## Main Question or Discussion Point

I took pre-calc last year, and I caught onto almost everything very quickly and found most of the homework easy. However, when we had a chapter on counting methods (combinations and permutations) and probability, it was the complete opposite and had me spending significant amounts of time on each problem, and even giving up on a few. I'm not to concerned about this or anything, but I was wondering what other people's weak spots in math are. Is probability a typical area of struggle?

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I was in the same situation as you when I took precalc (I will be starting my freshman year in college in a month) except we were never even exposed to counting methods. The only time counting methods were taught were in my geometry class and for no particular reason except that the administration felt that students should learn the basics.

I think one of the reasons counting and probability is an area of struggle, at least here in America, is that our typical math curriculum is nowhere near ready for such topics to be included. I went to a very good high school and even then there had to be compromise and trading to find the right teacher with the right knowledge(who didn't teach geometry) to teach us counting. I think you'll find many less K-12 teachers who have a firm head for combinatorics than for algebra. But even that there are many less than qualified teachers in the latter subject.

Granted that the ultimate goal of a K-12 math education is to prepare students for calculus, an early exposure to discrete math may keep more students interested in mathematics. But this doesn't look like it will happen anytime soon.

Anyways, as a consequence, most people are exposed to and familiar with continuous mathematics. I think in some cases this lends to the person having a difficulty (at least initially) with discrete math. As for myself, I have definitely improved in number theory (which I knew just as much about in precalc as I did about counting, practically nothing) but I will admit I have been avoiding counting/probability a bit. I guess I want to know if having an aptitude for one area of discrete math will lead to improvements in another.

I positively suck at geometry where solutions are based on "uniform objects" (not sure what the English term for that is) of different scales or angles.

Stuff like taking a right triangle and dividing it into two new ones with a normal from the 90 degree angle to the hypothenus, and then figuring which sides in the two new triangles correspond to which side of the original.

Basically I suck at rotating / mirroring geometric objects in my head.

k