As someone who focused on proof based mathematics in collage and is largely a self taught programer I think this proposal has merit. Begin forced to confront abstraction and formalism without any crutches as a freshman in college changed and expanded the way I thought. Learning to write down a correct proof without an external way of verifying it is an experience everyone should have.
However I think this needs to be coupled with an introduction to the concrete at a younger age. In mathematics we teach arithmetic to young children then step up the ladder of abstraction to high school algebra, simple proofs and linear algebra before eventually exposing them to abstract algebra (ie group theory etc). Teaching abstract algebra first would make theoretical sense but the mind tends to need to know at least one example of something before it accepts the abstraction.
I imagine a playful introduction to programing for young children coupled with a strong course in formalism for young adults could produce some great programers. Though, as with the proof based math series I took, I'm sure there would also be loads of freshman drop outs/transfers to more applied courses.
I also agree with others that insight rarely comes from pure formalism. The point of learning these things is to expand the way your mind works allowing you to think about abstract objects and allowing you to verify insight when it does come.
For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice:
"Master your instrument, master the music & then forget all that & just play."
For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice:
"Master your instrument, master the music & then forget all that & just play."
How very true across so many aspects of life!
Science doesn't happen through formalism. People learn the body of material that's been proven, then they get new intuitions, then afterwards they try to formally prove their insight. This isn't entirely inconsistent with EDW either. A lot of his point is that programmers need to know how to think symbolically, and if you truly prove the correctness of things, you can build the base of knowledge on top of it. If not, you're frequently wondering why things don't work.
Comments
As someone who focused on proof based mathematics in collage and is largely a self taught programer I think this proposal has merit. Begin forced to confront abstraction and formalism without any crutches as a freshman in college changed and expanded the way I thought. Learning to write down a correct proof without an external way of verifying it is an experience everyone should have.
However I think this needs to be coupled with an introduction to the concrete at a younger age. In mathematics we teach arithmetic to young children then step up the ladder of abstraction to high school algebra, simple proofs and linear algebra before eventually exposing them to abstract algebra (ie group theory etc). Teaching abstract algebra first would make theoretical sense but the mind tends to need to know at least one example of something before it accepts the abstraction.
I imagine a playful introduction to programing for young children coupled with a strong course in formalism for young adults could produce some great programers. Though, as with the proof based math series I took, I'm sure there would also be loads of freshman drop outs/transfers to more applied courses.
I also agree with others that insight rarely comes from pure formalism. The point of learning these things is to expand the way your mind works allowing you to think about abstract objects and allowing you to verify insight when it does come.
For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice:
"Master your instrument, master the music & then forget all that & just play."
For me Charlie Parker sums up the necessity of a formal education even if it is not explicitly used in practice: "Master your instrument, master the music & then forget all that & just play."
How very true across so many aspects of life!
Science doesn't happen through formalism. People learn the body of material that's been proven, then they get new intuitions, then afterwards they try to formally prove their insight. This isn't entirely inconsistent with EDW either. A lot of his point is that programmers need to know how to think symbolically, and if you truly prove the correctness of things, you can build the base of knowledge on top of it. If not, you're frequently wondering why things don't work.