Socrates 's method, as far a mathematics goes, is described by his student Plato in the dialogue Meno, which can be downloaded here.
As for more modern references, aside the great book by Lakatos mentioned by Carlo Beenakker, I would say that the so-called Moore Method goes a certain way in the same direction (though it does not seem to have much of the interactive Socratic approach) .
Moore was a legendary american topologist (Robert Lee Moore, 1882-1974), who taught topology (and other pieces of mathematics) in a peculiar way: an absolute minimum of knowledge provided (essentially basic definitions and key results) and everything else was to be discovered by doing. Apparently the method works, judging from the long list of Moore's "math children".
You can read it it and find refs here
ADDENDUM If you read French, please download a copy of Recoltes et Semailles, by Alexander Grothendieck. There is an entire chapter on his own view on how to do math research, which is difficult to summarize here, but that has definitely something to do with exploring rather than learning "techniques". I mention just one simple fact: Grothendieck and another great mathematicians, Ennio De Giorgi, share something: both, when still undergraduates, after learning basic real analysis asked themselves whether one could possibly generalize it to measure any set. They independently recreated Lebesgue Measure, without knowing it. Useless? according to modern math education yes, but neither of them thought so....