Basically, I think you aren’t going to understand what Hestenes is talking about until you engage with his work more directly than just this short summary. Me trying to explain to you all of his ideas about solving physics problems is not going to be a worthwhile use of either of our time. If you want to understand that, you should read his books and papers, try to solve the problems therein, apply those tools and approaches to your own problems, etc. Reading a few paragraphs on an internet forum is not going to make these ideas sink in.

You said:

> it sure sounds like he's talking about teaching vectors as geometric objects with various manipulation rules and avoiding coordinate descriptions. [...] This is actually the sort of angle that [...] is not [possible] for physicists. [... For] physics, it is absolute essential that you are also able to think about vectors in terms of coordinates if you are to connect them to the real physical world, which has rulers and T-squares and so on. Physicists are trying to understand the world, not the abstraction.

The laws of the “real physical world” are absolutely not defined by T-squares or rulers. Those are imperfect measurement devices which we use to help us learn approximate relationships between things in the world and some human-defined standard measurement, but there is nothing fundamental about rulers. The fundamental thing is the structural/spatial relationships between objects which are directly interacting in whatever system we care about, not the tick marks on some stick which were drawn by a machine based on other tick marks drawn on some arbitrary global reference stick.

In any event, it is obvious that Hestenes doesn’t want to abolish measurement devices or ban the use of coordinates. You’re basically arguing with a straw man.

If you really want to get Hestenes’s answer to your comments, I suggest emailing him directly, instead of trying to get some strangers on Hacker News to stand in as proxies. I suspect he’ll be willing to at least point you at other sources to read, even if he doesn’t answer in detail.

> In my teaching experience as a graduate student, students adopt the geometric picture of a vector as soon as they are able to, because it's vastly easier and more pleasant to work with. (That's why the abstraction was originally developed.)

The geometric picture of a vector is the vector, and insofar as it’s “an abstraction” it is because the concept of a vector is itself the abstraction in question. The geometrical properties and relations of vectors are the fundamental nature of vectors. If students “struggle to build the proper abstract machinery in their brains”, what that means is they haven’t actually learned or properly been taught what a vector is yet.

Many many scientists I have met, and especially many engineers, when confronted with a problem, immediately start reaching for measurement devices and coordinate systems. This is an approach to problem solving which is inherently limiting, sometimes severely limiting.