## Sunday, September 19, 2010

### Where They Falter

I just gave / graded my first Geometry exam for the year to all classes. I thought I'd post a comparison of how my regular Geometry kids did on a few select problems. I am very interested in seeing where their thinking breaks down, so most of my questions are fairly tricky. There is always a good chunk of explanation / multiple-choice questions on each test, where you have to be absolutely sure of yourself to not fall for any of my "common algebra misconception traps."

Can you see where kids would falter? (You might be particularly interested in this if you yourself also teach Geometry, but maybe not.)

Pg. 1 turned out to be surprisingly easy for most kids (even though the questions are NOT simple). Most of the points I took off were because of incomplete explanations, not because of big misconceptions. Here is one kid who did particularly well (as you can tell from his total score, he isn't one of the "hot shots" of the class... he's pretty representative of the average kid). His explanations showed that he avoided all the traps that got my kids last year, which made me very pleased. :)

Pg. 2 is interesting, because it involved some multi-stepped sketching of diagrams based on verbal instructions (always harder for kids than you might imagine, even if they know the meaning of all the vocab words), plus some TRICKY multi-stepped algebraic problems.

Excellent-understanding example:

Spotty-understanding example:

Poor-understanding example:

In particular, in my two years of teaching Geometry, I find that kids always want to jump to calling all missing angles x, and then rushing to write an equation. (Even though I keep reminding them that you can't introduce your own x if there is already an x in the problem.) That's one of the biggest "gotchas" on this exam; I hope that moving forward, they will gradually fix this.

Overall, the kiddies did okay (ie. not badly enough to depress me, but with a lot of room to grow). :) My honors kids also had a decent spread, which is also good. (A small kick in the butt is always good for the honors kids. Scarily enough, some of them honors kids couldn't figure out how to find the area and perimeter of a 3/4 circle, because by just looking at the picture, they couldn't reason out that it was 3 times the size of a quarter-circle, which we had practiced explicitly as a class. ---SCARY FOR BEING HONORS STUDENTS!!!)

Ok. Off to my week! :) By the way, I've got one super-sharp kid in my honors class, who works at roughly 2.5 times the speed of others. I kept him spinning last week with a hardish Ken-Ken puzzle, and he was super happy. Got other good things to throw my way?

1. It's nice to find a kid that's extremely sharp in math (when you teach it). I once gave a hard SuDoKu to all my 100 students, and gave them 1 class period and 3 extra days at home to finish. Only 1 kid finished in about half the class period (and had it all right). He was the only one to finish the SuDoKu.

Do you always have 1 or 2 kids like these (little math geniuses) in your classes? I'd assume so as last year you taught both honors geometry and Honors Algebra II if I'm not mistaken. Do you always give them extra things they'd like, such as these Ken-Ken puzzles?

And yes, I am an avid reader of your blog, as you can tell :).

2. I have issues with giving those puzzles sometimes, because I want to be able to facilitate all kids to finish, and that would take a lot of time. (But anyway, they work better as time fillers after an exam, I guess.)

Last year I taught regular geometry and honors Alg 2. :) (I prefer a mix of regular and honors, actually.) The Alg2 kids were sharp, but the sharpest ones worked slowishly (very cautiously, OR while chatting), so I didn't need a lot of filler activity for them. This is really the first time I've had a kid who works so fast consistently (and correctly). I think he's too smart to be stimulated by SuDoKus, honestly. He needs something else, better.

Cheers,
M :)

3. Have you tried kakuro with him? SuDoKus tend to be boring to me as well but I LOVE kakuro! Perhaps it would be more of a challenge for him.