I don't believe you're correct. As my 2nd & 4th graders' teachers tell them, they need to learn a set of level-appropriate "math facts" ... but they're not forced to start by memorizing those facts (my son, for example, has a printed multiplication table up to 15x15 to reference while practicing decomposition of 3 & 4 digit multiplication problems). I truly appreciate the Common Core principle of focusing on teaching methods over facts, and -- at least in my children -- it is apparent that it sets them up for problem solving success IRL. YMMV. It's not a perfect curriculum and is still tailored to the lowest common denominator student, but I do think there's value there. And again, in a classroom with a strong teacher who can take time for differentiated instruction, there are ample opportunities for advanced students to go beyond or to practice their learned skills by helping their classmates.
That said, I think your statement is absolutely incorrect in the context of higher math (and experimental science). The more facts you know -- whether literal facts, axioms, proofs, applied example or theories -- the more facile problem solving will be. This holds true in all disciplines (and not just math & hard sciences, but also engineering, social sciences & business).
That said, I think your statement is absolutely incorrect in the context of higher math (and experimental science). The more facts you know -- whether literal facts, axioms, proofs, applied example or theories -- the more facile problem solving will be. This holds true in all disciplines (and not just math & hard sciences, but also engineering, social sciences & business).