On Jun 29, 2012, at 3:04 AM, Jonathan Crabtree wrote:
> Making arithmetic simpler may reduce the number of children failing math at school.
I think you misunderstand my argument. It is the ability to understand arithmetic just as it is, that is the goal, not just adding numbers. If you simplify arithmetic then you haven't achieved anything with the student, you have only simplified the task for the student. At best, you are in the same place you started. Technically, you can simplify arithmetic altogether by removing it and using calculators. But that really isn't the point of teaching arithmetic and certainly not the point of successfully understanding it.
People tend to confuse the menial tasks in mathematics with the cognitive experience of understanding those menial tasks. When you say "simplify arithmetic" you could mean simplify the menial task of arithmetic or simplify the understanding of arithmetic. I don't think understanding can be simplified like I don't think running a hundred yard race can be simplified. 100 yards is 100 yards. The menial tasks can be simplified but in the case of arithmetic, they have already been simplified over 100's of years and during a long stretch when the menial task of arithmetic was quite important.
The difference between a successful student in arithmetic and an unsuccessful student is not related to the menial tasks. The difference is that the successful student thinks about those tasks while they are doing them and the unsuccessful student does not. After much study, self reflection and thought, I am leaning heavily towards the unfortunate reality that the unsuccessful student is not thinking about the tasks, not by conscious choice, but because they can't. I mean, they actually do try to think about the tasks but they just can't. Whether this is curable or not I have not decided yet. I'll explain my position with a couple of examples.
In sports (which I do fairly well in) one of the most oft used phrases is "Keep your eye on the ball." which is equivalent to "think about what you are doing". It would seem then that when a student is struggling with sports one would only have to remind them to keep their eye on the ball and the rest would follow. Well, I have seen kids try and try and try to "keep their eye on the ball" and still suck. And not just a couple of kids. And even when you break the tasks up into simpler tasks, the problem remains.
In music, namely playing the piano (which I do not do fairly well in), I see the same thing, in myself. Now, I am a pretty decent thinker I think, and you would think that if it is simply a matter of focus, concentration and study, I would tackle the task. Well, I can recite from muscle memory some pieces and even play them with feeling but it is as rote as rote can be. You ask me to reach for a particular chord, by name, and I will be counting keys. After several years of practice my mind is still simply not factoring music properly. I can think, I just can't think about performing music.
I have run the data on all of this a dozen times using every combination of nature vs nurture possible. The only way I can account for all of this is if there is an element that, when it is missing, no amount of nurture will compensate for it. Just telling the student to think or to keep their eye on the ball will not work. Making things simpler neither helps nor hurts, it does nothing, except to the students that possess the required element. And you know right away when the student has the missing element because the reaction changes from one that is endothermic to one that is exothermic.
If there is a cure then he only way we are going to find it is to separate the endothermic students from the exothermic students and see concentrate on the missing element. And this is by subject of course, which complicates things even further. Does every student need to be exothermic in every subject? I hope not, otherwise we are all screwed.