Thanks for your replies.
Looks like he's going the solving high-level problem approach, at least for the summer. His tutor assigned him a number of problems/proofs ranging in difficulty, expecting him to need one to two hours per day. If he gets the competition bug, this is not a bad start but it is also a way to think about and experience what mathematicians outside of a curriculum based approach. When school starts in the fall, we'll rebalance and shift some of the focus to moving ahead on a college level curriculum--mutivariate calculus and linear algebra.
Incidentally, he is using the book, "What is Mathematics?" by Robbins and Courant--a classic, which surveys the full-range of math fields with challenging problems.
