problem with math - no one is really happy...
using computers is the silver bullet for making math work
in the real world - math isn't done by mathematicians..
why teach math?
1) technical jobs2) everyday living - skeptical about stats, etc
3) logical thinking
we spend 80% of our time doing step 3 by hand
it's the chore - it's the thing you'd like to avoid if you can
math not equal to calculating
calculating was typically the limiting step
math has been freed
but that liberation hasn't gotten into ed yet
automation allows math
we should be assuming computing for calculations and only do hand when it's needed:
ie:
what's worth teaching by hand:
practical: mental arithmetic
conceptual
if people are interested in it - fine - great - but no forcing...
line between what we're making people to do
math myths:
what are the basics
are the basics of driving learning how to service or design it?
need to separate the basics of what you're trying to do and the machinery of how it gets done
automation has allowed freedom - driving is now a separate piece than design
in the same way it has automized math
order of the invention of the tools vs the order of the way you use it..
myth 2:
do we really believe the math kids are doing in school today, more than applying procedures to problems they don't really understand for reasons they don't get.
what's worse: what they're doing isn't even practical today.. maybe 50 yrs ago
computers can really help...
like anything - they can turn into a multimedia show - why show a student how to solve a problem by hand when the computer can do it for them anyway. - this is just nuts
how you can make problems harder to calculate - change quadratic to a quartic
normal in school:
normal in life - messy - hairy:
the problem we really have in math is not that computers dumb down math but that we've dumbed down problems
myth 3:
if you go through tons of examples - you can get how the basics of the system works better.
understanding procedure and process is important - but there's a fantastic way to do that these days.. it's called programming...how most procedures and process get written down these days..
programming is the way we should be doing that. - and a great way to engage students and check if they really understand
what we have here - a unique opportunity to make
simultaneously
can't think of any other subject where that's recently been possible - usually a choicewe want people to feel the math - that's what computers allow us to do
calculus has traditionally been taught very late - why is this? because it's hard doing the calculations
what about - adding sides to a polygon - looking at limits, diff calc - taking things to an extreme - a view of the world we don't let people see for many many years after this - yet very important practical view of the world.
one of roadblocks in moving this agenda forward - exams
in the end - test by hand
hard to let computers come into exams
but then - we can ask real questions...
this isn't some optional extra - letting people feel the math..
moving to the knowledge economy to the computational knowledge economy
this is not an incremental change - we're trying to cross a chasm
suggesting - we should leap off
completely renewed math curriculum
not even sure we brand it math - but it is the mainstream subject of the future
if this resonates with you - or intrigues you - go here to help out..
if you want to jump in but can't this soon with kids... join us.. - meeting monday..
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