Five uninterrupted hours of Geometry differentiated between credit recovery students and enrichment students turns out to be exactly as easy as everyone predicted it would be. After misjudging time-on-task about a dozen times and grossly overestimating our ability to construct an orthocenter by Just Playing With It, I did something at the end of class that I didn't hate.
I put up this slide and asked Mika to pick a point out. I asked her to tell Jason across the room which point she was thinking of. She stumbled and stammered a bit. "It's sort of to the left of the one that's near the center," etc.
And then I added labels.
And it became a little clearer why we label points. Mika relaxed. Everything looked easier.
In 2007, I told my students that we name lines using two letters and I gave several examples. Today, I asked Mike how he would tell Kelsie across the room which of these lines he was looking at. First, it was easy.
Then it was difficult.
The same went for how we name angles.
This math thing is easier to approach if I ask myself, what about this concept is useful, interesting, essential, or satisfying, and then work backward along that vector, rather than working toward it from a disjoint set of scattered skills. There is probably a book I should read somewhere in all of this.
Also: I didn't hate our opening exercise in which I gave each student a) a compass, b) a straightedge, and c) a map of the Meyer family's South Pacific archipelago, Meyeronia, and d) five questions. [pdf]
- How many miles is it from Kenneth to Christy?
- Which island is farther from David? Barbara or Christy?
- List all the islands that are three miles from Kenneth.
- Find a location in the water that is the same distance from Tom & Bob. How many are there?
- Find a location in the water that is the same distance from Tom & Bob & Kirsten. How many are there?
2012 Nov 24. Of course you could just take the concept straight on — defining the terms and defining the notation. No one would have any idea what purpose that notation served or why you'd need two letters to define a line. The concept would be just something else to memorize. But you could do that.