Tuesday, March 9, 2010


Joe works too fast.

Joe doesn't show his work.

Joe ends with the beginning in mind.

Today Joe took a test on being able to identify the graphs of quadratic and cubic equations. He bombed it.

Joe came back to my desk while the rest of his class was finishing their tests and had some good questions. He said he didn't know how to set up an input-output table so I showed him. I plugged in one x and found y. I plugged in a second x and asked Joe what the y-value would be. Joe did the rest himself.

Joe and I graphed his results. I asked Joe to graph a simple parabola with coeffieient of 1 on the same set of axes.

Joe said, "Hey Mr. Cox, if the number in front is bigger than 1, then it grows faster."

"And what if the number is a fraction?"

"Then it grows slower?"

"Are you asking me or telling me?"

"It grows slower."

"What if the number is negative?"

We turned the paper upside down.

Joe gets it.

His grade is different than he thinks it is.

Update (can I update a post I haven't published yet?)

Joe just informed me that a cubic with a positive coeffiecient will end up in the 1st quadrant and one with a negative coeffient will end up in the 4th. Yeah, better get on that grade change.


CalcDave said...

I don't know Joe, but will he know it next week? He is clearly making a few connections right now with the Socratic questioning you're leading him through, but will it continue to tie together in the future? I hope so. But if not, in the "new learning replaces old learning" system does his grade go back down?

Sorry to be a pessimist. Just wondering how you do it.

David Cox said...

That's the question of all questions. Not sure that I have a really good answer for it right now. I tried to stay out of the process as much as I could, because I didn't want him to depend on me for cues. I told him his score was going to improve, but I am leaving room for growth. It's up to him to come back next week and finish it up. I'm pretty sure he's going to do it.

The lesson that I think really hit home had nothing to do with quads and cubes. It was all about the process of questioning. He just figured out what it feels like to really question something to the point of understanding it. I don't think understanding like that goes away. Will he remember the shape of the graphs next month? I don't really care because he could question himself through it if he had to.

CalcDave said...

Right, and that's the true key. Will he remember the cubic graph in 20 years? Possibly, but likely not. Will he remember the "thinking how to think" moral? Very likely.

He seemed to already be making steps in that direction by asking you for help on it--even after the test.

Congrats on your work with Joe!

David Cox said...

Do you have a blog?

CalcDave said...

Heh, no. I'm still in the "I don't have anything interesting to say" stage of blogging (i.e. thought about it, but not really put it together). So, I'm an "active commenter," but otherwise not a huge contributer to the community.

David Cox said...

I'm sure you have more to say than you think. I felt the same way but figured, what the heck. In actuality, I use it more for a journal than anything else. It just so happens, some folks care to read, which I think is great. I'd like to get better at journaling about shortcomings.

iTeach said...

I'm still thinking about Joe.
And here's what I came up with.
My weakest subject in high school was US History.
The only things I remember were the ones I cared to question and then figured out through questioning and personal research. The only thing I remember my teacher telling me is that he would shave his beard off when it was time to study for the AP exam. Huh.... Joe might have a chance.

David Cox said...

Isn't that how it works? We remember the things in which we invest ourselves?