Tuesday, February 27, 2007

Mistakes

Algebra class. Teacher writes a list of 5 problems under the heading
Solve and graph each compound inequality

The teachers solves 4 problems, during which time the students are reminded that the compound inequality means that both inequalities need to be satisfied (not in those words), how to graph solutions on the number line, various notation, and so forth. They arrive at problem numbered 4 that reads:
-5 < -5x ≤ -20

While working out the problem the teacher says: "Now listen very carefully. We have to pay attention to our signs". They arrive at the following:
1 > x ≥ 4

and proceed to graph it:

Students make no comment, they copy down the solution and the class proceeds to the next problem. A conversation similar to this happens as the next problem is being solved:

Student: "So, if the bigger one is on the left then they go out, and if it's on the right then they go in?"
Teacher: "That's right"

After the class, I brought problem number 4 to the teacher's attention and got the following response:

Teacher: "I realized it as I was writing it down. I'll fix it by the fifth hour. I didn't want to confuse them."
I, dumbfounded: "?!"


How and when do we teach our teachers that making a mistake in front of the classroom happens, and is not something we should hide and sweep under the carpet. I remember making mistakes in classes I teach; we all do, sooner or later. I apologize every time I do as if I had wasted their time, and not taught them something of value. We make mistakes, but we need to deal with them in a responsible manner. Go back, fix them, show your students that even when you know something it is not shameful to make a mistake, but it is to hide it. Show your students that we are learning all the time. And that we should not think that we ever learned it all. I think I wrote about this before, but it seems that our teachers think that there is nothing more they need to learn once they have their teaching certificate. They are ready. Are we really?

6 comments:

jonathan said...

"but it seems that our teachers think that there is nothing more they need to learn once they have their teaching certificate."

Did you really mean to generalize based on one observation?

e said...

Of course not. I did sound rather pompous, didn't I? I apologize, I should have chosen my words little more carefully.

Another event that happened recently (for which I am not sure that can be categorized in the same fashion as this one, so I decided not to write about that one) reminded me of the story. The Teaching Gap talked about this culture more, and I think that they have more experiences regarding this matter than I do. I've been present when teachers were asked what they would do. They know the "correct" answer, which I am sure my teacher would have given as well: to correct the mistake. It's just that what we think we might do is often different of what we will actually do. I think when I wrote what you quote I was thinking more of the mistakes that we don't even know we make. Of which I've seen many examples. But I agree, I shouldn't hav generalized the way I did.

There was something else I was thinking of as I was writing. There were couple of my students last semester who were doing rather poorly, but not poorly enough that they would fail. I contacted their program leader and offered to work with them weekly while they student teach, so that they could talk about math they will teach and try to help them out that way. I thought that providing them with more support and opportunity to learn more would be something that a teacher educator would appreciate. I emailed him twice and never got a response. I shouldn't be assuming what he was thinking, but I can't help it.

Watching the people who blog has certainly provided some counterexamples to forementioned thesis. Admittedly it is hard to make any scientific statements, and I am not attempting to. Should I not mention it because I don't have statistical data? Anyway, you know more teachers than I do. What do you think?

Jonathan said...

I think it is uneven. In some places it is more of a problem than others. My school? Nah. Maybe one or two who coast a little.

My friend's middle school? Big problem. He told me about a teacher who changed subject areas because she thought her current area would have curriculum chnages more frequently.

I tend to surround myself with people who are dedicated to teaching, so I see even less than average. But even in my former large school, where the city, the state, the administration, the parents, almost no one seemed to really care, even there most of the teachers approached it seriously.

Lsquared said...

Having taught that topic several times (to college freshmen) I would say that the best thing to do with that problem would be to pause for a minute, point out that this one looks different than the previous ones, and then explain why there is no solution. I don't know that I would have handled it right the first time I ran into the problem though. You have to think about your content for a while as a teacher before you know the right way to jump.

I commiserate with you on your experiences with college of ed. Our teacher ed department is usually open to collaborations, but it takes a while to build up a relationship with them, and there are a lot of them who are math phobic.

e said...

sorry not to have remarked this before, i've been out of town. this teacher has taught for 10 years now :(

e said...

Lsquared,

you have a blog listed, but I can't get to it. Do you write but don't want to share, or do you not write?