Same here, but not with calculus and geometry. My problem was with statistics: I had always been able to solve high-school level problems by intuition alone, an

Same here, but not with calculus and geometry. My problem was with statistics: I had always been able to solve high-school level problems by intuition alone, and never needed the theory. That is, until 3rd-year university, when the problems became too complex to grasp by intuition alone. I had a really hard time that year, because I basically had to re-learn 4 years of foundational theory. So I'd say that teaching intuition first is a dangerous path: students may fail to fully understand the theory if they can get by on intuition. And intuition is not a solid foundation to build on.