Problem solving strategy
Specializing means choosing examples
randomly, to get a feel for the question;
systematically, to prepare the ground for generalizing;
artfully, to test a generalization.
In the event that no pattern emerges, specializing means simplifying the question, making it more specific or more special until some progress is possible.
Generalization means detecting a pattern leading to
WHAT seems likely to be true (a conjecture);
WHY it is likely to be true (a justification);
WHERE it is likely to be true, that is, a more general setting of the question (another question!).