Someone asked me:
どんな本を使って日本語を勉強していますか
I'm confused about the て-form here. The only sensible translation I can think of is:
What kind of books do you use (in order) to study Japanese
I've not come across て-form to indicate purpose before. Is this common? How does it differ from のに?
Your translation is perfect, but I think て is not indicating purpose. It rather means method.
More verbatim translation is:
By using what kind of books do you study Japanese?
"By" at the top of the sentence comes from て-form.
Related dictionary entry (quoted from デジタル大辞泉):
［接助］活用語の連用形に付く。ガ・ナ・バ・マ行の五段活用動詞の音便形に付く場合は「で」となる。形容詞、形容詞型助動詞に付く場合は「って」の形をとることもある。
手段・方法を表す。「歩い―通学する」「泣い―抗議する」
In this sentence the purpose is to study Japanese but not to use books. So you can use のに (that indeed means purpose) to say the same as follows:
日本語を勉強するのにどんな本を使っていますか。
どんな本を使って日本語を勉強していますか
This (the TE-form) is similar to the following (手段・方法) :
駅からは歩いて十分ぐらいです。
https://japanese.stackexchange.com/a/38582/16344
I think 歩いて is like 現在分詞 ( "walking" in English ), and it could be an adj. or adverb. ( --> Actually "歩いての" is the adj. form. )
使って -- adv.
使っての -- adj.
