[lmm]

> Those who can’t understand that x + 5/3 x is 8/3 x have a hard time understanding that 2xy+ay is (2x + a)y.

Sure - but that's just as true in reverse.

> Understanding rational functions helps to understand what vertical asymptotes are and as such are a fundamental source of examples when learning limits. They also aid in understanding why tan(x) has vertical asymptotes where cos is 0. Every complete algebra curriculum includes rational functions.

Meh. x^-1 is a good example of some things, sure, but I don't remember ever doing addition of rational functions which is what you originally talked about, and I went through an extremely reputable maths degree.

[skhunted]

You learned about rational functions in high school or middle school (most likely given your use of “maths”). I can tell you have very little experience with teaching. Most students who know that x + 5/3 x is 8/3 x have trouble, initially, with understanding that 2xy+ay is (2x + a)y. There is a reason for the order in which topics are taught.

[lmm]

> You learned about rational functions in high school or middle school

No middle school, and I very much doubt it. Searching I can see them mentioned in a further maths GCSE (which is something most schools including the one I went to don't offer, and rather suggests they're not on the regular maths GCSE, which would match my memory).

> Most students who know that x + 5/3 x is 8/3 x have trouble, initially, with understanding that 2xy+ay is (2x + a)y.

Who know that first or who have been taught it? I genuinely would like to see any actual evidence that the latter is objectively more difficult than the former.

[skhunted]

I can tell you have very little experience with teaching. But surely your thoughts on the topic must be on par or superior to those with training and experience. My wife is a doctor and lots of people like to tell her how the body works and why she must be wrong. They think reading a blog post on vaccines is equivalent to 4 years of med school. The same phenomenon occurs in education. Lots of people think that since they went to school they know about teaching and how it should be done.

[lmm]

I've heard you get the same phenomenon in chiropractic and fortune-telling and wine-tasting. Not so much in evidence-based fields thankfully.

[skhunted]

An introspective person would wonder why it is so obvious to others that they have no experience with teaching in the classroom based solely on their views of teaching.

[lmm]

There's no deep mystery to that; anyone who questions the dogma in any of the fields I mentioned is also obviously an outsider. The fact you went so quickly to attacking my credentials rather than giving any real rationale is not a sign that your field is full of legitimate knowledge; quite the opposite.