## Tuesday, March 8, 2011

### Happiness!

Four very happy bits of math teaching news:

1. I have launched my new "Precalculus algebra skills" videos website! Check it out. Some of my students (not sure how many... mostly the strugglers, I guess...) are very excited about this extra resource. Or at least that's what they say. We'll see if they actually follow through and watch the videos. The videos are very detailed and so are longer than the 2- to 3-minute length that was recommended to me by a reader. That might change in the future, but I'm not sure yet. (It really depends on student feedback, I guess.)

For now, the videos are just there on a voluntary-access basis. That might change in the future as well, if I can be sure that every kid has access to them from home. (ie. 6 weeks before the final, I might start assigning 2 or 3 videos a week, or something, as spiraling review at home.)

2. I'm going to Park City Math Institute in July! woohoo! I'm super excited. (It's a summer program for math teachers and other math geeks. I've read really great things about it!) It's going to be really interesting / probably very hectic, because I'll be bringing my same 2 suitcases-worth of stuff that I'll be lugging to Berlin. Berlin is expecting me to report immediately after the PCMI summer program so that I can begin working on my immigration paperwork -- I actually had to negotiate a later starting date with their HR department, in order to make this happen. Which means that I'll have to completely move out of El Salvador before I head off to the program. Which means that things can get verrrry interesting in June. :)

3. I came up with a GREAT new way to teach bisectors as a locus of points satisfying a property!! I gave my regular Geometry kids a Do Now where they had to:
A.) Copy down the definition of a locus (with examples: a circle is a locus of points equidistant from a center, and a line is locus of points (x,y) that fit into a certain equation y=mx+b).
B.) Draw two points, M and N, and find 5 other points that are each equidistant from both M and N.
C.) Draw an angle YXZ. Then, find 5 points that are equidistant from ray XY and ray XZ.

After the kids tried parts B and C for a good few minutes (and most of them had figured at least part B out), I picked a volunteer to stand between a plant (representing M) and a chair (representing N), so that he/she's equidistant from both objects. Asked the kid to step forward away from both objects, but still remaining equidistant to both the tree (M) and the chair (N) at all times. After the kid took a few steps, we noted on the board how the kid had no choice but to walk perpendicularly each step away from the original segment MN.

We then repeated the same exercise but using the corner of the class as the original angle. I picked a different kid to start in the corner, to walk away from the corner, but always staying equidistant to both walls. We noted that they bisected the angle, and connected this to the Do Now problem.

After these demos, kids thought this concept was so straight forward! The idea that perpendicular bisectors (or angle bisectors) contained an infinite number of points equidistant to both endpoints (or rays) became obvious to them. We drew the diagrams on the board, connected the points using a line, and discussed why that line is the locus of all points that satisfy those equidistant requirements. I was really excited because I believe that this is a really abstract concept, but making kids act out the points really made a huge difference!!

We also used wax paper to explore how to find a perpendicular bisector by folding. I gave these regular Geometry kids pieces of wax paper, told them to draw points A and B, and told them to figure out how to get the perpendicular bisector by folding. Everyone figured out that A has to go on top of B. Silly me for actually teaching it to them last year!! (Apparently it's just common sense.)

Then we went into this pizzeria / bisector project from NCTM. It has a lot of good math in it! (I've used it once before; thought then that it was really great as well. I use the scenarios where there are 2 pizzerias in town, versus 3 pizzerias in town, versus 5 pizzerias in town. Each one really highlights different skills, and do not become monotonous for kids in that succession. The only very time-consuming part is that in the scenario with 3 pizzerias, you have to find the area of each region by counting the blocks and estimating when the fractional blocks make a whole block. For 2 pizzerias, you can still use a trapezoid area formula, so it's not so bad.)

On Day 2 of the pizzeria project, we illustrated the definition of circumcenter again using objects and people. This time, I had two volunteers, one starting off in the middle of a plant and chair #1, the other starting off in the middle of a plant and chair #2. As they each walked forward along the perpendicular bisectors, the class observed how at some point they collide. And I stopped them and said that that point of collision is called the circumcenter, and at that point they are equidistant to the plant and BOTH chairs! Later during the pizzeria project, when kids needed to explain the significance of a house that was located on all 3 perpendicular bisectors, they immediately recalled it being the circumcenter and recalled that it was equidistant from all 3 pizzerias! Brilliant!!

4. Even though I had been a bit skeptical of my own group activity of writing composition formulas and analyzing domains using a "playing deck" of function cards (see bottom of this post), my 11th-graders LOVED it!! And every child's understanding of composition functions improved visibly between Round #1 and Round #5. By Round #5, they were consistently getting the equations and the domains correct. I was SUPER happy!!!

Love my job. Love, LOVE!