Possible harmonization of the two ideas: the intuition that we go into math at high school level can help serve us at that level of math. We have some idea of geometry-like objects and 2d-calculus like curves from our everyday life
At university level the objects become more abstract, so the intuition we use in normal daily life may no longer apply. New kinds of intuition may develop but it takes work, including lots of time spent with the formal processes and calculations along with reflection on that time, and the active creation of new metaphors to drive the intuition. For example, I still remember a professor using "Ice-9" (from _Cat's Cradle_) as a metaphor for how proving some local property of a holomorphic function on the complex plane made that property true for its global behavior
At university level the objects become more abstract, so the intuition we use in normal daily life may no longer apply. New kinds of intuition may develop but it takes work, including lots of time spent with the formal processes and calculations along with reflection on that time, and the active creation of new metaphors to drive the intuition. For example, I still remember a professor using "Ice-9" (from _Cat's Cradle_) as a metaphor for how proving some local property of a holomorphic function on the complex plane made that property true for its global behavior