101–110 of 257 posts
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…
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 homework, etc. Because of this real-world to mathematical-world translation step. By exploring ways to make math more accessible, "friendly" and useful, teachers might actually make it harder for students to pick up math.
This is an interesting thought for me, because I tutored kids in math who were not doing good in school. I kind of ended up with a typical scheme to get them from "risk of failing the class" to Bs and occasionally As.
First I would introduce a a few techniques (equation solving in every case and the mathematical topic of their class - logarithms, binomial terms, etc. - also) and then give them very simple drill exercises. And a lot of them that we would solve together. I.e. simplifying exponentials $exp(3) * exp(5) = exp(8)$ etc. I always made sure that they were able to solve these drill exercises eventually, and they were all able to, because they picked up the scheme.
As a next step, I gave them the applied problems their teachers would ask them to solve, and made it into a translation problem. I.e. I explicitly told them that this was now just a translation. They could often identify with this because they self-identified often as language persons ("I like the literature class best", or "I like french class most"). I wouldn't ask them to solve the translation result right away. But they often just naturally did because it was not so different from the drill exercises.
Point is, I do not at all understand why I was needed for this. The teachers consistently failed their students in class, by not providing them with the very basic math skills and confidence that they needed to solve more complex problems.
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…
Do you have any research to support that? Because from what I've seen we currently think that drilling does nothing to help with understanding, and that one of the problems people have with maths is applying the wrong technique to a problem because they don't understand the problem.
> You'll never understand even relatively simple things like complex analysis or Fourier transform just by reading about it
Very few 8 year olds are grappling with fourier transforms.
http://www.wsj.com/articles/the-best-language-for-math-14103...
It's an interesting question when you consider that in at least two university mathematics department rankings[1][2], the US holds 7 of the top 10 global spots. One could argue that for whatever reason, many of the professors, researchers and postdocs at those schools learned math in other countries, but, if these lists are to be believed, the US does have the richest mathematics knowledge in the world. So two questi…
Most math (and physics) programs, especially at higher tier universities, have not only a disproportionate number of foreign professors and researchers but also students . So it's largely people who had superior primary and secondary school math education teaching others who had superior primary and secondary school education. You can see this especially strongly in graduate programs, where US citizens can often get…
Oh yeah? What jobs are there for a physics PhD to do physics in that isn't academia? Government research lab? Military aerospace contractor?
It's an interesting question when you consider that in at least two university mathematics department rankings[1][2], the US holds 7 of the top 10 global spots. One could argue that for whatever reason, many of the professors, researchers and postdocs at those schools learned math in other countries, but, if these lists are to be believed, the US does have the richest mathematics knowledge in the world. So two questi…
I once heard an anecdote that might describe some of what's happening. In the trenches of WWI, when it was time to fight, soldiers would have to climb up a ladder onto a battlefield. The problem was that German snipers could see the tops of the ladders. The Germans would keep their rifles fixed on where they knew the enemy would emerge and simply shoot them down once they saw helmets appear. The European Allied soldi…
Earlier quoted context omitted.
We do a great job with the extreme students. The top 5% of private and public schools in the country produce more than enough folks capable in mathematics. It's the rest of the country that struggles. There are a lot of reasons why the US does well in Universities and poorer up until then relative to the rest of the world: 1 - In much of the world, the school you get into matters more than what you did there. (The lo…
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…
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.
> It's a mixed bad in K-12 Your typo is very accurate :-) I would say that our problem in K-12 is a self-perpetuating one. The teachers were taught math badly and so never really learned it (and learned to hate it into the bargain). So then they teach it badly. I'm not sure there's any solution except for tuning the students in to Khan Academy and suchlike programs.
> tuning the students in to Khan Academy and suchlike programs I think parents have an enormous role to play in the effectiveness of K-12 education. If they are not very much involved (e.g., enforcing, participating, encouraging) then school isn't valued or prioritized, nor will the average student see how fun many subjects can be to learn (assuming the teacher may not be effective at this). > were taught math badly…