Math Three-Act Plays

By Tom Gilbert, Upper School Math

I attended the 29th annual Anja S. Greer Conference on Mathematics, Science and Technology at Phillips Exeter Academy June 23-28, 2013.  The conference structure for each attendee included two week-long courses meeting each day, many “conference within a conference” 45 minute sessions, and three evening presentations.  My courses were “Teaching Effectively with Technology, Making Classrooms  Smarter” and “Using Mathematics to Analyze Issues of Social Justice” and I attended approximately 20 of the CWIC sessions.  There were about 300 attendees, including teachers from almost all US states and a large number of other countries.  There were concurrent programs running for Biology, Astronomy, Writers, Shakespeare, and Diversity.  All courses were taught using participant (student)-centered Harkness classrooms.  Not one of the classes or CWICs I attended used or referred to text books; every session used problem-based learning, discussions, explorations, simulations, and visualizations to teach mathematics.

There is an approach, while most visibly used by Dan Meyers on his blog http://blog.mrmeyer.com/, in widespread math teaching practice among the academic schools presenting at the conference.  Dan uses the name “three-act play” to communicate the process.  It is clearly related to problem-based learning and goes something like this:

  1. Show the students something from the real-world that seems curiously complex yet commonplace to them. What questions naturally arise?
  2. Support and facilitate the students’ involvement as they analyze and deeply understand their questions.
  3. Show the students the real-world outcome.

The teachers and schools pushing in this direction are focused on a student-centered goal of developing problem-solving skills, beyond the original goal of ensuring their students have math skills.  What is also interesting about this approach is its strong reliance on technology to deliver multimedia content to students.  Schools that use this approach prioritize reliable multimedia streaming capabilities both to the classrooms and their students’ studying spaces.

 

Here are two content examples from step 1:

http://101qs-media.s3.amazonaws.com/videos/880-coffee-traveler.mp4

http://101qs-media.s3.amazonaws.com/largethumbs/2360-gas-light.jpg

The problems are not defined by the chapter and section number in a traditional textbook.  A class works together to ask and then answer its questions.  The teacher chooses the visible content to begin the discussion and supports the class’s engagement as it works towards answering self-generated questions.  Questions naturally have their basis in applications and math enters the situation as the way to quantify and generalize solutions.  At the right time, the teacher can provide formal math content to the class, and within the context of the application and students’ questions.

Here’s another form of step 1: ask a strategic question.  The best example of this approach was a seminar in which we were asked how to maximize the number of ships that could transit the Suez Canal without rebuilding it.  The teacher made only one suggestion: look at the Canal.

https://maps.google.com/maps?q=suez+canal&hl=en&ll=31.179322,32.327271&spn=0.333089,0.676346&sll=41.117935,-77.604698&sspn=4.692042,10.821533&t=h&hnear=Suez+Canal&z=11

Using mapping, content search, quantification, and visualization software tools, the class was able to study the actual Canal, talk about physical, political, and historical issues, and get deeply into the original question.  Afterwards, the class was able to compare its analysis to the actual transit procedures used by the Canal.

One underlying theme was mentioned throughout the conference.  Almost every speaker stated that math text books – and perhaps math teachers by extension – give way too much information in advance.  Students are conditioned to expect all the data and methods will be provided in advance by the teacher or the text.  Three-act plays are a way to stress real problem-solving without being handed structure or data first, so that the students develop problem-solving skills.  In this approach, math skills are learned within the context of usefulness.

More information about the Exeter conference may be found at its home page: http://www.exeter.edu/summer_programs/7325.aspx

About Westtown School

Westtown School is a Pre-K through 12th grade Quaker, coed, college preparatory day and boarding school in West Chester, PA.
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