## Tuesday, November 16, 2010

### AMATYC Conference in Boston

Well, there wasn't enough math to suit me. But a few of the sessions were great. I especially liked two of the Saturday workshops.

One was on the history of pi, and the presenter, Janet Teeguarden, set it up as a game of Risk (her own version).  We got a sheet with 25 multiple choice and short answer questions, and put our answers down. As she presented, she'd stop at each question and ask us to put down how many points we wanted to risk. We started with 100 points, and each question allowed us to increase that if we were right. One person was sure of his answers on ten questions and didn't try any others, so he got 102,400 points. I was only sure on a few answers, but tried a bunch. I got up over 10,000 points. The game kept me listening much more intently to a presentation that I might have mildly enjoyed otherwise. (And I'm not good at listening to presentations that don't have audience participation, so I might have drifted away, even though it was interesting.)

Although this presenter used Powerpoint for her presentation and the game (it made a cool swooshing noise as each answer was shown), I think I could do something similar with just a worksheet and the board. I think I'll try this when we're reviewing for the final exam. I could give them a practice final to do as homework, and then play Risk with them as I go over it.

[Edited to add...]  Here are the first few questions of the 'Risk Your Knowledge of Pi' game:

 Risk Points 100 1. What is the formal definition of pi? 2. In what book will you find the following? “Also he made a molten sea ten cubits from brim to brim, round in compass, … and a line of thirty cubits did compass it round about.” 3. What ancient Greek mathematician determined that 3 10/71 < pi < 3 1/7? 4. He used circles with inscribed and circumscribed polygons to make this estimate. How many sides did his final polygons have?

I risked 100 on question 1, got it right, and entered a total of 200.  I risked all 200 on question 2, got it right and had 400. I think I risked all 400 on question 3 and got it right, for a total of 800. I risked 50 on question 4, and got it wrong, for a total of 750.

The next session was something about improving antiquated word problems. The presenter (a textbook author) talked about how silly some problems are, and how he tweaks them to make them more relevant. He said: "Functions are the heart of intermediate algebra." I've been looking for a way to tie all the topics together, and thought that might work for me. I'm excited to look at the text again, and see whether a function focus would tie most of it together.

The problem we worked longest on started out something like:
The 10,000 seat stadium will sell out for the rock concert. The better seats are \$65 and the cheaper seats are \$45. How many of each ticket type must be sold to bring in revenues of \$500,000?

Silly question. Why do we want that revenue in particular? If we change it to a function question, it becomes more interesting: Create a function that takes number of \$65 \$45 seats as input, and produces revenue as output. There are all sorts of things that can be done with this:
• Graph this function.
• What does the y-intercept represent?
• What does the slope represent? (Hey, the slope is negative. More tickets means less revenue? How's that possible?)
• What x and y values make sense?

On Thursday (backing up), I went to a fun workshop on using the abacus. Now I'd like to spend some time trying it out with kids.

I also visited a math circle on Sunday morning and had a great talk with one of the presenters afterward, just before I caught my plane home. The woman I sat next to on the plane liked to talk, and that made the time go faster for the first half. After 3 hours, she'd run out of stories and neither of us was looking forward to the 3 hours left to go. I offered to show her some math, and she said sure. I showed her binary numbers by starting with a magic trick. (Hey, I think I have to revise my post on binary. I left that out!) You normally start with 5 cards, each showing some of the numbers from 1 to 31. I just wrote them on my paper. She got into it, and I showed her a way to subtract by adding (decimal first, then binary). Our flight wasn't over yet, and she said she liked algebra, so I showed her some of the Pythagorean triple patterns. We were landing as we finished that up. Thank you, Helen, for being an eager student - you made my flight so much more fun!

It's good to be back home, and I'm pumped up for the last few weeks of the semester.

1. ‘The 10,000 seat stadium will sell out for the rock concert. The better seats are \$65 and the cheaper seats are \$45. How many of each ticket type must be sold to bring in revenues of \$500,000?’

I’ve done enough of those stupid mixture type problems, and I’m amazed at how little thought goes into making them relevant. I love the idea of setting up the revenue as a function of \$65 seats sold, although I disagree with your statement that the slope is negative, I think positive \$20 is more realistic.

By the way, if one wants to keep these type of problems for the purpose of having students solve systems of equations, why not introduce the idea of a linear inequality? The question ‘what is the minimum number of \$65 seats that must be sold to bring in revenue of \$500,000?’ has the students solve same systems of equations, and has more relevance to the real world.

2. Thanks for catching my mistake, Cody. I should have looked over my notes, or done it more carefully. In the workshop we set it up as a function of the cheaper seats. I'll edit my post to reflect that.

3. Any chance you could post the RISK worksheet you used, i.e. the rules for wagering points on each question and succeeding questions? I'm having trouble visualizing it well enough to be able to reproduce it.

4. I don't have an electronic copy yet, but I can post the first few questions. I'll edit the post again.

5. Thank you! Now I get it and can see some great applications, such as an alternative to "popcorn notes" from time to time.

6. So what are popcorn notes?

7. getting strangers to talk about math for fun
isn't easy... anyhow, not for me... so, wow.

(indeed one encounters outright *hostility*
to the whole idea more often than not
until, usually, one simply gives up trying.
i'm probably going to do that [again] soon
but meanwhile have all these zines to
pass out...).

functions-as-central-concept-of-precalculus
makes for a pretty good organizing principle
in my opinion (not that it'll be much use
*having* one's own opinion on such matters
in our actual day-to-day work since courses
are designed by other entities than us).

the precalc i did just before burning out on VME
(and wrecking my career at Midstate Community C)
http://vlorbik.wordpress.com/2010/01/13/partial-contents-version-ii/
(the 2009 stuff) began with
so-called "transformations"
of functions... how do changes
in the code correspond to changes
in the graphs... and this made
for a very exiting quarter to me
(and, though i say it that shouldn't,
for a goodly handful of the students)
as i experimented with notations
that'd be easy to use and understand.
(i think i even arrived at some answers,
though of course i despair at getting
anybody with any actual influence

i hope you don't mind my plugging
this ancient history here. it sure as
heck doesn't seem to do much good
plugging it at home. more of my
wellknown gives-up-too-easily
streak, i suppose...

OT his mark

8. for the cut-and-paste impaired
(a majority as i guess)
to Vlorbik on Math Ed's
"partial contents" post.

9. This course isn't pre-calc. It's the equivalent of a high school algebra II course, more or less.

So the function connection is at a lower level. But I do think I can enrich the course by trying to make that connection as clear as possible, as often as possible.

(And I never mind you plugging your ideas, Owen.)

I think the secret for getting strangers to play with math is being on an airplane. People will do things they usually wouldn't, to escape the boredom. For me, I start noticing how uncomfortable my seat is if I'm not immersed in something.

This is at least the second time I've had a fabulous math conversation on a plane. The previous time was many years ago. I'll post about it as soon as I have some illustrations done (the hardest part of blogging imo).

10. "So what are popcorn notes?"

Sorry, Sue, for the delay in answering your above question--Feed Demon doesn't consolidate the posts and comments together so I sometimes miss follow-up discussion.

Popcorn notes are often used in "basic" level classes of algebra, pre-Algebra and developmental math. They're designed to help the students stay focused during the lesson.

A quick example. The students get a hardcopy of the power point lesson that's on the smartboard. One of the ppt slides may say

Lines that have the same slope are _________________.

The students have to pay attention for when the teacher says the answer and writes it in the blank on the smartboard. The students then write the answer on their hardcopy.

From my experience, popcorn notes are mainly useful as a staying focused strategy rather than as meaningful notes for studying from: most students toss them away at the end of class.

Your Risk Game seems to be another way to help students stay focused during the lesson, hence the comparison to "popcorn notes."