I want to offer a few clarifying points: We homeschool. My son likes math but does not like the 'busy work' associated. Mom was wondering if my son just didn't get long division, ratios, and fractions. I was thinking that if he can program js, awk, lua, and objective-c then he can do anything that arithmetic might demand of him.
In other words I intuited a character issue not a cognition issue and wanted other opinions.
Also, I really do understand that programming cannot strictly be equated with math. I purposefully used the word analogy because they are not 'fungible' things. In fact the term analogy connotes that I understand that there is a resemblance in some particulars between things that are otherwise unlike.
I posit that the resemblance is effort of cognition (though, of course, some might disagree that there is even that point of connection).
Another common misunderstanding was that I was asking how much math does my son need to know/learn to be a programmer (or otherwise). We will explore the very limits of his education (sane, practical, healthy limits); that's the whole point of us homeschooling him. Once he hits mom's limit in any given realm we will out source. I hope his current love of math/science/writing will know no parental impediment.
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.
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.
I want to offer a few clarifying points: We homeschool. My son likes math but does not like the 'busy work' associated. Mom was wondering if my son just didn't get long division, ratios, and fractions. I was thinking that if he can program js, awk, lua, and objective-c then he can do anything that arithmetic might demand of him.
In other words I intuited a character issue not a cognition issue and wanted other opinions.
Also, I really do understand that programming cannot strictly be equated with math. I purposefully used the word analogy because they are not 'fungible' things. In fact the term analogy connotes that I understand that there is a resemblance in some particulars between things that are otherwise unlike.
I posit that the resemblance is effort of cognition (though, of course, some might disagree that there is even that point of connection).
Another common misunderstanding was that I was asking how much math does my son need to know/learn to be a programmer (or otherwise). We will explore the very limits of his education (sane, practical, healthy limits); that's the whole point of us homeschooling him. Once he hits mom's limit in any given realm we will out source. I hope his current love of math/science/writing will know no parental impediment.