Given that mathematics is not about number, and that it is not even about the cryptic notation used to describe mathematical problems, how much of mathematics could be taught without reference to mathematical notations?

When I ask "how much", I'm thinking of the progression in which mathematics is taught to children. Could you actually teach the patterns and concepts of mathematics up to university entrance level?

I realize that mathematical notation is an essential tool for communicating mathematical ideas, however it is a rather cryptic and convoluted way of talking about things, and one in which similar things do not necessarily use similar names and notations. As a result, the language can be a barrier to understanding for many people.