If I wanted to say, "Ken's getting better and better at Japanese", then would this be correct?
けんさんはだんだんじょうずになります。
If I wanted to say, "Ken's getting better and better at Japanese", then would this be correct?
けんさんはだんだんじょうずになります。
Your usage of だんだん is just fine. It's a standalone adverb which can be used without any other particle. An adverb is usually placed just before what it modifies (in this case, じょうずになる).
You have to use the progressive form of なります; otherwise the sentence would mean "Ken gets (or will get) better and better at Japanese".
けんさんはだんだん日本語【にほんご】が上手【じょうず】になっています。
To make this a bit more natural, you can add a subsidiary verb ~てくる and say:
けんさんはだんだん日本語が上手になってきています。
けんさんはだんだん日本語が上手になってきています。
orけんさんは日本語がだんだん上手になってきています。
– On The Net Again Nov 17 '16 at 14:55