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(Kalid from BetterExplained here) Thanks, really glad the site is resonating. My goal is to ask the genuine (and slightly uncomfortable) question of "Did I exp
by kalid 11y ago
(Kalid from BetterExplained here)
Thanks, really glad the site is resonating. My goal is to ask the genuine (and slightly uncomfortable) question of "Did I experience the concept beyond the technical definition?"
For something like Calculus, I could parrot out the formal definition of the derivative, using limits. But could I describe it as "X-Ray vision", where I look at a curve and see a sequence of tangent lines? A filled-in circle and see the constituent rings?
I think we've forgotten to let people hear the song, not just memorize the sheet music.
- birbal 11y agoGreat job Kalid. I try to do this with kids. Simple ideas like why anything to power zero is 1 ? why do we need complex numbers ? Why is limit of something tending to zero/infinity even an interesting and useful concept ?
- kalid 11y agoThanks. It's great exploring these "What if?" questions with kids (or adults). Math becomes more like a world to explore than something we're supposed to "learn".
- birbal 11y agoOne of the analogies i gave to the kids was that why did man have to learn to travel by water. Because walking on land wouldn't get them to the other island. Complex numbers sometimes sometimes are used to get to islands that aren't accessible from working with regular numbers. I was obviously referring to finding roots to cubic equations using complex numbers. Using complex numbers is in some cases like walking on water :-). These are not exact but they make kids excited. The fact that Math is replete with hacks just like real world is something that needs to be made more vivid and interesting
- kenOfYugen 11y ago> "Did I experience the concept beyond the technical definition?" Thanks Kalid! Wish there were more resources in that notion available when I was starting my Telecommunications studies.
- kalid 11y agoThanks Ken, same here when starting school :).
- kenOfYugen 11y agoFor when I was starting school, I wish the Web had existed :P
- vishnugupta 11y agoCame here to say "Thank You!". My interest in math got rekindled due no small measure to your site. Now as I try to learn more math, I try very hard to look for an "intuitive" meaning.
- kalid 11y agoThat's awesome to hear, thanks. I realize learning is more than knowledge transfer, you have to keep up the momentum to learn (for me, the joy of an intuition keeps me cranking away at tough topics).
- agumonkey 11y agoConvergent oscillation between formal definition and aesthetic intuitions is my teacher's goal. Smoothly going up to pure theory so you can forget it and go back to playing music. ps: I'm not a teacher. But I was I would ..