You should be… curious about how data becomes information, how information becomes knowledge and how knowledge becomes wisdom.Neil DeGrasse Tyson
Meanwhile in the class, instead of presenting the next definition, we started observing a few examples. And lo! There was something peculiar about a few examples. We tried to dig deep in. Turns out some examples were following a new pattern more beautiful than the previous one. We tried to describe the pattern, or as Neil said, make information out of the data we observed.
Next step was the hardest one. We tried to write it down as a definition in our notebook. We worded it, reworded it, spend two hours perfecting our definition.
Whatever they came up with was nothing but the next definition in the textbook. The guided discussions were aimed at training them to think like a mathematician. Even after I knew they had refined the perfect definition out, I put across a question or two to confuse them. I wanted them to be confident in their discovery.
Now, it’s knowledge. It’s a piece of knowledge we earned, not freely given to us.
The wisdom was in our next step, trying to frame examples and counterexamples for the new entity we just discovered or learning how to apply it.
The process was not as easy as I described here. Some were resistant to the idea of doing anything other than writing notes in the class. But somehow, the majority overpowered them. Then the time factor.
It took them 5-6 hours to formalize a concept I could have finished in 10-20 minutes by simply explaining it once in the class. Some raised concern about the pace with which we were moving.
But what was astonishing is, the next definition took 2hrs, next property took 1hr. And in the last class before Christmas, in an hour we finished a huge chunk of definitions and theorems that followed. A select few even went a step ahead to frame concepts of their own, thought irrelevant to textbook and syllabus, they were logically sound, original thoughts.
I was reminded of a simile Duraivel sir used to use back in PU. He would say, “When we start with a subject, it’s like an aeroplane on a runway. We start slow, increase our pace gradually and once we take off – there’s no stopping!“
We had just taken off!