by is the better choice, in my opinion.
through, though synonymous, is not used very often in this precise role. Both are correct, however.
It seems to me that
by is more used in association with actions (such as indicated with gerunds like "paying attention"). On the other hand,
through
is more used in association with nouns, possibly abstract nouns, that
are less indicative of action. Also, to my ear, the relationship
set up by
through is less direct than the relationship suggested by
by.
I learned a lot [?through / by] studying hard.
I learned about the lecture [through / *by] a friend.
Karen got the job [?through / by] reading the want-ads.
Karen got the job [through / *by] a secretarial agency.
Helen got the job [through / by] deceit.
Helen got the job [?through / by] lying.
You can get a promotion [?through / by] working hard.
You can get a promotion [through / ?by] hard work.
CJ