This is far more truer than most people may realize.
Because there is so much to teach/learn, "Modern Mathematics" syllabi has devolved into giving students merely an exposure to all possible mathematical tools in an abstract manner, dis-jointly with no unifying framework, and no motivating examples to explain the need for such mathematics. Most teachers are parrots and have no understanding/insight that they can convey to students and so the system perpetuates itself in a downward spiral.
The way to properly teach/learn mathematics is to follow V.I.Arnold's advice i.e. On Teaching Mathematics - https://dsweb.siam.org/The-Magazine/All-Issues/vi-arnold-on-... Ground all teaching in actual physical phenomena (in the sense of existence with a purpose) and then show the invention/derivation of abstract mathematics to explain such phenomena. Everything is "Applied Mathematics", there is no "Pure Mathematics" which is just another name for "Abstract Mathematics" to generalize methods of application to different and larger classes of problems.
As a maths teacher who is interested in (and sufficiently skilled at) programming, I find teaching programming to be very hard, even to interested students.
Teaching maths to interested students is not hard (for me).
rramadass|6 months ago
Because there is so much to teach/learn, "Modern Mathematics" syllabi has devolved into giving students merely an exposure to all possible mathematical tools in an abstract manner, dis-jointly with no unifying framework, and no motivating examples to explain the need for such mathematics. Most teachers are parrots and have no understanding/insight that they can convey to students and so the system perpetuates itself in a downward spiral.
The way to properly teach/learn mathematics is to follow V.I.Arnold's advice i.e. On Teaching Mathematics - https://dsweb.siam.org/The-Magazine/All-Issues/vi-arnold-on-... Ground all teaching in actual physical phenomena (in the sense of existence with a purpose) and then show the invention/derivation of abstract mathematics to explain such phenomena. Everything is "Applied Mathematics", there is no "Pure Mathematics" which is just another name for "Abstract Mathematics" to generalize methods of application to different and larger classes of problems.
gsinclair|6 months ago
Teaching maths to interested students is not hard (for me).