You Can't Teach Height, But Can You Teach Programming?

I think he cited the paper wrong here: It's not the meaninglessness of programming but the meaninglessness of programs. And it is obviously not meant, that a program makes no sense, but that a formalism can stand on its own, without any purpose. Programming, however, is creating programs for a purpose, thus, abstracting facts into a formalism and after running the program interpreting its results is not meaningless at all. I think I can back the observations of the original paper. I occured people which seem to plainly don't get what a program does. They are not talking about what they themselves told the computer to do but they are speculating why the program/computer isn't doing what it ought to do (what its purpose is).

I disagree with Steve's opinion that the level of abstraction is a general problem. I started programming early, and I hit walls all the time. Back from the early times to now I always found things I just couldn't grok. For long years I couldn't understand programming graphical things at all. I watched with awe how my three years older neighbor could program animations on his C64, all I managed to do were Fahrenheit to Celsius converters. Later I was crazy enough to start learning C++ with only knowing BASIC before. It took days to get 'Hello World' running. I kept trying and eventually I found the right book which made me understand OOP. Programming some graphics came very late. And the list still goes on... I can read a book without understand a thing. I come back to the book (or suddenly remember details) some weeks, months, years later and manage to understand what is going on.

The same applies to other areas: Playing piano is something where you hit your personal wall all the time. Sure, there is a natural anatomical caused level of virtuosity which simply can't be overcome. (See Robert Schumann, who tried to hack his weakest finger which ultimately failed) But there are "mental barriers" which can only be overcome (aside from exercising) by keeping cool and sometimes stop trying to come back to it later.

Another example: As a child I always divided the physical world from the living world (the christian heritage?). As such it was for a long time unthinkable that creatures are made from the same stuff as everything else. I recall that accepting this knowledge was really hard...

Regarding the original paper (they've done much research, I can only guess and tell from observation): The humps they observe, couldn't they just be the indication of a clear mental barrier which has to be overcome? Perhaps being taught and some pressure is just not enough to grok these abstract facts about programming? Perhaps, what is needed is just time to (un)consciously chew on the ideas? So, shouldn't be children exposed to 'some programming stuff' as early as possible?

In Germany at least it is left to chance when children become exposed to programming. In most regions there is no teaching at all before a pupil is about 16 years old (11-th grade).

Trying to deduce anything from the success of the consistently correct group is fraught. It sure looks like they have some prior exposure. The interest lies in the consistently incorrect group. Perhaps their success points to the importance of having a consistent model, to be corrected by instruction. Or perhaps the consistently incorrect group all failed. We don't know how many were in this group and if there were very few the aggregation of the correct and incorrect into a single group could completely wash their fate out of the overall statistics.

The argument largely hinges on the truth of this statement and frankly I have my doubts about its veracity. It seems more likely that people that manage to master certain math topics can master any topic, because the amount of extra abstraction introduced levels off.

For me, Discrete Math is something I've never been able to master.

I don't see how that subject introduces a huge new abstraction over the preceding subjects.

I don't see why it wouldn't apply to programming.