You contradict yourself. As you said, one does not need to be skilled in combinatorial search, er I mean, algebraic manipulations to be able to solve problems;

You contradict yourself. As you said, one does not need to be skilled in combinatorial search, er I mean, algebraic manipulations to be able to solve problems; one only needs a solid conceptual grounding and understand the symbols and the rules for their manipulation. I wouldn't be surprised if most students who pass college calculus courses with good grades are entirely unable to recognize the situations where calculus is applicable.