*is just about done with page layout - and it's looking so beautiful! I am sending in the last proofreading corrections today, and will do the last fixes to page number mentions as soon as I've seen the final copy. Then it's off to the printers, then all the copies get shipped to the publisher, and finally get sent to the hundreds of people who ordered copies during the crowd-funding last summer. If you're eager for your own copy and weren't around for the crowd-funding, you can order now. (You know I'd be tickled if we sell out our first printing quickly!)*

**Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers****The Links**

- Here's a nice multiplication model, using number lines, that makes multiplication by negatives, and by numbers like
*e*and π, make as much sense as 2x3. - I may have linked this before. But just in case I haven't, here's Fawn Nguyen's Hotel Snap activity. I want to play!
- Christopher Danielson has made a shapes book,
, that will tickle your logic funny bone. At first glance it's like the other books for very young kids, but this one will be fun for any age. This might be my new go-to present for 2-year-olds.*Which One Doesn't Belong?* - Using visuals and math to explain the process of segregation - a powerful combination, especially in the hands of Vi Hart.
- I always like Mr. Honner's photos. This one of Riemann Shadows looks good to share with my calculus class.
- Good post on the problem with factoring (it's not so useful in real life), and how much more useful completing the square is. Another post on Math Misery about two anti-derivative problems that look similar, use very different techniques, but
*could*be brought closer together. - Maria Droujkova has a question for you: What's one central idea of calculus you'd want everyone in the world to understand?
- Michael Pershan asks: What bigger ideas are proofs of the Pythagorean theorem connected to?
- A video of Donald Knuth (author of the lovely little book,
), talking about learning from his mistakes.*Surreal Numbers* - Kate Nowak pulls together what looks like a great (5-part) lesson on triangles - what you can figure out from what you are given (different combinations of sides and angles). I wonder if I can do anything with this in just one day with my pre-calc class... Shireen's lesson for inverse trig functions might be helpful too...
- Numberplay appears in the New York Times (at least online) every Monday. Last month Daniel Finkel (of Math for Love) provided this new take on a favorite puzzle type:
*There are two bags of coins. One contains genuine silver dollars, and the other contains a mix of two types of counterfeits, the first of which is too heavy by 0.01 ounce, and the second of which is too light by 0.01 ounce.**Using a balance, you weigh the two bags and find that they both weigh exactly the same amount. How many additional weighings will it take to determine which is the bag of real silver dollars if there are 32 coins in each bag?*

- Two Truths and a Lie: Get calculus students to make up stories from their lives, using the idea of rate of change, and matching given graphs. Brilliant, Shireen!
- I like this for a first day activity! (I just figured out how to link to this on my google calendar to remember to look at it in August!) Getting the students involved in discussing what education should be, and what productive failure might look like.
- Explained Visually has animated graphics for trig functions, exponential growth, statistical processes, and more. Fun.
- Beautiful teacher story. “You just listened, so then I could figure it out.”
- This post asks: Is there room for math that isn't hard? The post and comments are both interesting reading, and I'd enjoy seeing more comments. The blog is called Math Exchanges, and their more recent post, Over or Under, is great too.
- About half a year ago, I joined in the crowd-funding for the math game Prime Climb. It arrived in early December (or was it in Novemeber?) and we played it at my holiday party. People definitely enjoyed it. Now I've heard about another game being crowd-funded. Three Sticks is a geometric game, developed in India. It looks fun. For a $35 contribution, you get the full set (and escape the very high shipping charges).
- The math in the solutions may be too hard to follow, but this problem is charmingly simple: Your hallway is one meter wide, and turns a corner. What is the greatest base area of an object that can be carried flat through the corner?
- I'm not so good at making things (origami, etc), but these pretty mathematical sculptures do look fun.
- Every textbook I've seen that includes conic sections shows the conic, and then shows another definition, and never connects the two. This blog post makes some of the necessary connections. (Anything on Dandelin's spheres catches my eye.)
- Tricky puzzle. (Do you like that sort of thing?) The 7 at the bottom is NOT a typo.
- I'm always happy to hear about new math circles. Here's one in Santa Cruz, in the news.
- Estimation questions are a great way to build number sense. And Andrew Stadel has a twitter feed just for that. This week included a few questions about these Lego Lions: How many legos? How long to build? How many legos tall?

**A Question**

I'm teaching Linear Algebra, and I find it a bit odd that linear transformations by definition don't include lines like y = mx+b (with b not 0). A student asked the significance of the word linear (she thought it was a silly question, and I assured her it definitely was not silly), so I started searching online. I noticed this site, which defines a linear transformation for statistics - differently from the linear algebra definition. It looks like the two definitions contradict one another. Any ideas about how standard this statistics definition is, or pointers to discussions of this difference in definition?

[Oops! I lost a few weeks on the #YourEduStory challenge. Maybe I can get back to it. My pre-calc class is going better than usual. My calculus students loved having all those handouts in a coursepack. And I love thinking about all the connections in linear algebra. This week's topic: Define "learning" in 100 words or less.]

Did you get your question answered about linear vs affine transformations and "math linear" vs "stats linear?" If not, here are some quick points:

ReplyDeleteOne key point in reconciling the stats and linear algebra definitions is that, with one important exception, key statistics are calculated relative to the distribution mean. The exception is the mean itself. This implies that other statistics, standard deviation, skewness, kurtosis, correlation, etc, are not affected when you add a constant. Further, that means most of the time statisticians move into a world where means are uniformly 0 and linear transformations are the same as in linear algebra.

Now, why exclude X -> aX + b in linear algebra? Actually, these are called affine transformations and do have their own limelight of study. However, one (modern?) way of thinking is that linear transformations are the maps between vector spaces that preserve the vector space properties, thus are a natural place to focus.

Nice! (I Knew linear connected to keeping vector space properties, but you put it well. And thinking about "normalizing", by using z-score to equate the mean with z=0, makes it clear why you'd want that broader definition in statistics.)

ReplyDelete