I was confused about this when first learning it, as I don't think it was ever explained, so remember this: trở thành means to become, but only in the sense of becoming a noun. To say something that's becoming an adjective, like "the boy wants to become older", you would use trở nên instead (cậu bé muốn trở nên già hơn). You should find trở nên later in the course, so keep it in mind.
I think the word "cậu" was not pronounced clearly enough. I thought it was "cô" and I was confused. I also asked my brother and cousins and they agreed that they heard "cô".