Is this the right thing to do?

[Sioga]

Ok, so I am a freshman, and I am just ending Algebra 1, thanks to my last school, but most of my class is ending Geometry now. I am good at math, and have decided to take a credit Geometry course over the summer, so that I can be in Algebra 2 with the rest of my class next year. Do you think that was a smart thing to do? If I do it, then I will be able to get to Calculus by my senior year.  

[Layra-chan]

I'd say go for it, but I don't know enough about how summer courses are taught where you are to really give a good judgment. How much does pace matter to you? Can you learn quickly, since a summer course will be more compressed than a regular course?

Actually, I wouldn't be too concerned about it. If it's anything like typical high-school geometry courses, nothing you learn in that course will be useful later on. If you continue to be interested in mathematics or physics, everything you learn in that course will be completely overwritten by later classes, and until then nothing in the course itself will be relevant at all. I'm a geometer by trade, and I never even bothered taking high-school geometry; learned my geometry via doing puzzles and skimming Euclid, mostly the former.

Take the course, get it out of the way, get the credits, look at all the pretty pictures, learn the bizarre terminology that's never used outside of high-school, but don't worry about how much actually sinks in.  

[Sioga]

Well I go to one of the top schools where I live, and the school I am taking the summer course is also a really good school academically. Both are some of the few real good high schools where I live.

I can absorb information quickly, when I actually want to. So for six weeks, four hours a day, I will be in this class. And knowing myself, I will write notes for every lesson and then do a bunch of work at home so I can get an A. But I was always pretty good with angles, measuring, classifying shapes, and also the perimeter/area/volume stuff.  

[Layra-chan]

The basic problem is as follows:

High-school geometry attempts to do two things. It attempts to introduce the students to Euclidean plane geometry, and it attempts to introduce the students to Euclidean axiomatic proof. It does so by asking the students to perform a variety of calculations and manipulations of angles and lengths using a small set of rules; this usually involves long sequences of "applying this rule, we get this result".

This is entirely the wrong way to teach either geometry or proof. You'll come up with some neat little formulas for areas or volumes or angles, and once you finish the course, none of those formulas will ever be seen again. All the proofs you come up with will be flawed, lacking subtle (or not so subtle) but vital pieces that you won't get in a high-school course, and the "apply rule A, apply rule B, etc" IRS-form style proof isn't done by anyone except the most hardline logicians.

I'm sure you'll do well in the course. But I'm really, really doubtful that you'll actually learn anything useful in that course, no matter how good your high-school is; the fact that geometry is stuck between courses titled "Algebra I" and "Algebra II" tells me that.  

[Sioga]

Okay then. At least now I know that I will only have to remember a lot of the technical jargon and formulae until the exam, and then it will be gone. Thanks a bunch.  

[SuchSweetSadism]

I think youve made the absolute right decision.

Good luck. [:  

[Sioga]

I reject your reality...

Well, as an update on this:

I took the class, and aced it with a final grade of 98%. I am in Honors Algebra 2 now, and very very glad I did take the class.

...and substitute my own!