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Math from Three to Seven

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Re: Math from Three to Seven

#131

Post by nerdponx »

kreyenborgi wrote: post #80

This was a surprisingly interesting and well-written article. I hope people read it and not just the comments here :-) I'm unsure if it implies that "lame school exercises" are unnecessary or just not sufficient (I've recently read articles about how teaching "insight" without exercises is detrimental, though perhaps doing problems implies getting that repetition-work). Does anyone have good experiences with keeping…

Can't speak for my own kids (yet), but personally I was able to hold my interest in math through my teens for 2 reasons:

1. I had some good teachers who showed (glimpses) of the how and why, not just the "what", so it helped math feel like it made sense, rather than being just facts and calculating algorithms to memorize. One demo that left a particular impression on me was the teacher asking us to go around the unit circle in increments of 10 degrees and plot the ratio of the opposite side and hypotenuse of the inscribed right triangle. Watching the sine function -- until then some mysterious thing that just existed with no explanation or context -- materialize in front of me on graph paper was magical.

2. I was shown that math is useful. In another great high school demo, the teacher assigned every student a length, width, and height, to be cut from construction paper and taped together in a box. After we were done, we laid out all the boxes together and computed their volumes. Then the teacher worked through the calculus on the board to figure out the dimensions of the box with the highest possible volume, given that fixed amount of construction paper. That was a really big moment for me, because until then I "hated" math, being a silly waste of time messing around with numbers and shapes just for the sake of doing it.

Re: Math from Three to Seven

#132

Post by atemerev »

0xdde wrote: post #2

The author raises an interesting question as to how the Soviets produced so much scientific talent, but his discussion of math circles strikes me as more of a tangent than a convincing answer. Were these math circles really so widespread, and were they a big part of producing mathematical and scientific question? He doesn't address this. However, the book he is reviewing is available online [1] and I see from skimmin…

The real answer is that we (I speak as a Russian) didn’t have such advanced computers in the USSR. What was routinely solved numerically in the US, had to be painstakingly traced analytically, and new methods had to be developed for such approaches, and mathematical education had to be boosted so enough people could work in the field (mostly developing new weapons, sadly).

Re: Math from Three to Seven

#133

Post by nerdponx »

red_admiral wrote: post #130
kreyenborgi wrote: post #80

This was a surprisingly interesting and well-written article. I hope people read it and not just the comments here :-) I'm unsure if it implies that "lame school exercises" are unnecessary or just not sufficient (I've recently read articles about how teaching "insight" without exercises is detrimental, though perhaps doing problems implies getting that repetition-work). Does anyone have good experiences with keeping…

For the "exercises are important and also build conceptual understanding", see "BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING, A Bogus Dichotomy in Mathematics education" by H. Wu. The big challenge in teaching is not to make the exercises seem lame.

I haven't read this whole article yet (PDF here https://math.berkeley.edu/~wu/wu1999.pdf), but this idea is my #1 problem with Tom Lehrer's "New Math" song. His big complaint at the beginning is that the emphasis is too much on understanding and not on efficiently/correctly calculating an answer. As funny as the song is, I don't think that complaint has aged well at all. Also the old algorithm was just as complicated as the new one, but at least the new one makes it easier to see what's going on, so the whole joke kind of falls apart.

Re: Math from Three to Seven

#134

Post by antupis »

d--b wrote: post #89

The main cultural difference is that Americans don’t value maths and physics as much as they value law and business. Harvard Law school is still the thing you aim for when you’re a smart kid. MIT is what you aim when you’re good AND you’re really into it. In France, the top thing to do is go to Polytechnique, which is an engineer school created by Napoleon. So culturally French people push their kids towards learning…

It is so interesting that those are always so country-specific here in Finland it is Medicine and industrial management.

Re: Math from Three to Seven

#135

Post by hyperbrainer »

As a teenager who dislikes the current schooling system, what I am most curious about is actually why something like the "mathematical circles" do not exist in the west.

To some extent, a similar social group is formed by robotics teams in my experience. A dedicated teacher/coach and a bunch of people who like electronics can really get amazing things done. Why is this the case?

Re: Math from Three to Seven

#136

Post by harimau777 »

My biggest issue with math education is that after we learned the theory we never went back and developed an actual plan for solving the problems. For example, we learned a dozen different ways to approach integration, but after all this we never really put together a workable strategy for approaching a problem and deciding what tools to use.

It's like trying to teach someone to swim by just throwing them in the water over and over and expecting them to eventually figure it out.

As a result, the primary emotion students learn to associate with math problems is fear. Instead of the sense of confidence that comes with having a plan, each problem feels like "will things work out or will I get lost and waste hours without actually ever finding a solution".

Re: Math from Three to Seven

#137

Post by kurisufag »

harimau777 wrote: post #136

My biggest issue with math education is that after we learned the theory we never went back and developed an actual plan for solving the problems. For example, we learned a dozen different ways to approach integration, but after all this we never really put together a workable strategy for approaching a problem and deciding what tools to use. It's like trying to teach someone to swim by just throwing them in the wate…

The best strategy is one suited to you because you came up with it yourself, in my opinion. Other than the big kludges (u-substitution, etc.), teaching specific/mechanistic integration processes directly would have been an uncomfortable way for me to learn.

Re: Math from Three to Seven

#138

Post by masto »

hyperbrainer wrote: post #135

As a teenager who dislikes the current schooling system, what I am most curious about is actually why something like the "mathematical circles" do not exist in the west. To some extent, a similar social group is formed by robotics teams in my experience. A dedicated teacher/coach and a bunch of people who like electronics can really get amazing things done. Why is this the case?

Maybe you already know or could try to find other peers who like math, and see if you can get something started? I think there's a good chance that if you approached a supportive teacher with "my four friends and I want to start a math club, can you help us?", it would get the ball rolling. Perhaps you could put something up on the bulletin board or equivalent you kids have these days, data kiosks or hovergrams or whatever.

Re: Math from Three to Seven

#139

Post by tightbookkeeper »

082349872349872 wrote: post #126
komali2 wrote: post #32

Earlier quoted context omitted.

I've noticed this aspect in general of revolutionary societies. What I'm personally quite selfishly interested in is whether this is unique to leftist revolutionary societies - were Germans or Italians in 1936 having spirited debates about fascism and how best to serve the Fatherland? I have no idea, from what I've read so far it sounds like no. Meanwhile, for example in Spain in the same time period, there was a rem…

Fascism was explicitly and proudly anti-intellectual, eg https://en.wikipedia.org/wiki/Achille_Starace#:~:text=On%20o...

I think you’re missing a lot of historical context. If by “intellectual” you mean cosmopolitan university professors and government administrators then yes. This also closely associated with internalization, relativism, and Jewish culture.

If by “intellectual” you mean learning, reading, thinking, then no.

Re: Math from Three to Seven

#140

Post by tightbookkeeper »

Tomis02 wrote: post #66
com2kid wrote: post #26

From the book being reviewed: > All joking aside, we fledgling mathematicians understood that the single most important thing was not raw intelligence or knowledge (Americans tend to lag behind in the latter compared to all international students). What mattered was passion. The way to become successful in mathematics, like almost every endeavor, is to care about it, to love it, to obsess over it. And in this, Easter…

> IMHO this is what drove American superiority in software engineering for several decades. The people who self selected into software engineering really loved the field. IMO it was funding that made the difference. People outside of USA did not have any less passion towards the field.

Any amount of funding gets immediately sucked into the abyss. The entire mathematical research community in Soviet Union probably cost less than a series C startup.

The only sense in which this is true is if choosing that field is a death sentence relative to other society outcomes due to lack of resources.

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