Increasingly I have come to think that in the classroom there are two and only two genuine ways of teaching philosophy, that is, ways of teaching philosophy that are actually appropriate to philosophy itself. (There are other ways to teach philosophy in other contexts, and definitely other ways to
do philosophy; but our contemporary expectations about classroom education considerably constrain what can be done.) One can be called the Natural Method, after the approach to language education of the same name. If you take a language course taught according to the Natural Method, you are plunged into the language immediately: you begin with a lot of basic interaction in the language you are learning and you build on that. There is certainly something equivalent to that in philosophy; you can find the classic examples of how to do it in Plato's dialogues.
* The other method is the Historical Method, and it is precisely what it says on the tin: you learn schools, thinkers, and their interactions through time, and all that goes with them. All other approaches, when examined closely, turn out to be home-brew hybridizations of these. (And, indeed, I think common classroom expectations make it very difficult to stick only to one -- in practice it's most common to structure the course by Historical Method and fill in parts of that structure with the Natural Method. The danger here, of course, is that they can be meshed in ways that fail to do justice to either.)
There is a common distinction made by academic philosophers between 'doing philosophy' and 'studying philosophy'. In reality, nothing seems to justify such a distinction. If you are studying, say, Plato, this requires 'doing philosophy' -- you won't even understand Plato if you don't 'do philosophy' in reading him. This, indeed, is a very Platonic idea itself: Learning about philosophy requires learning how to philosophize. And, of course, for students (and teachers, who are, after all, just students farther along), 'doing philosophy' is not possible without 'studying philosophy'. Both the Natural Method and the Historical Method are ways of both 'doing philosophy' and 'studying philosophy'. It is always important to insist on this; people with less taste for the latter have a bad habit of treating the Historical Method as somehow a defective way of teaching philosophy, as if it were 'studying' without the 'doing'. This is a problematic assumption. Likewise, the Natural Method does not somehow get behind and around 'studying philosophy' to 'doing philosophy'; it requires 'studying philosophy' as much as the other, and the only question is how widely one's study will go.
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not the same as a focus on problems. The common distinction between 'problems' approaches and 'historical' approaches is a distinction between historical approaches, with one based on themes and one based on interactions. It's somewhat unfortunate that this distinction tends to be formulated the way it does, since it leads 'problems' people to think they are not doing historical work, thus increasing the amount of bad historical work that is done. Philosophical problems are things with a history, and the history is not incidental to what they are and how they are formulated. The only question is how much you are assuming without evidence.