In Today’s tutoring session, we looked at geometric series and their sums, and discussed formula derivation.
We talked about why memorizing formulae and applying them in the sort of contrived situations found in math books is like learning specific karate moves, and doing the multi-step questions is like doing a kata. We compared this to the sort of sparring one does in real science, and how the one builds off the other.
“You see a series looking at you suspiciously as you walk down a dark alley…you look it up and down…. compare its ratios… yeah they’re common. You could take it if you need to.”
We then compared that to Bruce Lee’s formless Jeet Ku Do, and talked about mathematical mastery, and the importance of being able to not just memorize formulae, but to understand why they work and where they come from, so that one can recreate them if needed, or derive new ones that relate to a specific area of research.
I recounted about Melanda‘s delightful tale of double negatives in linguistics and the lack of a similar double positive mechanism (I won’t spoil the punchline… it’s a story that always makes me laugh). and how it applies more rigorously in math (multiplication of double negatives vs. double positives)… Melanda, the brilliant retort the person called out would be the equivalent of a special imaginary number, I think!