I'm somewhat the short order cook or maybe Chinese chef (that'd be a stretch maybe) in that I keep hopping around twixt the same simmering pots.
Back burner becomes front burner, then back it goes, and so on. No, not so simple as "round robin". More "interrupt driven".
So on Math Forum, I'm back to: "sharing 'dot notation' with K-12 is overdue."
That sounds somewhat cryptic right off the bat.
K-12 is jargon for the ethno-cultural torch passing that goes on up through "coming of age" young adulthood. Kindergarten through 12th grade, in the USA system, with four years of college sometimes called 13-16, making K-16 a rather complete induction into adulthood, by academic means.
"Dot notation" means different things to different web pages. The chemists have a dot notation for indicating electrons, valence patterns.
There's a "dot notation" associated with Principia Mathematica, by Russell & Whitehead (I start my thread with an allusion to their approach), borrowed from Peano according to Wolfram.
Newton used dots for his "fluxions", first, second and third derivatives. That's considered a bit unwieldy. Typography went for Leibniz notation dx/dy, though Spivak had some problems with that too right? (thinking Calculus on Manifolds, my text at Princeton).
Plus one could argue that using a "dot" is not that conceptually critical i.e. you can use an arrow or double colon or... yes, yes, I agree.
I'm casting a net and pulling in enough fish to at least point to substantive content.
"These fish, lets share them, with loaves too, why not?" -- these languages are free and open source and replicate faithfully to the bit.
But saying the software is "free" in the Stallman sense (of four freedoms) implies an ability to read and modify source code in the first place. "Computer literacy" we were calling it in the 1980s. I'm just calling it "literacy" and, under STEM, I don't see the need to decide which pigeon-holes. These memes bounce around.
The key point is to share them, not pretend we only care about Leibniz notation, or Riemann. This bias against machine executable languages was surely overcome by Mathematica and Mathcad.
We're over that prejudice: that it can't be mathematics if it runs on a machine. On the contrary, Mathematica had to tighten up the old notations, with yet more precision.
Machines have helped us take our mathematics to a new level. Lets teach "dot notation" in K-12 to help share about this breakthrough. More SQL too while we're at it (different topic).