Hello, reader!

Now that I've retired from the classroom, my year is turned inside out: my life proceeds at a reasonable pace during the school year, but I am crazy-busy in the summer. In addition to my own workshops (see below!) I'm offering a 3-day professional development inservice program for a school district, presenting at Twitter Math Camp, and (as every summer since 1985) attending the National Puzzlers' League convention.

I write this newsletter ahead of a month or so of relative calm before the storm. I hope to use that time to finish organizing the math materials I have sitting in the basement. Plus, of course, I need to get ready for the summer...

I wish you a happy end to the school year!

## Links

### Polya Award!

You may have seen my blog post about this problem: "Arrange the whole numbers from 1 to 18 into nine pairs, so that the sum of the numbers in each pair is a perfect square." I followed it up with a post about seeking help as I tried to generalize the problem. In a yet later post, I used my own experience with this problem as evidence that well-targeted hints can be a good thing.

Brian Hopkins, the editor of the Mathematics Association of America's *College Mathematics Journal*, saw the blog posts and asked me to write an article for his publication based on this problem. I liked the idea, and worked on it with Kiran Kedlaya and Gord Hamilton, two of the people who helped me think about this. See the resulting paper here. The story has a happy ending: I recently received an e-mail from MAA letting me know that the article won the George Polya Award for 2016, and that I should feel free to share the news with friends and colleagues.

### Hyper-Acceleration

Too many students are pushed to race through math content because of the erroneous belief that learning things at a younger age is a mark of intellectual distinction. For most, this ends up being counter-productive. I have combined my posts about this crisis of hyper-acceleration into one article on my Web site.

As it turns out, thoughtful university mathematicians agree with my perspective. See a guest post on this topic by Penn's Robin Pemantle, where he argues that the trend towards more semesters of high school calculus has come hand in hand with a trend towards shakier understanding of pre-calculus topics. Like my original post about hyper-acceleration, Pemantle's post turned out to be among the top ten most visited posts on my blog.

### GeoGebra or Desmos?

Both GeoGebra and Desmos are powerful tools, and I would encourage you to get to know both, and to deploy one or the other depending on the specifics of the day's lesson. In a recent post, I outline how I drew a vector in Desmos, using parametric equations, complex arithmetic, and transformational geometry. Check it out!

And see my online applets (mostly GeoGebra).

### The Two-Color Theorem

At the recent NCTM Annual Meeting, I was asked to run activities at NCTM Central (thank you, Math Forum!) and at the Math Teachers' Circles' "cove" (thank you American Institute of Mathematics!) I used this worksheet in both. It is a puzzly approach to a topic in graph theory, which would work well in a discrete math class, or frankly in any math class as an enrichment topic.

### Visual Algebra Update

**At NCTM**: I also gave a talk on Lab Gear basics. It was well attended in spite of the 8am starting time, and seemed to go well. The handouts were taken from the Didax Lab Gear books, plus these two.

**On my Web site**: I added correlations between my animated Lab Gear slide shows (some of which I used at NCTM), with the relevant pages in the Lab Gear books.

**On my blog:** I responded to a correspondent's question about how to teach factoring a sum of cubes.

**In my summer workshops: **Visual algebra (including the Lab Gear and much more) is the central theme of all my summer workshops. See below!