State of Math ’17 : Learning Math Practically (With Examples From Everyday Life)
this is being permanently updated with any relevant progress on ‘practical math teaching/learning’
1 What’s one of the key problems with how math is taught?
in this linear algebra site ’15, it says:
it’s common to introduce vectors via definitions
this is done on the first 2 khan academy videos about ‘vectors’
i don’t feel like i’m learning anything relevant to real life because the videos are just about definitions/labels
if khan academy is going to test via definitions, and rote memory, they need to define Every. Single. Word. —
for example, i got the first test question on khan incorrect
- i thought ‘between’ (in this context) meant ‘between the first number (0, 0) and the second number (2, 7)’
- and that the ‘direction’ was from ‘0 to 2’ and ‘0 to 7’
this is all unclear.
2 Numerous problems and lack of polish with khan videos —
because he had initially (historically) just recorded them casually — and has never since redone/revised them
- info overload: he repeats himself many times which causes info overload
- unstructured presentation: the whiteboard is a complete mess and all over the place and i don’t know what he’s referring to
- i can’t read his whiteboard-writing
- 1 to infinity more problems
3 Abstraction needs examples from real life that all of us can relate to in our everyday life, or we need to see the effects of what something does like in programming —
a user says,
for math in general, this is an extremely large problem
to teach an abstract math idea like ‘vectors’, you should show multiple examples from everyday life that All of us would understand, or we need to see the effects of what something does like in programming —
and show which what is ‘velocity’ and ‘speed’ in our everyday life, and what the ‘direction’ could be for each of the examples
then we all can all understand the pattern that ‘vector’ means, and how other ‘things’ can also count as having a ‘direction’ (in the mathematical sense and meaning)
example like a plane that’s flying west, or sailboat, and anything else like google’s wifi balloon
should show real examples in real life going on RIGHT NOW to explain abstract ideas
a user from ancient times says,
“I hate how schools teach math” (a well-known & extremely widespread want)
100% or near 100% of p population do not see or know use math in their real life, or why they’re learning it, is a want
4 What good teaching is NOT —
on the (actual) first ‘page’ of ‘immersive math’, it doesn’t start with any examples from everyday life, just lots of abstract words.
let’s break this down:
- ‘is vector’ — ok what is that? you never showed me what that was
- ‘vectors are all around us’ — where?? i don’t see it, i don’t see where they are, i don’t even know what im looking for!
- ‘velocities, forces, acceleration’ — what!?! you just introduced 3 entire words that NOBODY understands or has any direct experience AND you still never explained what a ‘vector’ DOES
- ‘a more intuitive and hopefully faster’ — SO MUCH FILLERS, why don’t you just get to the point!??
these and so many more creates a whole bunch of compounding confusion, already from the start
5 Instant visual feedback can help —
a user says about that ‘immersive math’ site,
“let the learner edit formulas which represent figures and have figures update in real time. this is bi-directional instant feedback”
- this instant feedback is what bret victor (uc-berkeley) recommends in ‘explorable explanations’
- since 2011
it’s been said and known on HN (hacker news) that from personal experience doing/using programming is an effective way to learn math (didn’t keep, but should’ve kept the link for this)
6 MIT professor Sanjoy is likely the most ‘leading edge’ person progressing math teaching that i’ve ran into
someones says about ‘insight in science & engineering’ ’14 (.pdf),
- i’ve watched his youtube videos, and i personally don’t understand it — because there’s no real examples from real life even though someone experienced in math can just list and explain those examples
- there’s that physics example of dropping a ball but why do i need to know that? and how’s that helpful with anything else in real life?
7 Math notation needs to be reinvented —
from ’16 ’why don’t computer scientists learn math’ —
- math notation needs to be re-invented
- or if we shouldn’t, are we saying math is exclusively for mathematicians?
- and that nobody else needs or should learn math?
8 the entire field of ‘math teaching’ needs exceptional innovation and an entire reinvention —
want is slow as there’s (proportionally) few making want on these large desires
- example: a 📵 app teaching algebra for ~12 🔹🔹🔹🔹🔹🔹call ‘dragonbox’ made by jean-baptiste huynh
in a ‘talks at google’ video, a googler says to him,
..my daughter loves these games too. my wife loved math until she got to trig and then kinda gave up on it, when she played the game she couldn’t put it down till like 1am to finsih the game
- other examples but my notes on Onenote on everything in the universe are a mess and hard to locate
What’s the best practical math resource (with examples from everyday life)?