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.

Tuesday, May 22, 2012

On Problem Solving

Phil Daro:
The American teacher looks at a problem they're going to use in a lesson and asks themselves, "how can I teach my kids to get the answer to this problem?"  The Japanese teacher asks, "What's the mathematics they're supposed to learn from working on this problem? How can I get them to learn that mathematics?"

If you want better answers, ask better questions.

Monday, May 21, 2012

Classroom in Crisis

From the recent issue of California Educator:

“My pacing guide doesn’t fit these students, and it’s almost inhumane to do it this way,” says the El Monte Union Educators Association (EMUEA) member. “The rigor is really too much for these kids.

 I'm not gonna lie, things are tough.  With the budget situation in California looking as bleak as ever, Special Education services are being cut.  Many students with special needs are being mainstreamed without the support they need to succeed.  And "despite [teachers'] best efforts, most students with disabilities are flunking algebra."

I mean, how else are they going to be able to learn about the 10-16-18 right triangle?  It's difficult enough for students to grasp the 5-8-9 Pythagorean Triple, though we may be able to do it with limited resources.  But, to use similarity to derive 10-16-18?  No, it takes a fully funded program to pull that off.

Please, Governor Brown, give these people their money.  Otherwise, they're going to have to cancel their biology field trip to the unicorn zoo.

Friday, May 11, 2012

Did I Get It?

The Prompt

Given: The green, red and blue points are collinear. What is the dimension of the blue square if the green and red squares are 4x4 and 7x7 respectively?

After a few minutes, B comes up and says, "Mr. Cox, can you check this out. I think I've got something."

She shows me her diagram.

And her results.

Yep, kid.  You've got something.