"Approach mathematics like/as a creative activity"

Solution 1:

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.

Solution 2:

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.