Comment by pavlov | Hacker News Reader

Comment by pavlov | Hacker News Reader

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It was only when I realized that math begins (or does it?) with what you have (objects, sheep, anything you want to count) and what you can do with them (group, make a set, join two sets, etc). Then I went into a reading spree about all ofthose very basic and foundational aspects of pure math (pure as in "look around you, you can count things, you can group them based on some trait, you can do operations based on groups, you can now think of those groups as the entities to focus on, you can prove certain properties about those groups, etc") and I found it amazing that so much can be known and discovered from starting with just what you see around you.

In the early '70s, there was a global movement in math pedagogy that took this angle to elementary learning.

Instead of arithmetic, first graders were taught set theory. Elements and unions became the first mathematical concepts introduced to 6-year-olds.

In the US, I think they called it "New Math". Here in Finland, set theory was included in the national educational system's grand redesign. Regardless of country, set theory as elementary math seems to have gone out of fashion as quickly as it gained traction, and by the early '80s was out everywhere.

Maybe, if they had stuck with it, we would all be using Haskell now as a side effect :)

(Here's a picture of a very '70s styled Finnish math teacher doing set theory: http://1.bp.blogspot.com/-vWW22FRIdfc/TobxIw3xF3I/AAAAAAAAHa... -- "Now tell me children, what is the union of green swans and red bears?")

I took a History of Mathematics module as an undergrad and remember our lecturer telling us the main reason "New Math" never stuck was because parents were no longer able to help their kids with their homework.

This issue comes up every time new ideas enter education. This roadblock will never be overcome, unless parents try to learn math as well.

On a very abstract level, I don't really think it makes a difference. If you start from one sub-domain as a primary foundation in mathematics, you eventually wind up realizing you can define that sub-domain easily, using different sub-domains of math. Realizing that is I think, where category theory sprang from. That last bit, I could be totally wrong on - I tried to teach myself category theory and wound up building webs using abstract algebra and formal logic.

That's obvious if you program, though (to me). What you can do in one language, you can do faster, slower, more concise, more verbose, more symbolic, more literal, and so on, in another. You can build constructions and you can break them apart, depending on what layer of abstraction you can get to. You can call it by it's specific name and functionality, in how the part interacts in relation to the parts around it, or you can call it objects and morphisms.

I might be totally wrong, again, or using the wrong words and confusing everyone including myself (which is why I like to study formal languages, too). But I think that no matter where you start from, you will eventually find yourself in a place where you are scratching your head, confused about what you know, what you don't know, what everyone knows, and what everyone doesn't know.

Oh, and it's probably totally obvious if write proofs, believe in induction, and get very philosophical.

> believe in induction

Does it even make sense for someone to not believe in induction? It's a perfectly valid logical rule.

On some layers of logic, I agree. On some layers of meta-logic, I don't know.

  using Haskell now as a side effect

Very clever.

On the off chance there's a person who hasn't heard Tom Lehrer's explanation of the New Math:

https://www.youtube.com/watch?v=Vetg7vWitTU

(In case you don't know Lehrer, he did PhD studies in math at Harvard, and taught at Harvard and MIT, often performing his songs during his lectures (or composing songs FOR his lectures.))

"taught at Harvard and MIT"

... and Santa Cruz! I was one course shy of taking his last course (Infinity) before he retired.

Pretty interesting history of math education in the U.S.: http://www.nytimes.com/2014/07/27/magazine/why-do-americans-...

I'm the right age to have done this when I started school. My memory is of it is playing with lots of wooden bricks that were marked with lines to show their length. It felt well taught but I'm not sure how well the rest of the class picked it up.

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