Mary is a fourth grade student. She does very well in English and history, but abhors math with a hatred reserved in other circles only for monsters under the bed and little brothers. In addition, she thinks math is stupid, as her teachers merely ask her to solve the same problems over and over again.
The problem here is not that Mary is bad at math, indeed, once she gets to real mathematics, Mary may do quite well. The problem is that the way primary and secondary schools teach mathematics turns it into something which is very difficult for most people to learn.
I argue that the problem most children have with mathematics is that the mathematics they are studying does not use their minds. Primary and secondary school mathematics are generally just lookup activities. Arithmetic is taught as something to memorize, and even working with equations is something to be memorized rather than understood.
Minsky [SOM, 1986] suggests that the memory works in k-lines, in which bits of information from different senses are stored in associational trees. The way most elementary mathematics are taught does not lend itself to the formation of these trees. A k-line will work best when information is reinforced by multiple senses. However, math is taught as a visual exercise; a student looks at a group of numbers and symbols, and generates a new group of numbers and symbols. There is very little verbal or auditory stimulus, as the words taught to the students to describe the manipulations they are doing are limited to allowing them to repeat what the instructor has taught them. Students often lack the vocabulary to discuss things they have thought of on their own.
Evolutionarily speaking, lookup tables are not very useful. One seldom encounters the exact same situation more than once. As such, math problems, especially those encountered in primary and secondary schools are very artificial. Teaching methods not only encourage students to learn by memorization, timed tests often penalize students for trying to solve the problem each time as opposed to memorizing the situation and the method to use for it.
The brain did not evolve to do lookup searches. If math were taught as an associational subject, in which students learned a variety of methods, and studied places to apply these methods, they would probably have less trouble with it, as this sort of learning is better adapted to k-lines.While students currently repeat problems, they usually repeat problems which are, for all intents and purposes, identical, and so do not improve the student's ability to reason about numbers.