Regarding "helping", I don't mean that I never answer any questions, or even that I never give any information up front that he might be able to figure out on his own. I just mean that I keep a constant focus on him figuring things out, that I spend a lot of time finding challenges for him that are at just the right bit past his current understanding, and that I get annoyed when his growth opportunities are destroyed, whether they arose with or without me.
I don't know if this is the right thread to ask but you've mentioned how you teach your son logics and stuff and I'm interested in hearing more of your methods and resources.
It's nice of you to ask. I haven't taught him any formal logic yet, but do plan to sometime (I am currently putting together our first real home-learning curriculum with the wife).
One thing we have constantly done is play a lot of games. Off the top of my head, some games he enjoys or has enjoyed that involve various sorts of problem-solving skills: chess, Carcassonne, Risk, Bandu, Abalone, Othello, card solitaire, card games including Texas Hold 'Em and Hearts, Chinese checkers, Mastermind, flavors of Blokus, etc. (these are just a smattering based on trying to visualize the games section of the front hall closet). He has enjoyed solitaire logic games tremendously too at various times, including Rush Hour, Clever Castle, Hot Spot, Brick by Brick, Shape by Shape, and some other similar ThinkFun-type toys. He really likes the "Logic Links" toy, which makes me want to explore further offerings from that publisher. He has also played various sorts of computer games, some which are conquest-strategy types, some simulations, some essentially board games on the computer, etc.
We also have bought him various odds and ends of "brain games"-type books or card sets, the names of which I don't recall off the top of my head. I recently got him some workbooks with some problem-solving stuff in them, but I don't remember what the specific series is off the top of my head. My plan with those is to rip out the sheets, scan them to PDF, and combine them into fun little work sets. I want to get him the big Sam Loyd game/puzzle book, the "Moscow Puzzles", etc. but haven't yet, and have saved a long list of mathematical-recreations type of books for later. The IXL website has some types of problem-solving exercises on it; I would guess that Singapore Math does too.
We also have lots and lots of puzzles that he works when he feels like it. I have also given him mini-challenges at times-- I think I wrote before about asking him to put together a wooden train track, using all his pieces, in a restricted space and meeting some other criteria.
He has picked up some rudimentary programming skills with Karel and Java, but we haven't done that in a few weeks, which I will rectify soon. He is enjoying his Lego Mindstorms a lot; the first two robots were put together according to plans shipped with the set, but you can play with the programs with the stock robot bodies, and he's now building his own robot design. When he gets more advanced with his programming, I am going to give him lots of old programming chestnut problems to solve. I am hoping to use programming to increase his modular thinking, introduce him to more patterns, algorithms, etc.
