Wednesday, July 31, 2013

Zombies, Logs, Noticing, Wondering, Precalculus, and #TMC13

I attended the precalculus morning sessions at twitter math camp. Among other things, we made a list of topics that can typically be problematic when teaching precalculus. Then we each signed up to work on one of these topics and produce something useful.

I ended up working on logarithms with Summer (@mathdiva77) and her adorable southern drawl. I am not sure that she would appreciate the adorable adjective, but it's my blog.

We agreed that we both felt pretty comfortable with the procedural part of teaching logs, but we were missing some pizazz. We were missing a hook.

Our fearless leaders, Sam and David, had suggested that we start by trying to focus on our topic's big idea. We decided that logs, being the inverse of exponents, allow us to find an unknown exponent. Check.

So . . . How could we get our students wondering about exponents? We started talking about Max's session on noticing and wondering (one of my favorites!) and then Summer started talking about zombies because they're all the rage right now and we started getting super excited.

Zombies! We needed pictures of zombies! More importantly, we needed pictures of zombies multiplying exponentially. It took some effort to find some classroom appropriate, mild-looking zombies in groups of one, two, four, and eight. We pasted them onto a page in that order.

Then we typed the words "What do you notice?" and "What do you wonder?" at the top of the page and we were done. We basked in the glory of our creation. We envisioned our students noticing the number of zombies and wondering when there would be 1000 zombies, or when zombies would outnumber people. They would be putty in our hands. They would be begging us to tell them about this thing called a logarithm.

Next Sam said that it was time to share what we'd created. At this point I started to have doubts because, hey, did we seriously just paste four pictures into a word document and call that a project? The group offered some helpful suggestions, like attaching the pics to a timeline. We might let our students wonder about that, too, but we would ultimately have to provide that information in order for the questions to be answerable.

The more I think about it, being simple is kind of the beauty of it. Maybe it isn't that hard to bait students to ask the questions we want them to ask. Maybe the chasm between being teacher-centered and student-centered is much smaller than we think. Maybe all you have to do is start with a carefully selected picture, and then get out of the way.

We'll let you know how it goes. Stay tuned.

Monday, July 8, 2013

Unintentional Math Encounters of the Non-Mathy

If you are a math teacher, this has probably happened to you . . . Someone you know has come across a problem involving math and they ask you for the solution because, hey, a math teacher must know how to figure it out.

First, a little background story:

I grew up on a farm in Kansas. (So that's what me and Superman have in common.)

Over the years, my Dad's specialty has been modifying the equipment he uses to make it more efficient, user-friendly, and/or comfortable for the farmer. Several manufacturers have visited our family farm and utilized his ideas in their designs. I am proud of him, if you can tell.

On the fourth of July, after grilled hamburgers and before the small town fireworks show, my 73-year-old Dad pulled out a yellow notepad and sketched this:

He has been working on a piece of planting equipment, and he needed to know the length of x in order to form interior angles of 11 degrees and 6 degrees. It is a pretty simple right triangle trig calculation, but he didn't remember how to do it. I figured it out for him and we discussed the feasibility of my answer (x was smaller than he expected).

Since then I have been holding onto this sketch. It has me thinking about other times that I have been asked these types of questions . . . A former student building a garage with his Dad, another farmer calculating a complex feed ratio for her cow herd, and others.

It seems like these should be some of the best problems to put in front of our students because they are from non-mathematicians, unintentionally encountering math as a part of daily life. This, for lack of a better phrase, is "real life math".

I'll put this sketch in a folder and start collecting other questions as non-mathy people corner me for answers. But I am afraid my collection is not going to grow very quickly. And even if it did, the scenarios from the rural community in which I live are limited. I am always looking for ways to expand my students' perspectives.

I'd love to have help here. What math have your non-mathy friends asked you to solve?