## Wednesday, May 23, 2012

### On Chapters vs. Lessons

Phil Daro:

"Manage chapters; don't manage lessons.  As soon as you shift the focus to lessons, you shift it away from mathematics."

As a baseball coach, I always taught things from a whole-part-whole point of view. The game has a lot of moving parts.  If a ball is hit to the right-center field gap, everyone on the field has a job to do: RF and CF go after the ball, LF backs up 3B, 2B and SS line up for the relay to 3B [1], 1B covers 2B, P runs straight towards the 3B dugout and  reads the play and finally the C directs traffic.  If we look at everyone's job in isolation, it makes no sense.  However, if we see each responsibility within the context of the overall goal of keeping the runner off of third base, then it all fits.

In math, Daro argues, each concept has a proper "grain size."  If it's too large (strands), the math becomes fuzzy and incoherent.  If it's too small (lessons), the math becomes fragmented and incoherent.  It is important for us to understand the parts that make up a concept.  It may even be important for us to offer feedback on the parts.  It is never a good idea to teach the parts in isolation.

[1] Bonus points if you can explain why both the SS and 2B line up for the relay to third base.

Sue VanHattum said...

But managing the chapters puts the textbook in charge. I use units myself. And doing that has helped me to get away from depending on the textbook to define my course.

Joni said...

Depending on the size of the field and arm strength of the outfielder who gets to the ball first, it may require a "double cut" to get the ball to third.

Matt said...

Given Daro's comments about textbooks in the video, I'm guessing he would not be in favor of "putting the textbooks in charge" either. That makes me think that he was using the term "chapters" very loosely. He also used "units" on his slides to mean the same thing. I think "modules" could also work. Anything to mean "something slightly larger than the lesson".