Teach Math Procedures as a First Step to Conceptual Understanding

Stanford’s Keith Devlin, via Joanne Jacobs:

. . . professional mathematicians, scientists and engineers, want the schools — the pipeline that keeps those professions supplied with new personnel — to ensure student mastery of numerical, algebraic and computational skills. “We don’t want to spend our time having to reteach the incoming students how to add fractions!” is a common refrain heard in university science and engineering departments.
Basic skills are not all they want, but they don’t want them left out or de-emphasized.
Ranged against them (again, broadly speaking) is the mathematics education community, which argues that a focus on procedural skills is misplaced, and that the primary aim of school mathematics education should be to produce conceptual understanding. “If students understand the concepts, they can pick up any skills they need easily enough, as and when they need them.”
As a professional mathematician, I often have to learn a new part of my subject. Every time I have to go through the same process: Start by learning the rules, then practice using the rules, and keep practicing until understanding develops. Practically every professional mathematician, scientist, or engineer I have spoken to has said more or less the same. Understanding follows experience.