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>a world-class expert in the field of interest A world class expert in elementary mathematics seems kind of paradox? A pedagogy expert, sure, but how much expe

>a world-class expert in the field of interest A world class expert in elementary mathematics seems kind of paradox? A pedagogy expert, sure, but how much expertise do you really need? >This is basically how we train elite athletes, musicians ... but only after they've proven talent. Children raised to become top athletes aren't necessarily going to be successful, are they? Simply, the attention afforded to a particular student in a 1:1 setting is an improvement, I agree with that at least.

jacobolus 10y ago
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.
- posterboy 10y ago
  You are ignoring that I noted the difference to pedagogy beforehand

jacobolus 10y ago

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.

posterboy 10y ago
You are ignoring that I noted the difference to pedagogy beforehand