Still grinding on my Sputnik question, the failure of US education to teach skills.
There’s an obvious line between physical skills like typing and soldering and cooking, versus symbolic skills like arithmetic and writing.
New thought: There’s a more subtle line between symbolic skills like arithmetic and writing, versus symbolic description of the symbolic skills.
Meta-skill is familiar and well-separated in the teaching of language. First we learn how to write a letter or email. Much later and OPTIONALLY, we learn how to analyze what writers are doing.
Meta-skill is never separated in the realm of math.
Set theory is NOT math. Set theory is meta-math.
Along with ring algebras and topology, set theory is CRITICAL MATH THEORY. The post-Sputnik “reform” replaced actual math with meta-math. NOBODY NEEDS meta-math. Grad students in math learn how to discuss and analyze math, just as grad students in literature learn how to discuss and analyze literature.
Elementary and secondary students should be learning the ACTUAL skills of writing and cooking and soldering and calculating. The symbolic ACTUAL skills, writing and calculating, should emerge as a natural outgrowth of the physical ACTUAL skills.