double stuff

I grade AP Calculus exams in the summer for a week.  It's a festival of math nerds, and if it weren't for the grading, would be my favorite vacation.  As such, it's plenty of work, but still a lot of fun.

 

One of the things I am able to do is take note of national trends in how students think about calculus.  We grade thousands of papers and the data is overwhelmingly obvious in some cases.  The past two years, a particular concept has been tripping the kids up.  It's called the chain rule, and the calculus aficionados in the world will recognize that it is a simple rule by which we are able to take the derivative of composite functions.  I teach this idea in early September and use oreos to illustrate the concept. I think the kids grasp it pretty well. 

Yesterday we were doing SAT prep, an activity the students dread, and we also had oreos.  Now don't panic.  There is absolutely no calculus on the SAT.  But the oreo eating was an opportunity to reinforce an idea in a new context, an opportunity to talk about the chain rule for just a minute while in the middle of something else, thereby making a new link to the idea.  I'm talking about building memory and helping kids encode ideas successfully.  It turns out, the more links we have to ideas, the more likely it is we are going to remember them.  

Memory formation is a reasonably well-understood process in the brain, and although we don't know every detail of the brain's functioning, any teacher worth her salt has a pretty good grasp on how to help kids learn and remember in her particular discipline.   

Yesterday's oreos were not an accident.  Repeated exposure over time improves memory retrieval.  If I have the time, I can create a well-planned class where each activity is useful and most every minute is utilized.  That's what teachers do all day, every day, and why we get so upset when some random person off the street thinks they can come in and do it better. 

Random Guy thinks this was a waste of time. 
Concerned Mom wishes I didn't give her baby sugar.  
Joe Student unknowingly had his brain manipulated.  
Visiting Principal didn't see any calculus. 
You know different.



If you want to know more about memory, you'll find a decent discussion here.