@missradders I think it’s perfectly acceptable to list them as desirable but there’s plenty of phenomenal teachers without them and far too many appalling ones with them. If you want to know how good a teacher somebody is you just need to see them teach. Everything else irrelevant.
@ProfSmudge@C_Hendrick Interesting comparison- we’ve had this at quite a few insets now, do you have a decent meta-analysis in the public domain I could look at?
@honeypisquared@MrMattock None of these. Each ones looks like a different textbook front cover. Paraphrasing Mirzakhani, you need patience to see the true beauty
@mpershan Rationalising the denominator isn’t useless at all- it’s is extremely useful to know what quantity of a number is rational and what quantity is irrational.
@Transum And as a follow up- the multiplying by 2 is inevitable, and since 5 odd out of an initial 10 and 4 even out of subsequent eight both give a half, each expression contains a one, and a 5 out of 9.
@Whitehughes @ParkerMaths I like to to prove it from first principles with no need for the chain rule. Always snags me that a more formal proof of the chain rule isn’t particularly accessible for students