Friday, February 6, 2015

Linkfest for Friday, February 6

Before I share all the delicious goodies I've stumbled on, news of the book is in order:

Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers 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!)

The Links
  • 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.]


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

    One 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.

  2. 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.)


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