Great essay! As someone who has taught physics off and on for decades, I couldn't agree more!
See the discussion of Cognitive Instruction, Math Modeling at the ASU Modeling Physics Instruction site, http://modeling.asu.edu/CIMM.html, for an approach to math teaching founded on this insight. Verbal behavior and symbol construction, which is nearly all of what is taught in mathematics classes after 4th grade (excepting Geometry) do not represent conceptual understanding, and indeed aren't really mathematics. No wonder students hate it and most can't really learn it!