First, try learning what is given to you as it is: obey your master. Only then comes a stage where you realise, 'Hey, but this doesn't quite work with my body/in this context/etc.' - that's when you break the rules your master gave you, to suit your needs.
Then you live a comfortable art life for a long while - until you suddenly look at yourself doing the art from a distant, objective point of view. You are struck by the realisation that it is not you doing the art: you and the art are one, and the one just happens - and it is fun. No particular, prescribed methods need to exist for you or anyone. You are separate from the whole you-art thing, while making it happen by doing whatever is needed. Now that's mastery.
Wow. Do I sound like a Zen monk now?
So, while Brett made a fair point for stage 2 (or even 3?), I think teaching the basic, often exaggerated, pronunciation is the right thing to do for stage 1. This is especially the case with θ/ð because English uses other sounds close to them. I will show you what I mean:
The above is a portion of the IPA chart, where all the humanly possible speech sounds are represented. I have circled the relevant fricatives English adopts. Isn't it insane? English uses eight consecutive humanly possible fricatives! Compare, say, Japanese, where you start with the leftmost ɸ and then swiftly and discreetly jump to s (with a lot less air friction, I might add).
So this is what learners of English face: learn to distinguish between f and θ, between θ and s, and so on, in such cramped space. What little difference there is needs to be duly magnified and presented to them.
In fact, it is not just for learners: English speakers in general do need to do an exaggerated pronunciation of the right kind from time to time. Here is someone making her point (taken from a BBC programme 'Question Time'):
And here is a boy from the film 'The Wall':
|'... in THE classroom ...'|
I could go on, but I think I have made my point. Finally, though, I do admit that there is such a thing as too much exaggeration. Here is Britney Spears doing an L:
I could think of reasons for doing that, but in general, I will not recommend that. I do show it to my students though, because it's fun. And now I have done it to you. I hope you had as much fun; welcome to stage 3.