Shouldn't it be: saya pergi ke sekolah untuk.... ? To me it now looks like: I am a school to pursue knowledge
I think it should probably be bersekolah. Maybe in casual speech, it's ok to drop the ber- and you end up with sekolah, but it's a bit confusing for us learners.
From what I know and have learned, I agree with you that "bersekolah" is better. But wonder what the contributors think of this.