Woo hoo! Chat about infinity with a student who "hates maths" led to reasoned arguments and giggling at concepts, YES 😎
@_thegeoff Infinite is such a brain melter
I love watching videos about it/them
@mactunag And it's one of the first bits of abstract maths we try to wrap our heads around as young children, in my experience.
"Infinity plus one is bigger!"
"Infinity times ten!"
"Infinity times infinity!"
etc etc.
Aren't derivatives and notion of continuity earlier? (For momentary speeds and related concepts.)
I would expect most kids to see a speedometer at some point in very early primary school. Is my expectation wrong or does it not cause the concept to manifest?
Have you noticed kids considering it a leap? I'm somewhat surprised by this, because I assumed that the leap happens way earlier and calculus gives kids a formalization of it. How would a kid before the leap describe what does a speedometer/ammeter/... indicate?
(I suspect that it's me who has a wrong model here, given that I was surprised by some similar statement last year but didn't manage to get a good enough description of the before-acquiring-the-concept state to understand it.)
@robryk @mactunag We teach instantaneous v average speeds at ~14 years old, and the basics of calculus about the same time. I remember infinity being something we were fascinated by in primary school, maybe 7 or 8 years old.