## Wednesday, December 18, 2013

### Divergent and convergent educational outcomes -- the sour grapes effect

This is another topic that we've kicked around for a while that's recently become more relevant (from a previous post):
As much as I complained about them at the time, the education classes I had to take to get certified did have some highly useful concepts. One of those was the distinction between convergent learning (where you want all students to reach the same final answer) and divergent learning (where you want each student to come up with a unique answer). Before you made a lesson plan or write a test, you were supposed to ask yourself where you want to see convergence and where you want to see divergence.
...
There is an common but fatally naive misconception that convergent learning goes with math and science while divergent learning goes with arts and humanities. Almost all subjects start with a large convergent learning component including the arts (try picking up an instrument and see how much divergence your teacher tolerates in the first few lessons). More importantly, ALL subjects are fundamentally divergent at a high enough level. Writing a novel, composing a symphony, proving a conjecture or designing an aircraft are all creative exercises in constrained problem solving. We demand that certain conditions be met but we expect that each solution (or at least the method behind it) will be unique.
Pretty much by definition, divergent outcomes are problematic when it comes to metrics. This can lead to what we might call the sour grapes effect, convincing ourselves that a certain attribute isn't important because it's difficult to measure or to work with. "Looking where the light is good" is always a questionable strategy, but it becomes particularly worrisome when the results of the analysis are used to assign resources.

We are, of course, talking about huge amounts of money and there has been no real effort to insulate the parts of the reform movement coming up with radical changes in what we teach and how we teach it from the parties who stand to make billions of dollars from these changes.

One of the "benefits" of highly standardized teaching methods (taken to its logical extreme in the large number of scripted presentations found in Common Core-based lessons) is that they tend to produce more convergent outcomes. Pedagogically, this convergence may actually be a bad thing, and indication that these students have not actually thought through the questions on their own. It does, however, make the outcomes much easier to measure.