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She says: "The thing I was missing is that math is just a bunch of symbols that you manipulate to get new symbols out. Coding is basically the same thing. The m

She says: "The thing I was missing is that math is just a bunch of symbols that you manipulate to get new symbols out. Coding is basically the same thing. The meaning isn’t in the math or the code itself. The meaning comes from the interpretation of the mathematics or similarly, what your code is doing for someone." This is, I think, the most important thing to understand about mathematics, and failure to understand this leads to the travesty that is K-12 mathematics education in the US. I find it impressive that she came to this conclusion on her own, having started as someone for whom "Math was never [her] favorite subject".

girvo 13y ago
I taught myself to program when I was 11, using GameMaker, which had this neat scripting language called GML that hooked into the editor to control things above and beyond the simple actions built in. Learning about functions and variables made algebra ezpz when we learnt it later on. Matrices were multidimensional arrays (I know, not quite the same in terms of maths, but hey I was young). More importantly, programming taught me how to approach logical problems the correct way. I'm super thankful for it :)
- derleth 13y ago
  > Matrices were multidimensional arrays (I know, not quite the same in terms of maths, but hey I was young). In math, if something has all the properties a kind of object is defined to have, it is that kind of object. Mathematics is based on definitions, so things are what they are defined to be, no more, no less. In fact, you can implement mathematical structures in terms of other mathematical structures, as Peano did when he defined numbers and basic arithmetic in terms of set theory: http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms
  - girvo 13y ago
    Hey, set theory is neat although I never got to study it.
derleth 13y ago
> "The thing I was missing is that math is just a bunch of symbols that you manipulate to get new symbols out." This is the Formalist philosophy of mathematics, which isn't the only one (as you might imagine given that it has a name): http://plato.stanford.edu/entries/formalism-mathematics/ http://plato.stanford.edu/entries/formalism-mathematics/ Formalism is at odds with Platonism, to pick an obvious antithesis, as Platonism holds that mathematical entities do indeed have a reality beyond us finite, mortal creatures and our symbols: http://plato.stanford.edu/entries/platonism-mathematics/ http://plato.stanford.edu/entries/platonism-mathematics/ There are, as you might imagine, a lot more philosophies of mathematics: http://en.wikipedia.org/wiki/Philosophy_of_mathematics http://en.wikipedia.org/wiki/Philosophy_of_mathematics That said, at the K-12 level, formalism is what students need most; make mathematics a game and show them how well the game applies to reality. That unreasonable effectiveness is quite astounding the first million times, and it never really quits being astounding: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...
- andreasvc 13y ago
  Formalism in math states that mathematical truth is what can be proved. Manipulating uninterpreted symbols is part of math no matter what philosophy you subscribe to. The author of the quote is clearly making a practical, not a philosophical, claim here.

girvo 13y ago

I taught myself to program when I was 11, using GameMaker, which had this neat scripting language called GML that hooked into the editor to control things above and beyond the simple actions built in. Learning about functions and variables made algebra ezpz when we learnt it later on. Matrices were multidimensional arrays (I know, not quite the same in terms of maths, but hey I was young). More importantly, programming taught me how to approach logical problems the correct way. I'm super thankful for it :)

derleth 13y ago
> Matrices were multidimensional arrays (I know, not quite the same in terms of maths, but hey I was young). In math, if something has all the properties a kind of object is defined to have, it is that kind of object. Mathematics is based on definitions, so things are what they are defined to be, no more, no less. In fact, you can implement mathematical structures in terms of other mathematical structures, as Peano did when he defined numbers and basic arithmetic in terms of set theory: http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms
- girvo 13y ago
  Hey, set theory is neat although I never got to study it.

derleth 13y ago

> "The thing I was missing is that math is just a bunch of symbols that you manipulate to get new symbols out." This is the Formalist philosophy of mathematics, which isn't the only one (as you might imagine given that it has a name): http://plato.stanford.edu/entries/formalism-mathematics/ http://plato.stanford.edu/entries/formalism-mathematics/ Formalism is at odds with Platonism, to pick an obvious antithesis, as Platonism holds that mathematical entities do indeed have a reality beyond us finite, mortal creatures and our symbols: http://plato.stanford.edu/entries/platonism-mathematics/ http://plato.stanford.edu/entries/platonism-mathematics/ There are, as you might imagine, a lot more philosophies of mathematics: http://en.wikipedia.org/wiki/Philosophy_of_mathematics http://en.wikipedia.org/wiki/Philosophy_of_mathematics That said, at the K-12 level, formalism is what students need most; make mathematics a game and show them how well the game applies to reality. That unreasonable effectiveness is quite astounding the first million times, and it never really quits being astounding: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...

andreasvc 13y ago
Formalism in math states that mathematical truth is what can be proved. Manipulating uninterpreted symbols is part of math no matter what philosophy you subscribe to. The author of the quote is clearly making a practical, not a philosophical, claim here.