This could be a good example of how an application of that new published result (with respect to self-testing) could be included, this application in line with ways I suggested in The best way to retain information is by self-testing http://mathforum.org/kb/thread.jspa?forumID=206&threadID=2232135&messageID=7370690#7370690 on how to possibly apply that result, this result being that self-testing seems to force a processing of the information that otherwise might not occur.
That is, this situation could perhaps benefit from including some "repeat after me" type of the thing regarding what the various variables mean with respect to the overall behavior of the function, where students try to produce the information ("by memory", without "looking it up") after having been given it.
This reminds me of an episode I experienced in a Calculus 3 class:
The professor on the first day of the course, while doing some review, asked for the definition of the limit of a function. Several people tried to give it, but as they tried, he clarified that he wanted the formal definition, that chunk of information that would actually be applied in some problem solving requiring the application of the definition. No one who tried could. (I could have, but I chose to stay silent, something I typically preferred in my math classes - whether it because the class was made up almost entirely of engineering and science majors, I don't know.) The professor used this as an example of how one can't apply something if one doesn't know it (and for whatever reason one is not able to look it up). And as to what is means "to know it", he said, "If you can't say [or write] it, then you don't know it."
- --- On Wed, 2/23/11, Joshua Fisher wrote:
> From: Joshua Fisher > Subject: Re: Pseudoteaching > To: email@example.com > Date: Wednesday, February 23, 2011, 12:46 PM > I don't have any issue with Meyer's > methods. I have an issue with the rusty, broken chain of > reasoning he and others use. > > Dan's post is a perfect example. First, af introducing > the working definition of "pseudoteaching," he presents an > example from his student teaching. This was the result: > > "I thought my students understood the behavior of r = > acos(btheta) on a deep level but they were only responding > to superficial patterns in notation." > > Very well. It looked like good teaching, but students > didn't learn. How would he correct this? > > "The students have to develop the algorithm themselves. > Given a second chance at that mess, I'd get students in > groups of three or four and let each student pick a member > of the family of the functions ? 'Okay, you do r = > 1cos(2theta). I'll do r = 2cos(2theta). You do r = > 3cos(2theta).' Rather than watch me mashing buttons at the > front of the room, students would graph their functions by > hand and then summarize their findings to each other and > then the class. Maybe with a poster ? your call." > > Fine. But all he's done here is present a different-looking > instruction and suggest that it's now suddenly not > pseudoteaching. > > The other posts are at the same pitch. In a nutshell: My > explanations suck, so students are better off figuring it > out for themselves. > > Actually improving the explanations is--as far as I've > read--not considered as an option. Changing the conclusion > is out of the question, and folks are simply figuring out > different ways to get there.