NWMC ‘19 Post Conference Thoughts

Once again, I went and spoke at the NWMC conference. This year it was conveniently located down in Tacoma.  That meant, no hotel or extended travel. Instead I drove down early Friday morning and spent the day going to sessions and then ran my own workshop in the late afternoon.

Overall, I once again had a fun time. It was not quite as thrilling (or as big) as being at Whistler. But most of that feeling was due to it not being a novelty the second time around.  What did really excite me the most was meeting people I’ve know online.   There were the organizers: Joyce Frost, Art Madoff et al. whom I know a bit.  But the two most exciting moments happened in sessions (one planned, one not)

First I went to a Math Circle presentation by Brandy Wiegers and Emilie Hancock out of  CWU on their work with Math Circles. I’ve known Brandy in particular online through her work especially the recent Jornal of Math Circles: https://digitalcommons.cwu.edu/mathcirclesjournal/   So it was great to have a chance to connect in real life and even chat a  bit about strategies for growing Math Circles within Seattle (A subject near and dear to me).

Secondly, I knew Bowen Kerins would be at the conference but his talk was cross scheduled with mine and I had written this off as a missed opportunity. But by great luck, I chose a talk at 3:00 by Joe Obrycki on some material from Kerin’s Pre-Calculus textbook, sadly now out of print.  Sure enough about 15 minutes into the process, in strolled Bowen. The room was fairly small so that afforded me a chance to go up and chat.  He showed me a piece of his talk about game shows that had a very clever approach to the combinatorics of ball picking. This piece of luck made my day.

[Imagine: a large equal number of black and white balls in a bag. If you pick 3 white ones you win, if you pick 2 black ones you lose. What’s the probability of winning if you pick a series of balls blindly one after another?]

CrossRef:  Here’s a book review I wrote recently on one of Kerin’s books.    book-review-some-applications-of-geometric-thinking

Session-wise, I was very happy with the talks I chose. Given only a day and the schedule of talks I notice in retrospect I leaned more heavily towards content over pedagogy than last year. I think this reflects the timing and people giving talks that I wanted to see more than any shifts on my own part. Some other highlights were:

• An interesting presentation on the use of dilation in particular to solve geometry problems by James King.   I left thinking that there is a lot more opportunity than I realized to make transforms more central beyond a basis for triangle congruence proofs.

• A fun Math History talk by Jessica Cohen out of WWU centered on the problems from the Rhind Papyrus which made me think of Jorge Nuno Silva and his video from this summer

• Joe Obrycki’s talk on polynomial Division and tangent lines. This is a familiar topic to me via Bowen’s book but it still is thrilling and I learned a new twist.  

Since the remainder when a polynomial f(x) is divided by  $ (x - p)^2 $   is the equation of the tangent line to the curve at p. This technique can be used to justify many of the basics of differentiation including the power rules.

• To find any individual power you simply divide $ x^n $  by $ (x-a)^2 $ and out pops as the remainder the expected result for the slope $ n \cdot a^{n-1} $
• But as soon as you start computing a few these results an interesting thing happens: all the decompositions start looking a lot like Pascal’s triangle:

Example:   $  x^4 =   (x-a)^4 + 4a \cdot (x -a)^3 + 6a^2 \cdot (x-a)^2 + 4a^3 \cdot (x-a) + a^4 $ 

• And this is a very natural result!  $ x^4 = ((x -a) + a)^4 $ which then is expanded via the binomial theorem.  This is where the Pascal’s triangle connection comes in and how we can generalize the result.

Finally my own workshop ran well this time albeit with a few less people attending  than I had hoped for (that was my general impression of most sessions / they were emptier than the BC versions ) :

My Slide Deck: math-circle-talk-slide-deck

The big difference was  I took two activities that worked well last Spring and ran them with the participants. These were chosen for ease of materials and on how well they ran with real kids.

• Some work with randomess: around 114-randomness   I ended up coming up with some new ideas just watching adults do the same thing.  First its interesting to generate the random sequences from digits in an irrational number and compare. Secondly you can blend results and that tends to increase true randomness quite a bit. Also I think this would pair really well with a talk about pseudo random number generators and or something with a random walk problem.

• A version of this dya415-weve-found-a-correlation   These problems are still captivating.