Elementary mathematics took thousands of years to develop, and understanding basic arithmetic in a deep and fluent way is a highly advanced skill (really, a constellation of dozens of inter-related but distinct skills), which most students and even most teachers never fully develop, but which is incredibly helpful for becoming a fluent mathematician, scientist, or engineer.
Beyond basic understanding, teaching elementary mathematics effectively is a difficult job which can take decades to fully master. There are a large number of potential conceptual and procedural errors which various students can make, some of which are subtle and hard to correct. Someone who can perform elementary mathematics is not necessarily able to properly teach it.
As for world-class expertise, that really depends on what our goals are. There are undoubtedly world-class experts in elementary mathematics, who have spent decades doing extensive research in the history and practice, and have thought very deeply about the nature and meaning of numbers and mathematical relations. My comment was about the “ideal” case, if you want the student to learn as fast and effectively as possible.
But you can also get by okay with just a typical trained professional teacher (ideally a specialist in mathematics education).
I recommend Liping Ma’s book Knowing and Teaching Elementary Mathematics for some basic analysis.
Beyond basic understanding, teaching elementary mathematics effectively is a difficult job which can take decades to fully master. There are a large number of potential conceptual and procedural errors which various students can make, some of which are subtle and hard to correct. Someone who can perform elementary mathematics is not necessarily able to properly teach it.
As for world-class expertise, that really depends on what our goals are. There are undoubtedly world-class experts in elementary mathematics, who have spent decades doing extensive research in the history and practice, and have thought very deeply about the nature and meaning of numbers and mathematical relations. My comment was about the “ideal” case, if you want the student to learn as fast and effectively as possible.
But you can also get by okay with just a typical trained professional teacher (ideally a specialist in mathematics education).
I recommend Liping Ma’s book Knowing and Teaching Elementary Mathematics for some basic analysis.