3 ms·

I feel like on #4 that at least some exposure to rigor is in order somewhere in high school, for everybody. I say that because that would have helped me a lot b

I feel like on #4 that at least some exposure to rigor is in order somewhere in high school, for everybody. I say that because that would have helped me a lot because I took a lot of math and really grokking rigor made all the difference once I got there. And then both my kids had exactly the same experience. Is a high school CS course that place for that? Probably not. So I vote for a much tougher algebra course that then of course nobody would ever take.

thearn4 11y ago
> I vote for a much tougher algebra course I've played with the notion in my head of teaching something rigorous (but not arduous) like basic Group or Ring theory somewhere in HS. Perhaps in place of the rather large amount of time spent on the algebra of second-order polynomials? Hard to say. I'll admit I have zero training in pedagogy.
- arthur_pryor 11y ago
  i've thought for a while that a good survey philosophy course would be a great thing for high schoolers. it could introduce a certain sort of rigor (not quite the same as a programming class where things have to run, or a math class where you have to write proofs, but important and maybe easier for many to grasp at first). plus, it'd introduce a wide variety of other belief systems, things like the need to honestly address objections the other side might have, etc. but a good CS course would be great too, because computational literacy and facility/comfort with computational thinking are only becoming more important for making it through the world and having some control over your own fate.
  - ArkyBeagle 11y ago
    The course that made it for me was based on "Transition To Advanced Mathematics" by Egger , Smith and St. Andre. Just learning the actual proofs ( beyond calculus style proofs ) techniques was a big leg up, especially induction and contradiction.
groovy2shoes 11y ago
I agree, along with proofs, intuition, and elegance. For most of my academic career, I hated math. I was always good at it, typically getting good grades without needing to study. But I found it so incredibly boring, because it was presented as "memorize these rules and formulas, then use them when the test prompts you to". It wasn't until my third year at university that something finally clicked. I was taking automata theory, and the mix between rigorous thinking, writing proofs, and applying intuition nearly as often as theorems (along with the sudden realization that writing proofs is a lot like writing programs) flipped a bit in my mind. I suddenly loved math. It made sense to me for the first time. And I could look at a proof and tell whether it was beautiful or an ugly hack. I've got high hopes for the Bootstrap curriculum [0]. I think that kind of interactive, rigorous introduction to mathematics and programming would be very beneficial for students (and the research agrees). If I ever have kids, that's how I plan to teach them algebra. [0]: https://en.wikipedia.org/wiki/Bootstrap_curriculum https://en.wikipedia.org/wiki/Bootstrap_curriculum
- ArkyBeagle 11y ago
  It was my "third" year, too ( I mucked around and took a year off so ... more-than-three :) But that's when I took the third year courses . Maybe your brain's not ready until then; dunno.

thearn4 11y ago

> I vote for a much tougher algebra course I've played with the notion in my head of teaching something rigorous (but not arduous) like basic Group or Ring theory somewhere in HS. Perhaps in place of the rather large amount of time spent on the algebra of second-order polynomials? Hard to say. I'll admit I have zero training in pedagogy.

arthur_pryor 11y ago
i've thought for a while that a good survey philosophy course would be a great thing for high schoolers. it could introduce a certain sort of rigor (not quite the same as a programming class where things have to run, or a math class where you have to write proofs, but important and maybe easier for many to grasp at first). plus, it'd introduce a wide variety of other belief systems, things like the need to honestly address objections the other side might have, etc. but a good CS course would be great too, because computational literacy and facility/comfort with computational thinking are only becoming more important for making it through the world and having some control over your own fate.
- ArkyBeagle 11y ago
  The course that made it for me was based on "Transition To Advanced Mathematics" by Egger , Smith and St. Andre. Just learning the actual proofs ( beyond calculus style proofs ) techniques was a big leg up, especially induction and contradiction.

groovy2shoes 11y ago

I agree, along with proofs, intuition, and elegance. For most of my academic career, I hated math. I was always good at it, typically getting good grades without needing to study. But I found it so incredibly boring, because it was presented as "memorize these rules and formulas, then use them when the test prompts you to". It wasn't until my third year at university that something finally clicked. I was taking automata theory, and the mix between rigorous thinking, writing proofs, and applying intuition nearly as often as theorems (along with the sudden realization that writing proofs is a lot like writing programs) flipped a bit in my mind. I suddenly loved math. It made sense to me for the first time. And I could look at a proof and tell whether it was beautiful or an ugly hack. I've got high hopes for the Bootstrap curriculum [0]. I think that kind of interactive, rigorous introduction to mathematics and programming would be very beneficial for students (and the research agrees). If I ever have kids, that's how I plan to teach them algebra. [0]: https://en.wikipedia.org/wiki/Bootstrap_curriculum https://en.wikipedia.org/wiki/Bootstrap_curriculum

ArkyBeagle 11y ago
It was my "third" year, too ( I mucked around and took a year off so ... more-than-three :) But that's when I took the third year courses . Maybe your brain's not ready until then; dunno.