Just for the heck of it, I did a yahoo search of "Taking the time
to". I came up, believe it or not, with 5,300,000,000 hits. For "by
taking", I had much less--just over two billion. That should tell us
something. The chances that the student in question had already heard a
"by taking time to..." construction are fairly good.
Take the time to and taking the time to are in a
sense fixed constructions, but they do have syntactic content, and they
are also open-ended. So they are in that in-between lexico-grammatical
world that construction grammar or cognitive grammar addresses with
some facility. In this lens, grammar is suddenly far more fluid and
dynamic than it would be if we only looked at a handful of sentence
types and a fixed set of formal rules.
It's also interesting to think about what cognitive content is
assumed or expressed by the notion that time can be "taken", or that
taking the time can be a purposeful way to accomplish something else,
like "showing that you care." These are highly purposeful, highly
meaningful constructs, and learning a language involves, at least in
major part, picking up these kinds of structures. The assumption is
that grammar is a meaningful part of it, not just a set of forms that
the words get cast into.
I see no reason to suspect that the student can't follow a shorter
version, such as "By taking the time to study, you have improved your
chances on the test." By smoking, you ruin your health." ("*By smoking
ruin your health" might work with a comma after ruin.) In which case,
a short conversation might reveal that the construct is already there,
but, as Bruce says, just a routine slip. Beyond that, with no student
to talk to, this is conjecture, and a flexible range of approaches
might be best.
What does it mean that time can be "taken"? Or that it can be spent
or lost or wasted or saved? That is another
question that would be routine in cognitive linguistics, as it has been
for Lakoff and Johnson (among other texts, Metaphors We Live By.)
I have a hard time characterizing "taking the time to show that you
really care" as a noun phrase, as Bob has suggested. (Maybe I misread.)
Am I wrong in saying prescriptive grammar won't allow a "by phrase"
as subject? I said that once about prepositional phrases, and Martha
Kolln was kind enough to correct me. ("Over the fence is out of
bounds." I keep hearing these now on the golf course.) I still think
that might be an easier prescriptive approach than saying a noun phrase
can't be both object of preposition and subject, particularly when the
construct in question doesn't look at all like a noun phrase. In a
course devoted wholly to grammar, all that will come up, but it might
just be too much to lay on a developing writer.
I'm very happy that this debate has provoked such rich and
interesting responses. I'm once again happy to part of the list.
Craig