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Given the sentence:

Teachers in this country have generally been trained either to approach mathematics like/as a creative activity or that they should force students to memorize rules and principles without truly understanding how to apply them.

Should I use like or as?

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Approach or force? Seems like an odd either or pair to me. What about the case where teachers force a creative approach to mathematics? Do you mean to imply that some teachers encourage students to take a creative approach to mathematics, while others teach students to approach math prescriptively? – Wayfaring Stranger May 10 '13 at 21:52

At least to me, they mean two quite different things. I'm not sure if that is owing to grammar, semantics, pragmatics or just my individual perception, though.

approach mathematics like a creative activity

--> approach mathematics like you would approach a creative activity

approach mathematics as a creative activity

--> approach mathematics as if it (mathematics) were a creative activity

Some may still argue that the two interpretations are also essentially the same.

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You can get to the same place by numerous routes, depending on the context. Though it's not necessary to presuppose a deleted counterfactual were with as if; it might be, after all, just one of a number of hypotheses, rather than something not hypothesized at all. – John Lawler May 10 '13 at 14:39
Kris, I hadn;'t seen your answer until I posted mine, but I think we agree and you've phrased it more concisely. – TrevorD May 10 '13 at 14:43

I would definitely say "as". I find it difficult to analyse/explain exactly why, but: I think "as" implies that mathematics is (or can be a creative activity), and hence mathematics is within the group of creative activities. On the other hand, mathematics is not "like" a creative activity: it either is one or it isn't one. With "like" you are comparing mathematics with another (parallel) activity, not with a group which contains it.

With "like", you are effectively saying "Teachers ... approach mathematics like [they approach] creative activities." With "as", you are effectively saying "... approach mathematics as [if it were] a creative activity.

I think I would use "like" where there are two parallel, but separate, activities being compared, but "as" where one activity is being compared with a group within which it fits.

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Good thing we posted almost at the same time. And great we think alike. I'd say the answers complement each other to form a reasonably sound explanation. – Kris May 10 '13 at 14:56

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