There is no discussion of how much time would be taken up by the more rigorous proofs that he advocates. The difference between ten lines and ten pages is enough to overturn the (!! implicit !!) contract between school and student, whose terms, to order of magnitude, were set in the 19th Century.
First up, I agree that mathematical pedagogy is usually pretty rough, more or less from Kindergarten to Postdoc.
But, this article implicitly assumes that a mathematical proof has to be utterly rigorous in order to be useful. I would assume that the author leans hard towards a "formalist" view of mathematics. I think this is an insufficient understanding of what mathematics _is_ and that embracing some amount of mathematical platonism and using "incomplete" proofs to gesture at important understandings is necessarily a valuable part of mathematical pedagogy.
My opinion is basically that of David Bessis, see a recent blog post [1], and his excellent book on the subject [2].
There is no discussion of how much time would be taken up by the more rigorous proofs that he advocates. The difference between ten lines and ten pages is enough to overturn the (!! implicit !!) contract between school and student, whose terms, to order of magnitude, were set in the 19th Century.
First up, I agree that mathematical pedagogy is usually pretty rough, more or less from Kindergarten to Postdoc.
But, this article implicitly assumes that a mathematical proof has to be utterly rigorous in order to be useful. I would assume that the author leans hard towards a "formalist" view of mathematics. I think this is an insufficient understanding of what mathematics _is_ and that embracing some amount of mathematical platonism and using "incomplete" proofs to gesture at important understandings is necessarily a valuable part of mathematical pedagogy.
My opinion is basically that of David Bessis, see a recent blog post [1], and his excellent book on the subject [2].
[1] https://davidbessis.substack.com/p/the-curious-case-of-broke...
[2] https://www.goodreads.com/en/book/show/200128457-mathematica