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Comments:
<0> Tables will hurry things along, sure.
<1> ekiM : don't use it and you lose it
<0> But we have calculators
<0> so it's insane to be wasting all this time on it
<2> i count in sixes in my head to find out what 6*7 is, just really quickly :p
<1> na
<1> standard multiplication (until) are the base for everything that follows
<0> The fact that 6 * 7 = 42 is something far less important than the distributive property, for instance.
<1> you start with data to find structure (and not the other way around, though mathematicians do that)
<0> Or even the proof that sqrt(2) is irrational. :)
<2> i hate how they all tout the commutative property as a universal property, inviolable, and then next year in highschool, they teach you about matrix multiplication.
<1> Cale : you understand the distributive property by using tables
<2> it's like "..."
<0> kmh: No :)
<1> Cale : yes
<3> Seems likes as I think about it, most of my highscool's algebra 1 is mostly about simplafation and they don't seem to teach it very well.
<2> being able to simplify expressions is very important.
<0> kmh: In fact, that's something which I've never done
<4> What, use tables?
<1> Cale : i did
<0> kmh: I've never used a multiplication/addition table to check that distributivity holds.
<4> I think I was just sort of taught it
<1> Cale : however that's how it works for most people imho
<4> I'm not sure if I even had examples
<0> I think you understand distributivity, for naturals, based on the idea that multiplication is repeated addition.
<4> I probably did, though
<1> Cale : and follows the historical development
<3> Kampen: But I want them to teach me, not shove exmaples at me that. That cause me to glaze over.
<4> Exampls have their use.
<0> The distributive property, for me, was first *mentioned* in grade 9.
<0> (and described)
<0> also, people struggle with fractions, why do you think that is?
<5> people should be learning about groups when they're 10
<1> Cale : usually that is taught in 5 or 6th grade latest here
<3> Dacicus: Yes, But I like to have a good explanton of it too.
<1> including the name
<4> PyroTechno: Of course
<0> It's because reduction to lowest terms involves prime factorisation and the lcm.
<4> First, the explanation, then the example
<4> Actually, I guess you could reverse the order
<0> and while they did give us some vague description of the LCM in grade 5, it was really out of place.
<6> elementary group theory could indeed be taught to a child
<0> ekiM: yes, it certainly could
<0> or graph theory!
<6> and it's a good introduction to axioms, proofs...
<6> but if you don't know a few different mathematical structures you might not see the point
<0> There's a lot of nice simple things one can prove about graphs
<6> in groups I mean
<6> I guess "clock arithmetic"
<0> Dacicus: A group is a set of elements together with a binary operation on those elements, usually called multiplication, which satisfies the following three things:
<0> For any a,b,c in the group, (a * b) * c = a * (b * c)
<0> There is some element 1 in the group such that for any a in the group 1 * a = a * 1 = a
<5> Basic group theory is especially tractable for young people because of the wealth of nice, simple examples.
<0> For any a in the group, there is some b in the group so that a * b = 1
<3> Cale: I'm trying to figure out why my school brings up fractions after you have to simplafiy a fraction of two roots!
<4> Doesn't seem so hard
<0> A good example of a group is the set of marching orders {attention!, right face, left face, about face}
<0> with multiplication being to give one order after the other
<0> PyroTechno: hehe
<4> um
<4> idk how familiar kids are with marching
<4> orders
<2> i don't understand that analogy.
<2> yeah haha
<2> or how familiar i am with it
<0> okay
<6> I think "do nothing, left, right, about turn"
<0> {stay as you are, turn left, turn right, turn around}
<0> right
<6> but yes kids can understand geometry qute well
<6> reflection and stuff too
<6> rotations
<6> then you have clock (modular) arithmetic as I said
<0> turning to one's left twice will result in turning around
<4> Same with right
<0> right
<2> right
<2> we just turned left together :p
<0> and turning around twice will result in putting you back as you were
<0> and so on
<4> Hm, this is a problem
<6> so this is the klien four group
<6> or one of those groupds
<6> I forget
<0> No, it's Z_4
<6> damn
<4> Does anyone here use Bochs with FreeDOS?
<6> {0 1 2 3} = {attention, left, about, right
<6> ?
<0> yeah
<6> klein four group is the symmetries of a rectangle?
<3> Are there any good texts online about simplifying expressions?
<0> ekiM: yep
<6> where all elements are self inverse
<0> ekiM: yeah
<0> PyroTechno: hmm... http://www.purplemath.com/modules/index.htm is probably more directly useful to you
<6> been a while since I've done group theory
<4> What course is group theory in?
<0> PyroTechno: it's sort of based around the whole curriculum which seems to be present in the US and Canada
<6> Dacicus : group theory
<0> Dacicus: it's usually a whole course
<6> sometimes it's done along with numer theory
<4> oh
<0> or Ring theory
<6> number
<6> yeah
<3> Cale: Thank you.
<0> In the cases that group theory and ring theory are together, the courses tend to be called things like "Abstract Algebra"
<4> Doesn't seem to be in my number theory book
<2> or algebraic structures (which i'm taking this semester) :p
<3> Man, there's a alot of netsplits tonight.
<4> Hm, this cl*** has it, Fundamental Concepts of Modern Algebra
<6> it is The End of Days
<2> starring arnold schwarzenegger.
<0> But yeah, probably if I was to teach basic addition and so on to kids, I'd start off with the axioms of a ring. I likely wouldn't call them that, but that's how I'd build up the idea of numbers.
<1> Cale :lol
<2> yeah ha, imagine terrorizing some kid by trying to tell them about ideals in the language that mathematicians use
<0> And I wouldn't give them all at once either
<2> they'd probably go catatonic
<0> I'd add them one by one, and play games with what we had so far.
<0> Ideals and so on are out of the question at that point :)
<6> first day into elementary school, we give the formalization of ZFC
<2> yeah, i just wanted to pick something that would be especially terrifying :p
<0> hehe
<0> I'm actually being serious though
<7> how would you explain a ring, im a good fertile kid to try it on
<0> Well, a ring in general?
<1> ekiM : actually (naive) set theory in elemntary school was popular in the 70s
<7> it was in 80s but only because kids got venn diagram easily
<7> yes cale what is a ring?
<3> ekiM: Such is true.
<8> nah. don't be too hard on the poor little pupils. First day of elementary school we do Peano Arithmetic
<0> zaphyBeeble: Okay, a ring is a generalisation of what we think of as "numbers". A ring consists of a set R of elements, and a couple of binary operations: + (addition) and * (multiplication)
<0> They're required to satisfy a number of properties
<7> ok so i have these funny symbols
<0> right
<6> ok, first day peano, second day ZFC
<7> and these funny symbols which go between those other funny symbols
<0> yes
<6> and i want a full derivation of elementary calculus results by the end of the week
<1> zaphyBeeble : well in 80s they reverted it again
<7> and that wen applied gives me another funny symbol
<0> yep
<7> ok so that is a ring?
<0> Not quite
<2> if it didn't give you another funny symbol the operations wouldn't be binary :p
<7> :D
<0> I've yet to list the rules
<7> ok go on
<0> 1: For any a, b, c in R we have (a + b) + c = a + (b + c)
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