Having a crummy language, though, can get in the way.

I find these distinctions (in the English language) to be more of an obstacle these days (crummy programming), when computer languages have become far easier and more interactive. In APL, for example, just coming on-line at Princeton in my undergraduate days (1970s), you can invert a matrix with a single operator. But that might be too "black boxy" for beginners, as it's the technique of matrix integration they need to follow.

Wayne's early edition Linear Algebra text (which I got a copy of) has lots of code in the back for doing linear algebra. The language (BASIC I think) is not taught in the regular text and in the back it's somewhat dense and uncommented. You're just supposed to type it in and cross your fingers you didn't make too many typos.

You go back and forth quickly and *both* sink in, because they're "in dialog" (Python and traditional math notation are covering the same concepts in close proximity). It's like seeing in stereo.

I think rather than putting all eggs in one basket and saying "here's the best new way to do things" our approach should be "lets do many experiments".

To some here, the "many experiments" model seems unethical because there's a "chalk 'n talk" method (direct instruction) that's proven to work. I don't think so. For some people it works, in some circumstances.

Plus one might argue one learns different things.

If you learn calculus or trig or statistics in concert with learning a computer language (say Mathematica, or R, or Pandas, or APL, or J....) then you end up with this added language skill as well, so there's value added we should take into account (apples and oranges, to compare calculus with Mathematica versus calculus without in some ways).

I'm against 'one size fits all'.

I'm pro 'lets experiment'.

I'm against "we've tried that for 60 years and it hasn't worked so lets give up.'

Many interesting experiments have produced positive results for many people (including the late Jerry Uhl's Calculus&Mathematica at University of Illinois -- where I'll be tomorrow, visiting one of the spin-offs of that effort) and the tools continue to change, so it's anything but a static picture.

Kirby