練習してうまく話したり、書いたりすることができるようになりたいです
I usually would interprete ように like that: "to reach A, I do B"
Here I'm a bit confused because the verb なる follows the ように clause. "To reach A, I wish to become."
Obviously this doesnt work. So are there any omitted phrases I'm missing or is ように in a different function here?