Poll: What level of math is programming roughly analogous to?

In my opinion programming doesn't have very much to do with math, sure both are problem solving, but they aren't related at all. You can be good at one and suck at another.

undoubtedly programming is more engaging to work on than solving arithmetic problems in long division.

there is relatively little utility in learning arithmetic by rote and its not surprising that your son doesn't want to do it. however, as I'm sure you know, rote arithmetic problems are present on state exams and your son will need to be able to do it in order for his home schooling (which is great, congratulations to you) to be officially recognized.

there's a certain point at which the learning process stops being about gaining knowledge and skills, and starts becoming more about learning how to conform to institutional requirements. this sucks. it sucks real bad. you already know this though, which is probably one of the reasons why you chose to home school. unfortunately sucking it up and learning how to play ball with the institutions of our society is actually a really important thing, painful and boring as it is. long division by rote is some kind of proxy for this. better get started with building up your son's tolerance for annoying shit.

Mmm.

Could we say that programming is: part codified reasoning, part automation, part creative practice, part figuring out how computers and networks work, part figuring out how your toolkit works, part figuring out how the platform your coding against works?

I guess that it is only mathsy insofar as the problem domain is mathsy.

I see a whole wave of non-sciencey people learning how to code in the near future. These people are not very math-oriented.

Bog-standard CRUD? If we're just talking that, then I'd say it's symbol manipulation, potentially with some basic transformations thrown in. I'd put it on the level of algebra.

Depending on what he's actually doing with that data, though, the level may change. Got links?

Can I offer this unsolicited advice?

Don't knock rote mathematics. 'Busy Work' in most other fields is called 'practice'. And like all things, practice is the key to improving a skill. Repetition, memorization and muscle memory are all key fundamentals.

If your son wants to be a quarterback, you practice throwing a football. Over and over again with slight variations to the angle, distance and speed. A meaningless procession of skill building that builds the muscle memory and "know how" required to be successful at the more complex task of managing a game and leading an offence, which is what a quarterback really does. You can't be good at throwing to a receiver on a button hook or on a screen play if you are still mastering how to manipulate the speed and position of the ball as it leaves your hand.

We would laugh in the face of anyone that suggests otherwise.

Your brain is no different. It needs practice in the basics before it can progress to more advanced topics. You need to spell before you can write a story, and you need to know addition and multiplication before you can perform calculus. The basics for math need to be implanted in your brain for immediate retrieval, so that your processing power can focus on the higher level task.

It's not enough just to know that "there" can be spelled three different ways. To be a good writer, you need to know instantly which one to use when, otherwise you just simply aren't very efficient. Likewise, a person needs to know instantly that 8 and 64 have a distinct factor/product relationship to be able to understand that a rectangular floor with an 8 foot length, 3 foot width and total area of 64 square feet cannot possibly exist and has been measured incorrectly before you proceed to buy all that carpet.

The most skilled in any field have the greatest mastery of the basics. Mathematics is no exception.