[lmm]

> Whether it is causative or not it is still the case that someone who doesn’t know fractions will have a hard time in algebra.

Doubt. Do you have any evidence at all for this claim?

> It would be bizarre to teach someone how to add rational functions before they can add fractions.

Sure, rational functions obviously sit at the intersection of algebra and fractions and require both. But they're hardly some deep foundational piece of algebra; I'm not sure my classes even covered them.

[skhunted]

Do you have any evidence at all for this claim?

Only anecdotal evidence. I’ve taught beginning algebra courses at a community college for 23 years. Students who don’t know fractions have a very hard time in algebra. 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.

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. I say complete because algebra is usually broken up into 3 courses (2 at the pre-college level).

[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.