Kriston - I'd like your notes as well.

About 6 1/2 years ago (note that son is 6 3/4 YO), I got into a funk and gave about 15 boxes of books to the library. With them were all my college textbooks, which I had been saving for over 15 years. There went Calculus, Diff E, Latin, Logic, everything. Boy do I wish I had those back! Lessons learned: don't throw anything away in the midst of post-partum depression and EVERYTHING is worth keeping! Not that the fist part of the lesson will ever apply again!

Lori - my son figured out negative numbers when the teacher gave him a "2nd grade brain teaser". There were flowers and numbers on each petal and one in the middle. You were supposed to subtract the petal number from the middle number. He did them all backward and got negative numbers, which he didn't know how to notate, so he put "2 but 2 that is less than 0". I explained negative numbers to him and told the teacher about it at a conference as an example of his math skills. She told me "you shouldn't teach him something that we don't learn in 1st grade - that's a 5th grade concept". I read something about "subtraction with renaming" and had no clue what it meant. Now, you've described it for me. Totally counterintuitive to me - unless it's the same as borrowing? Okay, totally rambling now and not contributing.

This has been a very good thread and I'm glad to hear all of the thoughts, ideas, and theories of everyone.