Harry Keller* tells this story:
I once had a student come to me … and say, “I tried all of the different pendulum masses, and they all had the same period. What did I do wrong?”

To my great delight, the Adult learners in my ABE class got caught up in making the non-Euclidian planes.  (See previous posting) After some initial “We did this in Kindergarten” murmurs, I saw them begin to engage as the things took shape. They quickly recognized that the hexagons and pentagons would make a soccer ball if they kept going.  I put on my lecture hat and explained that this is a curved plane, guided them to recognize that if it is pressed flat, there is not enough material to cover the ground – there are gaps between the hexagons.  Then I asked them (deliberately misleading) to speculate whether combining the hexagons with the heptagons would make larger or smaller gaps.  They weren’t sure, some guessed larger, some smaller, and some guessed one way then changed their mind.

When they went to assemble the pieces and found there were overlaps instead of gaps, I pointed out how my question had misled by implying that there would be gaps at all.  I then asked them what kind of curve they thought they would get once they finished.  If a shape with gaps made a ball when they were brought together, would overlap make the opposite? And just what is the opposite of a ball?  Would it be like the inside of a ball?  I threw out these questions without demanding answers.  They were playing various songs from YouTube as they worked.

Suddenly D. voiced what has to be my favourite quote for the month (if not semester).  “Hey! Something weird is happening.  Look!  Is it supposed to be like this?“  The beautiful serendipity was that he was playing Pink Floyd’s “Another Brick in the Wall” at the time:

We don’t need no education!
We don’t need no thought control!
Teacher, leave them kids alone!

We laughed together in the joy of his discovery.  Only later did I point out the relationship of his question to the song.  It didn’t really matter what I told him was “supposed” to happen, he would free himself from thought-control by discovering the reality for himself.

*Harry Keller in a second-page comment on Edutopia post Sep 2011 http://www.edutopia.org/blog/benefits-mistakes-classroom-alina-tugend