Exactly. In the case of mathematics, if you aren't doing proofs yet, you don't even know what math is. Most high school math curricula are completely devoid of proofs or abstract reasoning with the exception of at most a few months during geometry. How many college students have wrongly expected "Modern Algebra" to be a rehash of what they learned in high school? The distinction between mathematics and what gets taught in high school is very similar to the distinction between computer science and computer programming.