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A Group of American Teens Are Excelling at Advanced Math

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Re: A Group of American Teens Are Excelling at Advanced Math

#71

Post by poshenloh »

j2kun wrote: post #5

I am continually surprised by how many emails I get from teenage students thanking me for writing my math blog. On top of that, I try to occasionally make it out to high schools to give guest lectures. I posted an example experience from one of these online [1] and I am usually looking for other opportunities to do this sort of thing. I think that if every math graduate student who is a reasonably good teacher took a…

Thanks, @j2kun for your contributions to the math scene! :)

I agree! I think that many people have interesting ways to communicate where they see the excitement in math. Your blog lets you scale your impact through the Internet, which is great, and it's even more powerful when coupled with the in-person experience from guest lectures. :)

Indeed, when thinking of effective ways to scale up the in-person outreach efforts that I was engaging in (as National Coach + teaching at CMU + expii.com), I started posting my weekly math enrichment discussion topics onto the Internet. I think that's the way that we'll ultimately be able to completely level the playing field for everyone in the world.

Re: A Group of American Teens Are Excelling at Advanced Math

#72

Post by mahyarm »

NDizzle wrote: post #19
rayiner wrote: post #7

Earlier quoted context omitted.

The difference between "good schools" and "bad schools" is much more about the kids that go there than anything about the school itself. You're seeing this starkly in D.C. where gentrification in certain neighborhoods is shifting the student demographics from 90% low-income to 20% low-income over just 4-5 years. Test scores are shooting up, but it's not like they fired all the teachers and hired new staff at twice th…

Unfortunately, the other kids variable is something that you can only control by moving away. I had to do that in the east bay, California, when the schools started taking more inner-county transfers and running busses. The greatschools score went from ~7.5 to 4 in 2 years. The test scores plunged and they pulled money from the school because it wasn't performing. Like that helps. You can try to work with the school,…

Private school or some sort of shared homeschooling association are the alternatives. Not great alternatives :/

Re: A Group of American Teens Are Excelling at Advanced Math

#73

Post by poshenloh »

Ntrails wrote: post #25
j2kun wrote: post #5

I am continually surprised by how many emails I get from teenage students thanking me for writing my math blog. On top of that, I try to occasionally make it out to high schools to give guest lectures. I posted an example experience from one of these online [1] and I am usually looking for other opportunities to do this sort of thing. I think that if every math graduate student who is a reasonably good teacher took a…

The sad thing is that the cool stuff isn't even always complex. It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules. But at the same time - I know I'd have/did enjoy that stuff but maybe 60% of my classes would have played up if a whole lesson was spe…

I think that one main issue is that many people unfortunately equate math with routine calculations or rote memorization. I think it's valuable to communicate that actually math is the art of creative thinking. To do this, it helps to share some "gems", or examples with powerful "Aha" factors.

Along these lines, I have a very fresh one: last week, I just had a very shocking (mathematical) realization while thinking about football:

There is a way to instantly see the optimal running angle when evading an equal-speed defender in football: eyeball the line which runs through the midpoint between you and the defender, and see where it hits the edge of the field - run straight there.

I was immediately floored by this observation, because it is so easy in retrospect that it should be common knowledge. Yet literally everybody I've told this to has said that it was new to them - mathematicians & people from the general public. I quickly threw together a video to share it across the community:

https://youtu.be/9sxVgJ_wPaM?list=PLqv4sKOD1bsUoSs-SbzlA2BE1...

I think that by thinking of and packaging cool nuggets of "math" like this to share, we can help rebrand the image of math. :)

Re: A Group of American Teens Are Excelling at Advanced Math

#74

Post by poshenloh »

shmageggy wrote: post #28

The example problem they give is pretty neat, but they don't mention the (IMO) interesting part of it. After sketching out the answer, I was suprised that the height you gain is independent of the size of the underlying circle . That certainly suprised me, as my intuition was that the height you would gain would shrink as the underlying circle grew -- after all, you'd be adding a constant length to an ever growing va…

Thanks! :) We were really thrilled to post the problem.

Our rope question from expii.com/solve is a multi-layered math puzzle. If you haven't seen it before, the answer is often quite surprising: a human can walk under the circle even though the 710 inches of extra length are shared over the whole earth's circumference. Basic human intuition produces the most common answers, which are the bacteria or the ladybug. This helps to illustrate the purpose of math: to help us reason to determine the truth when basic intuition fails. If basic intuition were always right, then we wouldn't need math!

If you had seen the puzzle before though, you would already know that the rope lifts high, because it lifts by 710/(2*pi) inches, which is 113.0000095... taking us to the second layer of math embedded deeper in the problem. That is remarkably close to a whole number, which is surprising because pi is an irrational number. This means that pi is very close to 355/113, which brings us to the topic of Continued Fraction representations of irrational numbers, and amazing rational approximations of pi: https://en.wikipedia.org/wiki/Mil%C3%BC

So, this problem hits at both basic and advanced levels. :)

There are many interesting ways to teach math through multi-layered puzzles which have something for everyone, no matter where you are in the experience spectrum. Our goal is to provide these for free, disseminated over the Internet. :)

Re: A Group of American Teens Are Excelling at Advanced Math

#75

Post by mineshaftgap »

anonymid wrote: post #65

I was frustrated by this article because I find it taking for granted the idea that math is only accessible to a small group of people - 'talented, gifted, with an affinity for, confluence of specific abilities'. I find similar language around programs like the Russian School, Brilliant and quite obviously the 'gifted' programs. Yet in this article they quote the following statistics: - High achievement in math: US 9…

> We spend the least resources on the children who need it most.

Actually we spend a lot more with no returns. No amount of investment will ever offset bad parenting. Short of removing the children, which will never happen, what can be done?

Re: A Group of American Teens Are Excelling at Advanced Math

#76

Post by mixedmath »

VLM wrote: post #54
mixedmath wrote: post #4

I've taught a summer program in number theory for high school students for the past several years. Each summer, my classrooms fill with high school students that are intrigued by the idea of math and extremely capable. That is nice and inspiring, and generally more rewarding than when I teach calculus classes to university students during the school year. But my program is prohibitively expensive, and I'm acutely awa…

"But my program is prohibitively expensive" Why? Just curious if there's any brainstorming to be done. Also expensive relative to what? Some people think Kumon is expensive. My kids did it for a couple years. Its about $100/month. Its very popular among immigrants who make a whole lot less money than I do. Of course Kumon isn't "real" math because its very drill -n- kill (which is why we quit, more or less)

> Why? Just curious if there's any brainstorming to be done.

I'm afraid that I don't know about the actual costs. There are several classes offered, and though students only take one at a time, they sometimes link a few and stay for up to 8 weeks. It's a pretty large board-at-the-university-for-x-weeks style summer program.

I'm an instructor, and I don't set prices. I also understand that there is a non-negligible cost to house and feed a student for a month. But program costs each student about $6000 dollars. I think that's enough to be called "prohibitively expensive," although I'm not sure how to compare these things really.

Re: A Group of American Teens Are Excelling at Advanced Math

#77

Post by rhino369 »

lintiness wrote: post #20
venomsnake wrote: post #18

Earlier quoted context omitted.

Aren't schools financed by local property taxes in US. And the rich parents pay more in taxes and there is more resources in the system. Also well off parents could help school in other ways.

teachers in bad / poor areas in the states aren't paid less than teachers in the "good" areas. cps for instance, chicago public school teachers are among the best paid and worst performing in the country.

It's not as simple as that. There are a lot of rural areas where teachers make almost nothing. Chicago can afford to spend a lot of money (since it has rich areas it can tax). So they spend a lot on schools in poor areas of the city.

And then educational outcomes of the poor rural and poor (but expensive) urban schools aren't different.

Re: A Group of American Teens Are Excelling at Advanced Math

#78

Post by jimbokun »

fluxquanta wrote: post #48
Ntrails wrote: post #25

Earlier quoted context omitted.

The sad thing is that the cool stuff isn't even always complex. It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules. But at the same time - I know I'd have/did enjoy that stuff but maybe 60% of my classes would have played up if a whole lesson was spe…

>It's little things, like going through how the quadratic formula is derived instead of just telling someone to learn it by rote. Explaining differentiation with a bit of the logic behind it instead of just teaching rules. Once you get in the mindset of deriving equations, rote memorization becomes insanely difficult, at least in my opinion. During my last year as an undergrad majoring in physics I got a 4.0 in quant…

  10 - 1 = 9

  9 * 7 = (10 - 1) * 7 = 70 - 7 = 63
I often do little calculations like this when I forget multiplication table entries.

Re: A Group of American Teens Are Excelling at Advanced Math

#79

Post by jimbokun »

anonymid wrote: post #65

I was frustrated by this article because I find it taking for granted the idea that math is only accessible to a small group of people - 'talented, gifted, with an affinity for, confluence of specific abilities'. I find similar language around programs like the Russian School, Brilliant and quite obviously the 'gifted' programs. Yet in this article they quote the following statistics: - High achievement in math: US 9…

"What would a group of people that cater primarily to the best-served students in the system have to say about how to help the worst-served? What would they know about the obstacles faced by poor children and parents; overworked, undertrained and unsupported teachers; and underfunded schools?"

Hopefully they wouldn't get caught up in all that and just teach some math to whoever's interested, regardless of income level.

Re: A Group of American Teens Are Excelling at Advanced Math

#80

Post by shmageggy »

poshenloh wrote: post #74
shmageggy wrote: post #28

The example problem they give is pretty neat, but they don't mention the (IMO) interesting part of it. After sketching out the answer, I was suprised that the height you gain is independent of the size of the underlying circle . That certainly suprised me, as my intuition was that the height you would gain would shrink as the underlying circle grew -- after all, you'd be adding a constant length to an ever growing va…

Thanks! :) We were really thrilled to post the problem. Our rope question from expii.com/solve is a multi-layered math puzzle. If you haven't seen it before, the answer is often quite surprising: a human can walk under the circle even though the 710 inches of extra length are shared over the whole earth's circumference. Basic human intuition produces the most common answers, which are the bacteria or the ladybug. Thi…

Ahh, I had assumed you had chosen that length because 2*pi is close to 6, which easily divides into 60 feet. But this is way cooler. Very neat!
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