I think I've already mentioned how much I like my calculus 2 instructor Dr P, who is like a really great high school teacher in many ways, including obviously treating teaching us math as his job (and who I do not think that I like simply because "Dr P" has such strong positive associations with my favorite soft drink of my childhood). I have found him inspiring enough that when he mentioned that he also teaches the differential equations class, I had this feeling like, maybe I will take that class after all. (We'll see if this feeling survives contact with Taylor series.)
Another thing I like is how he respects the fact that math is not, generally speaking, extremely easy. He does not present calculus as something you were either born "smart" enough to understand and do instantly or not at all. Amazingly enough, math is something you can practice and get better at doing.
On Tuesday, he said that in addition to the homework (which is not graded, you may recall) that he has specifically assigned, he would encourage us to do all of the odd-numbered problems in the section review section, and then do the even ones and get the answers from himself or the TA. Today he said that after doing about 100 integrals, you will quickly see how to do new problems from the cummulative experience of solving other problems and that things will start to "pop out" at you. So I figure if I can there after doing less than 100 integrals, I am just ahead of the curve. (I've actually gotten pretty good at doing integrals already.)
So whatever the sexist implications of Talking Barbie telling its girl owners "Math is hard!", I'm not sure that some alternative message, like "Math is easy (so you're just stupid)" is any better. For me, thinking of math as difficult and approaching it with the proper appreciation of that fact is actually much more useful in giving me the mental fortitude to keep working at math when it feels challenging. There is an important difference between something being hard and being too hard for a person ever to achieve. Why denigrate the accomplishment of mastering some element of mathematics by pretending that it's easy and obvious?
This is not to say that I think girls are not (at least sometimes) shortchanged when it comes to math education, etc., but that the framing problem goes both ways - it is just as possible to position math as being too easy, such that the girl (or boy) who does not immediately get it will feel dumb, incapable, and just not a "math person" as it is to scare someone off by saying how hard it is. Really, it's not very helpful when mathematical ability is seen as some inherent trait of the individual. While yes, individual differences exist in this as in everything, one does not actually need to be a math genius to learn enough to earn a bachelors degree in mathematics, let alone become competent in the fundamentals of college-level math. The fact that Mozart composed his first symphony at age 10 (or whatever) does not mean that a normal person cannot learn to play the piano.
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I like this perspective a lot, as you'd no doubt guess. Kids (and adults) would be well-served by the perspective that many topics are difficult but amenable to study and effort. Thinking that some subjects are easy (such that no effort should be required) and others hard (such that they will not yield to effort) is just totally wrong-headed.
Incidentally, this general framework is part of the reason I've always rejected topics like history. They simply aren't amenable (for me) to my usual techniques of simply understanding something and then not needing to remember it particularly. They require a different kind of effort, and I've never quite "gotten" that I can put in that effort.
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