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Teaching off topic 1

January 19, 2009 am31 5:27 am

I haven’t written about teaching all term. Don’t know why. Just wasn’t moved, I guess. Classes are similar to previous years: Algebra I, a half-year-advanced Algebra I, College Algebra (at the college), and my first term senior elective: Combinatorics.

I go off topic all the time; it’s how I teach. But I was miles away twice last week, and both may make interesting stories. Here’s the first:

Combinatorics wrapped up. We counted in September, October, and November, learned a little probability in December, and then expected value. This month we analyzed a few games, including roulette. I don’t think the kids did spectacularly, but, most of them really calculated the expected values for each bet in roulette, and were surprised by the result. There’s a big deal hidden in there: each kid had enough confidence in both their ability and in the mathematics that they did not challenge their result, or question their result, they were simply surprised. That sort of big deal can pass unnoticed, but it shouldn’t. It makes me smile.

Anyhow, I was getting ready for review, and padding out a few extra lessons. I tossed them some dice games. We did the Monte Hall problem. And then, last day before review, I show up and tell them to put the blackboard away (yes, that’s a story. another story. and I’m not telling it. at least not today). So away goes the blackboard, and I start to talk:

Most of you are waiting to hear back from schools now. You know that there are some objective factors that go into the decisions – grades, SATs. They look at extra curriculars. Right?

[half-hearted nods]

But you all have the sense that there is a random aspect as well. Two people with similar records, one gets in, one doesn’t, sometimes there’s no reason. And I think many of you are suspicious that there is even more. Some people have advantages. You know the right person who knows the right person. There may even be elements of corruption. I think most of us believe that we have some combination of these elements, both the fair and the unfair?

[I have their attention, with focus]

Most of you know I am from New Haven. Grow up. Have family. Certain connections. So, every year, in the fall, I take out a shady ad on the internet – I need to tell you, I don’t do this to [my school’s] students – I take out an ad, targeted to Stuyvesant students, and I offer them admission to Yale, in return for two thousand four hundred dollars.

[I ignore the cries of “really?” – answering would break a great flow, plus I’ve been in the school longer than they have, and they should have known. Should have]

I do this with a money back guarantee. And I have done this for years. No problems, no complaints. Talk it over at your tables. How do I pull this off?

Now, for those of you who don’t know me, no, I don’t do this. The scam used to occur with university admissions in the Soviet Union, and Tanya Khovanova explains it nicely here: Probability Theory for Crooks. But my kids didn’t know that.

And I had them hooked. There was buzz at all five tables. And apparently at four of them, they arrived at the answer.

I do nothing, politely return the cash to the 90% who don’t make it (drop that number a bit for a specialized high school), and keep the 10 – 20% who do.

If someone gets their money back, even though they did not get in, their final interaction with me is gettin something – a lot of money (so what if it was theirs). Even better, one girl pointed out that I need to make sure that those who do get in whisper around about my services… to increase business the following year.

It was gratifying that so many of the kids disected this one. I did need to clarify for a few that this is a real scam, but that I don’t do it (!) but most knew from the start… What class are they supposed to learn this stuff in?

Then we talked about lotto, I handed out tickets, calculated some odds and checked against the back, discussed the Australian syndicate that tried to buy all the tickets when the odds tilted heavily to the players. (I flubbed the story, badly. The pitfalls I mentioned were real – multi-split pot, not being able to buy all the tickets – but these guys made out. I will correct myself Tuesday)

8 Comments leave one →
  1. January 19, 2009 am31 9:07 am 9:07 am

    The school admission scam sounds very much like a simple version of a sort of scam I’ve heard about involving the stock market. You pose as a company giving financial advice and send a letter out to a huge number of people inviting them to join and including a free prediction. Half the people you tell that the market will go up, and the other half that the market will go down. A month later you send another letter to the half that got the correct prediction, and you do the same thing. Iterate this process maybe five times, and at the end 1 out of every 32 people will have gotten an astonishing string of five correct predictions. Those people will be so convinced of your expertise at making financial predictions that they’ll pay a fee to keep getting your services. If you’ve started with a sufficiently large pool, then even 1/32 of that is enough suckers to earn you a lot.

  2. January 20, 2009 am31 7:21 am 7:21 am

    Speaking of the Monte Hall problem — which explanation gets the most nods of agreement for your groups?

    • January 20, 2009 am31 9:52 am 9:52 am

      I’ve done ok, but never hit that one out of the park. This year I played it differently. I took an assistant, and divided the room into the keepers and switchers. The assistant whispered the right door to me, a kid picked one. I revealed a loser, and the switchers switched and the stayers stayed, and, know what? After a bunch of trials, it was clearly 2:1. So I asked for explanations and got reasonable but uninspired responses. Running the trials had stolen the mystery.

      I’m not sure if I will repeat it like this next year.

  3. January 23, 2009 pm31 5:01 pm 5:01 pm

    here’s what got *my* nod of agreement.
    we’ll play a game: pick a card out of the deck; don’t look.
    if you end up with the jack of hearts, i’ll give you a dollar.
    don’t look yet. now i’ll go through the rest of the deck,
    looking at each card in turn … and i throw fifty cards
    one-at-a-time face-up on the table. now i’ve got
    one card; you’ve got one. i pay a dollar if you’ve got the jack.
    wanna switch?

  4. January 31, 2010 pm31 5:35 pm 5:35 pm

    Are there a few pool players in this board. I am simply thinking.And I do not think about the swimming sort. I mean the sport.Me and my friends shoot pool several times a week and I love to talk with new players online.Hope to find out from you soon. Thank you.


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