Friday, June 14, 2013

Loves Me, Loves Me Not: Using Differential Equations to Model Love

A couple days ago I picked up Steven Strogatz’s The Joy of x from my library.  After reading the table of contents, I immediately decided to start with Chapter 20:  “Loves Me, Loves Me Not,” in which Strogatz uses differential equations to model love.

Obviously, I have to use this next year with my calc kids.

A slightly shortened version of the chapter can be found in a New York Times article here.  Please go read it if you never have!  But, I recommend having kids read it straight out of the book (or a photo copy of the chapter), which has a lovely graph to accompany the situation being modeled as well as the differential equations right in the meat of the text.

This week, I attended a 4-day workshop by MAX Teaching, to improve literacy skills across all disciplines.  On the last day, we got to put some of our new-found knowledge to the test, creating different activities for the upcoming school year.  I typed up a summary of “Loves Me, Loves Me Not,” and then, with the help of one of the MAX consultants (also a calc teacher!), we created this “Interactive Cloze”:

Here’s what you do with this Cloze (copied verbatim from Max Teaching with Reading and Writing:  Classroom Activities for Helping Students Learn New Subject Matter While Acquiring Literacy Skills):

  1. Give to students a copy of the Interactive Cloze passage that you have created to summarize the reading and focus on key vocabulary terms.
  2. Students individually guess by writing (preferably in pencil) the terms they think will best complete the passage.
  3. Small group discussion to compare guesses—students may change some.
  4. Silent reading to determine better responses from the text.[1]
  5. Small group discussion to attempt a consensus on correct terms.
  6. Large group discussion to achieve class consensus.

So, that’s that.  I’m pretty excited to try it out.  I’m also excited to expose the kids to mathematical reading beyond their textbook.  The plan is to give them this shortly after introducing differential equations.

[1] I will have copies of the actual chapter from Strogatz’s book for the kids to read.

Thursday, June 13, 2013

Intro to Average Value

Last week I had an idea about how I could introduce average value in calculus next year.  When I've taught average value in the past, I felt like students just memorized a two-step procedure and several didn't see the connection to the definition of average that they've been using for years.  I know I won't be teaching this concept until...mmm...December?...but when you get excited about a lesson/idea, you just gotta follow through with it, right?

What I like about this little packet:
  • It starts with an application to motivate the discussion and the why should we study this?
  • It recalls previous knowledge.
  • It applies the fundamental 3-step process of all calculus topics: (1) Start with a non-calculus idea, (2) apply a limit, (3) arrive at the calculus concept.
  • It lets students practice a FRQ from a previous exam, but forces them to search through the problems to find which one would require their new tool.
  • Students discover a main idea of calculus using what they already know, each other, and the text (not me).
I recently read that four classroom characteristics important for brain-compatible learning are: (1) challenge (with support), (2) relevance, (3) novelty, and (4) a positive emotional climate.  I think this packet offers all four of these.

This is new for me.  I usually never post material I haven’t actually tried on students yet.  So, feedback, please!  Like I said, I have puh-lenty of time to revise and make this better.  I’ll probably be posting a few other things for next year that I would also love feedback on before I test them out on real, live kids.