So I’ve come to realize something. Actually, this is something that I realized quite awhile ago, but it’s still relevant: statistics is very intuitive to me. Math is not.
I can’t recall any specific instances or anything like that, but it just seems like anything statistics-related has just made sense to me on some intuitive level that a lot of things in math do not. Even back when I was first starting (like back in STAT 251), I felt like I had a more intuitive grasp on stats.
It’s like…I can explain why some elements in a variance/covariance matrix cannot be larger than someother values and it makes intuitive sense to me, but I can’t (at the same intuitive level) explain what to do with the powers when I’ve got something like (52)8.
Blah. I don’t know. I know that’s a crappy example, and it makes it hard to explain to people why I teach statistics but am still only in calc II.
Eigenblogger 
I have the reverse problem! Just don’t seem to get statistics, no matter how hard I try… Couldn’t tell you the reason for the difference in innate ability between the two, because I have no idea.
Most people never make it to calc II though, so you’re already ahead of the crowd in that area.
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I have the reverse problem! Just don’t get statistics … couldn’t tell you why though, because I have no idea.
But most people never make it to calc II, so you’re still ahead of the crowd there too.
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I’ve been thinking about this a little, and I guess the way I’d try to explain (5^2)^8 to somebody is that it’s basically a matter of nesting. (Really I think most things “order of operations” are a lot more intuitive when thought of in terms of nesting, but maybe I’m just weird.) Since “5^2” is nested within parentheses, it gets treated just like any old “x” would when it’s taken to the 8th power, giving
5^2*5^2*5^2*5^2*5^2*5^2*5^2*5^2
Then because 5^2 = 5*5,
5^2*5^2*5^2*5^2*5^2*5^2*5^2*5^2 =
(5*5)*(5*5)*(5*5)*(5*5)*(5*5)*(5*5)*(5*5)*(5*5) [by substituting equivalent objects–(admittedly extraneous) parentheses included to emphasize said objects] =
5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5 [because parentheses are irrelavent when all operators are * or + (i.e., extraneous parentheses are extraneous)] =
5^16
Or would it just confuse the heck out of everyone if I tried to use that explanation? I am starting to realize I have a knack for overcomplication, which is not so good because I am working as a tutor this semester. I keep running into the problem of “exactly where do I stop explaining?”. I can’t stand the “this is the way it is because this is the way it is” approach because that’s what turned me off from math until high school (not to mention it’s circular to boot), but then I don’t want to overwhelm the poor little freshmenz either…
Sorry, that last part was a tangent.
Also, I looked up variance/covariance matrices and it broke my brain.
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