Yes… there’s still some proofs in high school geometry, I believe, but no real explanation of what a proof is and why you should care, so I suspect it’s totally forgotten at the end of the year
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Put another way, our minds seem very well prepared (evolutionarily) for certain types of abstraction, and very poorly prepared for other kinds of abstraction. All other things being equal, one wishes to target the former when designing new abstractions.
For, er, concreteness: Dehaene and others have argued that we have some innate capacity for number. I have, unfortunately, forgotten how or whether they relate this to Piaget.