Those four parts sound like one unified, cognitive algorithm -- having an ontology of the problem by breaking it into subgoals; checking your work properly; thi

Those four parts sound like one unified, cognitive algorithm -- having an ontology of the problem by breaking it into subgoals; checking your work properly; thinking backwards to debug a mistake and retrying; and thinking ahead and reasoning backward from the end result. It's all just one algorithm for solving hard problems. A skill that can be practiced, and then it builds on itself.