Child centered, problem centered is vague. More practically, the big things are: you want material that's novel to the learner but also somewhat familiar (this is true, regardless of age). Children's attention is more distributed and worse at blocking out irrelevancies. Therefore, more complex tasks (such as math) should be presented in a way such that the signal meant to be learned can be extracted with minimal ambiguity (less extraneous information in presentation). Few other things have replicated.