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Comment by j2kun | Hacker News Reader

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 day or two out of every year to visit a high school math class, we would see much more interest in math. Many of us (myself included) were not particularly interested in math in high school and didn't discover the cool stuff until college. So we were once the audience we'd be appealing to.

[1]: http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t...

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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 spent deriving and exploring concepts without rote learning.

Being a maths teacher has to be pretty rough, especially given the number of students who are openly hostile to it as a subject.

As an aside, I often think about my Religious Studies teacher who'd disparage topics like Maths as being irrelevant after school. We'd never use them she said. RS was vital to life success, Maths a pointless exercise. It still winds me up to remember.

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. :)

Very nice video. I like how you actually made it out to a football stadium to start the video. One suggestion if you want to make this more 'shareable': start with the 2d graphics and then transition to video shot using a drone. This will let you get overhead video illustrating the defender/attacker scenarios. If your stand-in extras can't run fast, just have them run in slow-mo and then speed it up in post. Please keep up the good work!

>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 quantum mechanics, but very nearly failed introductory chemistry (which I was taking to fill a science distribution requirement at a liberal arts college), despite many of the chemistry concepts just being edge cases of applied quantum mechanics.

There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was. I understood the solution to the problem itself, but when the professor started giving me hints I had to admit in front of the whole class that my issue wasn't with the number theory proof -- it was with the multiplication table we learn as children.

> There was also the very embarrassing case of being called to the blackboard to complete a problem in an elective course on number theory only to draw a blank on what 9 times 7 was.

If it's any consolation, the great mathematician Alexander Grothendieck (https://en.wikipedia.org/wiki/Alexander_Grothendieck), when asked to supply a prime number (at some point in a lecture)—and being puzzled by the idea of actually naming a specific prime number—famously thought for a while before suggesting 57. (https://en.wikipedia.org/wiki/57_%28number%29#In_mathematics)

You can also use your 10 fingers to instantly multiply by 9s.

Spread out your fingers. Number them from 1 to 10, left to right (i.e. left-hand little finger = 1).

For 9 * 7, simply curl finger 7 downwards.

Now you have 6 fingers on the left, and 3 fingers on the right. Voila, 63. :-)

  10 - 1 = 9

  9 * 7 = (10 - 1) * 7 = 70 - 7 = 63

I often do little calculations like this when I forget multiplication table entries.

As do I, but the pressure of the situation didn't help, especially when the natural assumption of the professor/rest of the class was that I didn't understand the much more "complicated" aspect of the proof and not something most people take for granted as just "known" from elementary school.

>what 9 times 7 was

Is there a reason you didn't whip out a calculator and do it there? Although I must say that I remember everything till 20x20 :P

I was standing at the blackboard in front of the class. I've always been flaky on multiplication tables for some reason, and doing arithmetic in my head isn't my strongest suit.

That said I excelled in math throughout high school and college. It just goes to show that elementary math really has no bearing on the type of mindset one may have for "more complex", logic based math and computation.

Trust me -- since that experience of being humiliated in front of the best students in the math department at my college, I haven't forgotten what 9 times 7 is.

Once in a graduate abstract algebra class (without being prompted) I interrupted the professor's lecture to remark that he had skipped the prime "15" in a list of primes he wrote on the board.

To anyone else confused, apparently “played up” is a British colloquialism for “misbehaved”. :-)

Consider all the people who had the opposite experience though (I'm certainly not one of them however).

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.

Thank you for doing this. I would have appreciated someone like you in high school.

I remember going to the "best" math teacher in my high school with a math question about my science fair project. He couldn't answer it. That was so demoralizing. I had already taught myself so much of the math and stats I needed to know for analyzing my project, so I only went to him out of desperation.

It would have been awesome to have a more advanced instructor available to talk with and learn from.

Thank you, your students appreciate you way more than you may know.

Let me add one more thank you for that blog, it's one of 6 I have saved to bookmarks. I love it!

What are the other 5 bookmarks?

FWIW, I really like your blog too! Not a student or teenager any more, though. :P

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