**UPDATE:** Wow, thank you everyone for the great insights!

A couple of months ago I stumbled across Paul Lockhart's essay A Mathematician's Lament and it made perfect sense to me. I'm not meaning to argue this essay one way or the other, except to say that 12 years of what I did in math class really isn't mathematics as you -- and I, as an "enthusiastic amateur" -- enjoy it.

We're probably going to homeschool our daughter, who will be kindergarten age next fall. I feel there's a place for knowing your times tables and the like, but there's also a place for knowing that mathematics is more than arithmetic and formulas: it's discovery, playing with ideas, etc.

Where I'm going is that I know enough to understand the difference, but I'm not quite confident enough to teach (or lead) this process effectively, since I'm not a professional mathematician.

**Are there any curricula that would help provide some structure to facilitate this kind of learning**, so that there is one less student who has a shortchanged opinion of the mathematics profession?

Or, alternatively, if you felt that your elementary school math education hit the mark, how was it done?

Thanks for your time!

Math Circles for Elementary School Students. $\endgroup$