Math Teachers at Play #14

Is it back to school for you this week? Or are you still enjoying summer vacation? Maybe you’re an unschooler who enjoys math, and there is no on button for school! Whoever you are, enjoy the feast!

We have money problems (doesn't everyone?), a dish of art with math on the side, probability and statistics, factors and primes, problem-solving, and a miscellaneous bunch at the end.


A Riddle for the number 14: What’s the next number? 1, 5, 14, …


For those of you working in schools, here's some food for thought. JD writes:

In the United States the number of actual teaching hours (not planning, not meeting, not improving) is almost double the number of hours in Finland, more than double Japan, and the greatest in the world. Look at the data, read the analysis, over at 3σ -> left.

Money
Maria Miller, at Homeschool Math Blog, has great ideas about how to help kids Learn to Recognize Coins.

Chad Orzel, at Uncertain Principles, offered an estimation contest; Mary O'Keefe, at Albany Area Math Circle, analyzed the contest, first in terms of winner's curse, and then in terms of information cascades. I chimed in with some ideas about improving your estimation skills. The contest's over, but the posts are still fun.

Tanya Khovanova presents a group of puzzles about weighing coins, and explains the concept of 'revealing coefficient', in her post titled Unrevealing Coin Weighings.


Math and Art
Dan McKinnon has put together a great post on origami and its mathematical side, over at Mathrecreation, just in time to help me out with my upcoming math salon. Thanks, Dan! An older post of his on Sonobe units also looks helpful. (This photo comes from Sara Adams' blog, Happy Folding.)

Here's a math, art, and literature resource I found while wandering around Math Hombre's blog. Make your own One Page Wonder, a story book that can be read in lots of different orders. The geometry of it is mind-boggling. Hmm, I like writing, but I'm no good at drawing, I wonder if I can do this... It reminds me of some weird form of poetry.


Probability and Statistics
The best lessons seem to produce lots of noise or none. Ryan O'Grady has a lovely one, The Quietest Lesson, analyzing first bad jokes and then other writing samples, to find average word length and average number of words in a sentence. The same sort of analysis, Stylometry, was used to determine the authors of some of the Federalist Papers, and some writings that might have been by Shakespeare.

Mr. D's (I Want to Teach Forever) Deal or No Deal game in the classroom sounds like lots more fun than that TV show. And he's got some more ideas to make teaching and learning probability fun and successful, including 3 fun probability games and projects.

And I figured Jonathan's (jd2718) puzzle belonged here, because I think it takes the kind of counting we work so hard on when we're figuring probabilities.


Factoring and Primes
Jimmie thinks of blogging as electronic scrapbooking. At Jimmie's Collage, she's posted a great article, collecting resources for Living Math with Factors, Multiples, and Primes.

John Golden, at Math Hombre, gives us a word game and a factoring game that are both about Running Out of Options.

Sam Shah, at Continuous Everywhere But Differentiable Nowhere brings us Factoring, Schmactoring. I'm enough of a math nerd to enjoy factoring polynomials, and if you look in a textbook, most of them factor. Sam has put together a table to show us that most quadratics are not factorable. Hmm...


Problem-Solving
When math books turn to the topic of problem-solving strategies, they almost invariably either mention George Polya or just show steps similar to those he proposed:
1. Understand the problem.
2. Make a plan for how you might solve it.
3. Carry out your plan.
4. Look back. (Check your work, see how it might apply to other problems, etc.)

Math hombre gives us a good introduction to Polya, and calls those steps phases because he wants us to know we might need to go back and forth between them. He also recommends an article by Alan Schoenfeld. I'm hoping to post a review of Schoenfeld's book, Mathematical Problem Solving, soon, and was excited to see that link.

I can't leave the topic of problem-solving without mentioning Paul Zeitz, whose book, The Art and Craft of Problem Solving, gives a whole new take on how to think about it. He talks about strategies, tactics and tools, and then offers some killer problems to help you practice the tools, tactics and strategies he shows you. Oh yeah!


Miscellaneous
Evelyn Saenz loves to blog about frogs. Frogs for skip counting, frogs for game playing, and frogs in their natural habitat. Her contribution comes to us through her Squidoo lens, but she also has her own blog, Hands-On Learning.

Sam Alexander, aka Glowing Face Man, has written a great post about applications of higher math: why scratches on cds don't interfere with them playing well, how search engines work, and modern encryption.

I've been finding so many gems in my wanderings lately, I just had to include a few of those here as well:

• There's a totally approachable book about Fourier Series called Who is Fourier?, by (get this!) Transnational College of LEX. This group is interested in learning lots of languages, and when members wanted to understand language, they decided they needed to understand sound. That's usually done using Fourier series. They researched the topic, and ended up writing their own refreshing text on it. I was reminded of this lovely book when I happened across Matt Springer's blog Built on Facts, with his Sunday Function, most of which addresses using Fourier series to mimic a simple periodic function.

• Marcus du Sautoy is one more voice added to the chorus of folks saying there's lots more to math than what you see in classrooms.

• This last post will become my reference list each time I'm deciding what to learn next among the technological wonders available these days. My goal is to be totally tech-savvy in my classroom next year. Maria Andersen taught a Technology Boot Camp at Muskegon Community College (my old stomping grounds), and gives us a rundown.


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The next Math Teachers at Play blog carnival (#15) will be hosted my Maria Miller at Homeschool Math Blog, on September 4. Submit your blog article using the carnival submission form. Past posts and future hosts can be found on the blog carnival index page.