There is a large chance than next year's math isn't going to be too challenging for dd next year. I think it's going to be ok (she will have a lot of other opportunities/adjustments to make), but just in case, I am wondering -- essentially -- what topics do you wish they taught in math that aren't "on the Algebra/Geometry/Trig/Calc. path. For example, I know AOPS has a number theory class and a probability class and i just read about a cryptology summer camp. Finance? Ideas would be great. Resources would be really great. Thanks.

Herenow, how old is your DD?

We just received a nice book from the credit union-- covers things like compound interest. I think the money-discussion path is well worth taking with all kids, whenever they're ready for it.

And having a real understanding of probability has been very valuable for our DS; helps him cope with anxiety (thinking about likely and unlikely eventualities).

DeeDee

You listed several good alternatives to "standard" math, such as probability, cryptography, and number theory. I'll add mathematical logic, set theory, game theory, and computer programming.

The EPGY math curriculum covers logic and set theory. Set theory was an important part of the "New Math".

Financial mathematics employs probability and calculus (or at least algebra). Applying math to finance may be difficult without some grounding in algebra.

I am interested in the computer programming idea. I understand that is a very useful skill for people interested in the sciences (like my dd). AOPS has a class that teaches something called python. How would someone (like me) who knows absolutely nothing about the topic be able to decide what kind of programming language a child should take? Is there a place to get an overview that isn't technical?

I looked at the EPGY math curriculum for logic and set theory, and the only classes I could find had prerequisites of pre-calculus. I will keep my eyes open for other opportunities in these areas.

Considering what you've said, I think studying finance may be a few steps up the pyramid from where we are now. She has had some exposure to growth/decay which I will continue with informally. I agree that the money-discussion is critical and ongoing!

Python's a great first language, and is always the front runner in conversations I've been part of on the subject "what programming language should X learn first" - it has lots of powerful libraries but very little in the way of stuff you have to do to get anything to work. However, there are lots of other good choices too (some of them specifically for children - Scratch is good, for example, and my DS loves TurteArt which is a language for making a "turtle" go where you want and draw patterns on the way - there are several languages like that). In the end, it doesn't really very much matter - if someone has a reason for finding it convenient or exciting to try some language, it's better to start programming in that than to hold out for the perfect language. I would expect an AOPS Python course to be interesting!

You've had some good ideas already but may I put in a word for problem-solving taking up a lot of time that could be spent on new stuff? In school they often jump from one bit of stuff to the next and don't do nearly enough solving hard problems with what they already know for optimal mathematical development, IMO. There are lots of resources in the form of books of contest questions, Olympiads etc. - if you need specific stuff I'm sure I or others can help.

I meant the EPGY K-7 math curriculum. For example, grades 5-6 http://epgy.stanford.edu/courses/math/M0WC/ cover

Multiplication and Division
Introduction to Plane and Solid Geometry
Sentential Logic and Sets
Operations on Fractions and Mixed Numbers
Decimal Arithmetic; Percentages
Functions and Graphing
Area and Volume
Prime Numbers; Factors and Multiples
Probability

If your child does EPGY math there will be some overlap with school math but also some unique topics.

I agree with ColinsMum's comments and recommend the essay

Computer languages for kids
http://gasstationwithoutpumps.wordpress.com/2010/08/07/computer-languages-for-kids/

for more information.

http://www.eimacs.com

This is an online training for logic and computer programming.
My son did the Introduction to Logic over the summer when he was twelve. This was a prerequisite for a group class that he took over the school year. At twelve, he was among the oldest students from the group, however, he did have an easier time with it than most too.

The below quote is from their FAQs section;

That looks fun - but pricey enough to put me off, and I don't think of myself as especially price-sensitive for such things. A cheaper do-it-yourself alternative is this package:
http://ggww.stanford.edu/NGUS/lpl/
which we have. DS7 hasn't so far had much time for working through the book (though he has encountered much of the material elsewhere) but he loves playing with the software, Tarksi's World especially. NB it has an auto-grading facility which seems to work (you do some exercises and send them off to their server which marks them) so it's not *totally* do it yourself.

wow. I love this forum.

Thank you for the advice and the links. I have some reading to do!

CollinsMum- I couldn't agree with you more about problem solving. My dd is taking an Art of Problem Solving course right now and it's a real eye opener! We will definitely pursue this path.