When Grover Went Viral

About a month ago I walked into my office and found this problem on the chalkboard next to my desk:

Do you think Ryan should have made option "C" zero percent? ;)

My officemate, Ryan Grover, had put it there to tease us with what I quickly believed was a paradox. Having dealt with paradoxes before, I knew the first rule of paradoxes: "Don't try to reason with paradoxes." Instead, I thought I'd post it to Google+ to see if some of my math-oriented followers could have some fun with it.

Ryan will be the first to admit that he is not the creator of this problem. He told me that he had seen something like it, had given it some thought, and then searched for similar problems. Ryan found variations of the problem on Reddit, got his wording just right, and wrote it on the chalkboard. He knew it was worth sharing, just as I did. But I had a different sharing mechanism in mind.

I posted on October 20th and nothing much happened the first few days. Then things really took off. You can get a sense for some of the progress thanks to Google+ Ripples. But what really got my attention was seeing Brian Brushwood share the picture on October 27th. I follow Brian because of his work on TWiT.tv, not because I expect him to post interesting probability problems. Because the picture had made its way to Twitter, where Brian saw it, and then back to Google+, it was no longer connected to my original post. Still, Brian's post quickly got over 2000 reshares -- including one by Terence Tao. I argued to Ryan's (and my) advisor that "getting cited" by Terence Tao should satisfy Ryan's "publishable work" requirement of our PhD program, but I don't think he bought it.

The same day Brian posted the picture it hit Reddit (and again in days following), getting over 2300 comments, probably 10 times more than in previous posts. I wonder if it's the placement of the problem on the chalkboard that added to its appeal, or if it was just the right question at the right time to engage people's interest. The next day the picture appeared again in Google+, this time in Ed Yong's stream where it got over 1500 reshares and 300 comments. It was also quite a treat to see the picture show up at FlowingData.com. I'm a pretty big fan of Nathan Yau's blog and book, and in an email Nathan said the 788 comments were probably the longest thread of any post ever made on FlowingData.

There's no way to count precisely, but the picture was reshared publicly on Google+ (where an estimated two-thirds of posts are private) around 5000 times and comments on Google+, Reddit, and FlowingData also number in the several thousand. Some good things have come of this:

1. It's been fascinating to watch people try to reason through the problems in the comments. Math teachers like to watch people who don't give up easily.
2. I've picked up several hundred followers on Google+ from all over the world. Many of them have interests in mathematics and how it is taught and learned, and what they've shared with me is many times more valuable than even seeing the comments and shares from Brushwood, Tao, and Yau.
3. It's bolstered my (and my colleagues') belief that if something is interesting, it should be shared. We're not in the business of keeping good ideas to ourselves.

As far as I can tell, maybe only two bad things have come from this:

1. We've experienced a little bit of "sharer's guilt" because neither Ryan or I deserve any credit for actually coming up with the problem. Someone who shared the problem before we did, such as in those previous Reddit posts, might be feeling justifiably peeved that they aren't getting the credit they're due. We're sorry.
2. We've avoided erasing that portion of our chalkboard, even though we could use the space. Next time Ryan has a perplexing problem he'll have to write smaller. :)

CCTM 2009: Guidelines for Assessment and Instruction in Statistics Education: Progress from K to 12

Presenter: Jerry Moreno, John Carroll University

I attended this session because I'm very interested in the growth of probability and statistics education in K-12 mathematics. I realize now that it was a neglected part of my own education, but as a teacher I find statistics interesting, relevant, and powerful. I also realize, however, that placing greater demands on students to learn probability and statistics means new curricula needs to be developed and other areas of math might be compromised.

Moreno made his feelings towards high school math sequences clear up front: integrated math sequences are the only way to go, and he's helping push the effort in Ohio to rid schools of the traditional Algebra 1-Geometry-Algebra 2 sequence. (I believe he said Ohio was trying to standardize class names such as "Math Reasoning 1, 2, and 3" in their place.) Moreno sees probability and statistics as the single largest piece of a puzzle that connects mathematics, science, and social studies, and much could be gained by increasing the use of data analysis in all three subjects.

Moreno's presentation summarized many of the efforts put into the GAISE (Guidelines for Assessment and Instruction in Statistics Education) report, an effort of the American Statistical Association to guide implementation of the NCTM Data Analysis and Probability standard. The ASA has produced a collection of student investigations called "Making Sense of Statistical Studies" for upper middle school and high school students. (They're working on sets of investigations for lower grades, building off work found in ASA's Statistics Teacher Network (STN) and other sources. Collectively the projects are known as GAP, or GAISE Activity Project.) During the session we discussed/experienced several quality investigations, dealing with varied topics such as the fairness of pennies, Mentos and Diet Coke, growing dahlias, and death certificate analysis.

There is clearly no lack of quality content available to teach probability and statistics to all levels. It remains to be seen, however, if schools are willing to break with traditions and reallocate their precious time to include more probability and statistics. I'm still wondering where the textbook publishers stand on this, particularly those who sell the traditional Algebra 1-Geometry-Algebra 2 series. Could we ever see a Algebra 1-Prob/Stats-Algebra 2 series, where geometry is reduced to supplementary materials, as many teachers have to do now for probability and statistics? Or will the massive educational inertia be too resistant to such a change?