Learning is a combination of logic and memory. All problems can be reduced to search. Thus, problem-solving boils down to exploring some solution space, and optimization problems involve finding some solution which is better than a solution you already have, up to some time budget. Being able to jump directly into a promising region of the solution space is much faster than having to traverse there step by step. This is what happens when you remember the result of a complex calculation, and in computer science, we call it "memoization".

Grandmasters play strong chess because they can compute far more positions than masters. And they can do this not because their brains work faster, but because they have made good trade-offs between time and space. Their brains have saved the results of previous board states and sequences so that they can shortcut to the outcomes of certain lines of attack, thereby allowing them to push deeper into the solution space in the same amount of time.

But memory is a funny thing: you can only remember something if you have seen it already. Thus, the best way to build up a memory of good moves and strategies is to see a lot of good moves and strategies. Not only that, but our brains are very good at throwing away data, as they must, so that they don't overflow each day. How does our brain decide what to keep and what to throw out? We don't know for sure, but it's pretty obvious that emotionally charged events get saved, and boring ones get thrown away. So how do you remember the good board states and move sequences in chess? One way is to create an emotional event: either a clever sub-victory, or a painful defeat. And here is the crux of the matter.

You want your daughter to avoid the defeats by thinking harder and only playing good moves. But your daughter is learning optimally on her own. Defeats are actually helping her remember how not to play, which helps her build up the rules and memories for quickly pruning bad branches of the search tree! You see it as wasteful, but only because you have never tried to train an artificial neural network on your own.

We know how to teach machines to learn, but our methods are both very crude and very precise. They are crude because they take thousands of times more data points than humans require, but they are more precise because the answers they give are far more consistent and well-defined than humans can generally provide. Each one is a different engineering trade-off. A computer would need to play thousands of times more games than your daughter to achieve the same level of competence from scratch. So stop thinking about those blunders as wasted learning opportunities and start viewing them for what they really are: essential manipulation of her bio-computer learning machine.

At this stage of the game, she is building up an internal mental model of how the chess universe works. And the fastest way to do that is to explore quickly and blindly, so she can set up a rough scaffolding. Yes, she will make mistakes. Yes, she will model some things incorrectly. Yes, she may even form some bad habits that she later needs to break. If there is a more efficient way to learn something complex from scratch, no computer scientist alive has demonstrated it in a working program. But I would argue that the most valuable thing for her at this stage is to play as many games as possible, as quickly as she is comfortable, so she gets to see the "big picture", which you yourself have already built up over many years.

This is frustrating for you, because you are looking at a map of the world and she is looking at a giant blank canvas with a few dots filled in. You can tell her exactly where the mountain ranges and rivers and lakes are, but she must earn this knowledge herself, the hard way, in order to build up that model. If you spoon-feed her precise data points, she will only own those data points. She needs to follow the paths to victory on her own, mapping out the walls and dead-ends, so that she sees the map as fully as you do.

Creating sub-problems is great. That lets her focus on a small room in the chess universe, and explore it in detail. But you need a good mix of barnstorming and 40,000' surveying to build up a good mental model of the problem space. Otherwise, relax, and count your lucky stars that your daughter enjoys playing chess as much as she already does. The best thing you can do as a father is to continue to make the game as enjoyable as possible, so that she practices as much as she is able.

When she gets stuck or reaches a plateau, she will probably ask for help. And then you can go over chess books and study the game more formally. But she is SIX! Let her play. Let her be a kid. Her brain is doing a fantastic job already. Give it some credit and watch the miracle of human intelligence in action. If you think she is learning slowly, download any of the open-source ANN projects and teach one to recognize hand-written letters, or identify shapes in pictures, etc. That is more boring than watching paint dry.