[snipped] 3. Do you think that differences in accomplishment in school mathematics are due primarily to differences in innate ability, to differences in individual effort, or to differences in opportunity to learn? [snipped]
The differences in accomplishment is school mathematics as in other school subjects is due to a multitude of things - firstly, we have only recently begun to plan for the varied styles of learning that our students bring to us. Since we were generally only teaching to one style of preferred learning, we were basically preventing many students from achieving their potential. Secondly, students come with a multitude of different life experiences, and if teachers do not seek to learn what the students know and what they do not know so that they can teach to the need,the students will probably not learn, because they are missing links, or because the materials is repetitious.
Does innate ability play a part? Perhaps it does, but if so, it is nowhere near as important as we have led people to believe, and may infact ony be related to rate of learning. Differences in opportunity are definitely the most pronounced differences.