Yes, the 'natural approach' to language learning is definitely popular. But in most classroom settings I would be surprised if students weren't exposed to the translated meanings through homework or the textbook. Class would not get very far once students started learning abstract concepts otherwise. Of course, translation is just the very first step in lexical acquisition - it's still a long journey to acquire a word.

>Less philosophically, each language you master gets its own language center in your brain, just as each finger you can control individually maps to an identifiable region of your motor cortex (and if you can't control your pinky, it's because they've blended together).

That's not really true, though, and it also depends on what aspect of language we're talking about (phonology vs. syntax vs. lexical acquisition, for example). In the case of the lexicon, there's good experimental evidence that bilinguals, when hearing one language, activate lexical competitors from both languages (i.e., they are not fully able to inhibit activation of one language in listening). The mind is far more complex than having different "centers" for different things. It's a complex network of signal activation and inhibition.

Of course, that doesn't relate to my original point, which was simply that language learners should not purposefully limit themselves. The incredible amount of time it's going to take to learn abstract concepts without translation far, far outweighs the possible co-activation of translation equivalents.