this suggests that teaching mathematics in a one-size-fits-all is difficult. Also, imagine trying to grade 120 guesstimations for weeks on questions the students come up with. This is the essential difficulty of our current teaching mindset, namely the single authoritarian figure blessing or cursing the work of others.
The key to true learning is excitement and motivation and little external judgement. Interested people will largely self-correct with a few subtle pointers here and there.
Even at the level of Fourier transforms, most students probably fail to understand the problem. So how can it possibly make sense? Math is about working around hard problems, but the teaching of mathematics leads one to believe that there are simple algorithms to apply and we are done.
A lower level example of this is Newton's method. Solving f(x) = 0 in their experience (quadratic formula) is easy and graphing shows the zeros anyway. What is the problem it solves? But what if you just give them a graphical piece of the curve and ask where they think a zero is? Then the problem becomes clear and the solution can make sense. Then it gets translated into steps (draw a line that fits well, find its root, find out what it looks like around there, repeat). And then to master it, one can do a number of drills.
Good luck doing this, however, with people who do not care one iota about it and live in a culture where the majority of Americans have disdain for math (probably born out of a mixture of shame of how poorly they did in math class and bitterness that this most wonderfully human tool for exploring the world has been denied them).
One very interesting thought I read about: Modern math classes tend to be very applied. I.e. the primary objective is to get the student to be able to solve real world problems with math. (A farmer sells 3 potatoes for a dollar. How much do 8 potatoes cost?). There seems to be some indication however, that abstract math is more accessible to some children, especially if they aren't supported by parents during their h…
Finding a good math teacher in America is difficult because the good math students rarely become teachers.