Teaching in absentia...

So, I missed three days of class to attend a wedding in Belize... feel bad for me? Three days is a lot, and I really wanted them to be somewhat productive. For my Precalculus classes, I designed some worksheets that just barely pushed the boundaries of what we'd been doing. We'd been translating graphs, and I inched them into some dilation (or "scale-change" as our text book calls it) on top of that. I think they were productive, mostly because I didn't try to go too far.

In Calculus, I was ready to push the class a little harder, so I recorded a video introducing them to related rates. This is the first time I've ever done this, and it was (eventually) pretty easy. I used CamStudio (free), and didn't even bother with any editing. A single take... eat your heart out, Scorcese.

I think the video got pretty boring, but I like the idea, and might try it some more. I know there are tons of this type of thing out there, but I like making my own and I'm interested in tips for making them better. For instance, if anyone has any recommendations for editing software?

As for the effectiveness of the video, I think it worked well as an introduction. I didn't push things too far (no substitution of variables from another equation, for example) and I tried to hammer on the idea that this is just the chain rule. This is just the chain rule. This is just the chain rule. Now I've been back for a couple of days, and  we can start to explore those realms. But the video helped me at least feel like I had a head start in making up for the three days I fell behind.

Graph Translation Reflection

   So  I did my graph translation lesson with two of my three Precalculus classes (the conversation in the third class went a different direction, and it seemed to me at the time that the students in that class were more comfortable seeing the correct direction in a horizontal translation). The lesson ended up being much smaller in scale than I initially imagined, with 5-6 students in the front of the room, each with an assigned x-value. I then gave them each a different shape to hold (I borrowed some extremely large pipe cleaner type things from a colleague). I explained carefully that the shape represented the "value" of the function. Finally, I said, "Instead of your value, please take the value from x minus 3." After some fumbling, the function moved three spaces to the right. After a few repeats, they had it cold.

   So did it help them understand? They seemed to shrug it off as if I had gone to a lot of trouble to demonstrate the most obvious thing in the world. However, in the days since, I've not had a single question about why the graph moves in the "opposite" direction... except from the class that didn't do the demo. Feels like positive feedback to me!

Note: I didn't end up video taping the lesson... it felt like that would make the students think it was more of an "event" than it actually was. Plus, I started worrying about putting my students out there on the internet without notarized consent from their parents, their attorneys, and their parents' attorneys.

Brainstorming: Graph Translation

    I'm working an idea out in my head... I'm about to start discussing graph translations with my Precalculus students, which is a topic that I've never quite felt like I've really been able to guide my students to understanding. Instead, they memorize rules (this happens in all sorts of topics, of course, but I'll leave those for another day). In particular, I'm not satisfied with their understanding that when x is replaced by (x -2) in a function, the resulting graph has shifted by 2 in the positive direction, while (x + 2) would shift the graph in the negative direction. They seem to balk at first, and then just accept it as one of those weird math rules that I invented to make their lives a bit more complicated. They don't seem to reach the level of understanding that I want to see...

   So here's my idea, though I'm changing details as I write: I want to line the students up (outside?) so that each of them represents a number on a number line (the x-axis). They will literally hold a function (colored ribbon at certain heights? a rigid model of a function?) in their hands. This way each student (x), will have a value for the function (y) in front of them. What I want them to see is that when I ask them to take the y from the person (x) who is two to their left as their own, the function moves to the right.

Still TBD:
--will they have a solid object as the function? numbers to hold up? a ribbon? a lane line from the pool? does it matter?
--will all of the students participate, or will some watch? is watching or participating more effective?
--shall we record some video to look back on and share with the world?

--is this going to help them understand the concept?

Compelling Problems

   So I've stumbled into the math teacher blogosphere, and I like what I see. I like it so much that I steal lessons, videos, pictures, and even entire grading systems. So far, though, I've been engaging with the Web 2.0 world in a very Web 1.0 way, so I figure it's time to give back.

   After having my world opened to the kinds of compelling problems that excite and pull my students into the process, I'm hungry for more. I figure the more voices in the conversation the more great ideas that will come out of it, even if one those voices is just my own. To do my part, I'm trying desperately to train myself to spot mathematical applications in the wild. Maybe blogging about it will keep my eyes open...