I agree with you there, My only point was that for a student to get a grip over maths and to appreciate its beauty he needs to first go through the practical applications.
In my country a lot of people start hating maths when they start learning calculus because the way its taught is currently very theoretical. Students are suddenly introduced to limits and derivatives which are just words for them. Newton didnt start with a theory, he started with a problem.. and developed the math needed for it.. other then built on it.
I am sure nobody would have thought of calculus if the problem didnt exist.