# Critical thinking vignette; or, why people think I am mean

**Update below.

I’m going to break with protocol here and describe something that my current calculus class did (not all of them) that illustrates some of the problems with dependence on authority and on uncritical thinking that I’ve blogged about recently.

Episode 29 was on graphing derivatives of functions, given the graph of the original. The focus question for the lesson was, “How do we graph the derivative function?” and this is boldly printed in a schoolbus-yellow box at the header of the handout. I did a couple of examples at the overhead. They worked on a couple of examples themselves. We introduced the idea of differentiability as part of the group work (they tried to sketch the graph of the derivative of y = abs(x2 + 1)).

So the lesson is clearly, glaringly, obviously about graphing derivatives and is about nothing else.

There was a typo on the episode handout that listed the right exercise numbers for homework but had the wrong pages given. The pages given on the handout put them 70 pages back from where they are currently in the book, in the introductory section on limits. The derivative does not make an appearance until 55 pages after this. So this is clearly the wrong section; and it’s easy enough to just correct it to the right section, no?

Apparently, no. Fully 5/6 of the class did the limit problems instead. It appears to have never crossed their minds that it’s a bit unusual to be doing problems on limits, for a lesson that is not only not about limits but is actually 70 pages past the limit section, and which problems they had already done and submitted for homework two weeks ago. Either they just believed what I wrote, despite the obvious, or thought they were getting a decoy when we learned about that derivative graphing stuff.

And I, being a mean old professor, took off points for it. It may be my fault for screwing up the page numbers, but they have to bear the responbility of thinking carefully and believing things on the basis of common sense and obvious evidence and not because some professor says so. (Before you get excited, we’re talking 2 points out of a total of 850, so this is a slap on the wrist to tell them to pay attention next time — not a make-or-break thing.)

**Update: The same thing happened on the most recent episode handout today, and one of the students who did the wrong section’s exercises emailed me about it to ask what the correct list of exercises was. So they’re doing what good students should do — learn from past mistakes.

1 Comment

Filed under Calculus, Education, Teaching

### One response to “Critical thinking vignette; or, why people think I am mean”

1. I’ve been in a class where that happened and we talked about the wrong v. right pages after class. Most students decided to do the assigned homework because 1) they’d already done it so it would be way easier and 2) no teacher would count off for the teacher’s mistake.

I actually did BOTH assignments, rather than ask the teacher and appear foolish. (My sister has been told, in college classes, by three different teachers, that she was stupid. I’m not going there.)

It would never have occurred to me to count off on the students’ papers because they should have been able to figure out what the homework was. I have been frustrated with this before, but I am the teacher.

I thought your take on the authority and personal responsibility was interesting.