<p>Basic math facts and algebra. </p>
<p>When people talk about basic math facts, they usually mean arithmetics: addition, subtraction, multiplication and division. Even at that level, according to Liping Ma, American teachers are not good at explaining; they fall back on teaching the procedure but cannot explain why students should follow it. And too often, they get it wrong.
Many students can be good at arithmetics simply by memorizing.<br>
Algebra, however, requires different skills. This is why it is such a threshhold and why there is such a debate as to whether it should be introduced in 8th grade. Many American teachers argue that most 8th graders do not have the maturity to learn algebra, even though this argument flies in the fact of foreign countries’ experiences.
But for students to be good at algebra, they have to be good at fractions–something that American teachers are often terrible at explaining, again according to Liping Ma.
I also think that to be good at upper-level math, a student has to be good at logic.
I have seen students who were terrific at advanced math but could be stumped by simple arithmetic calculations. I have also seen students who knew their math facts cold but did not do well in algebra and beyond.
Obviously, knowing one’s math facts is crucial. As in the Whole Language debate, a good math teacher will combine the teaching of math facts with a more discovery-based approach. When my S was taking math enrichment classes, I loved seeing the way young kids lit up with a “Aha” grin when they found the solution to the problem posed by the teacher. His basic role was to pose the problem and to keep the discussion from straying too far afield.
I also remember the look of pure panic on my S’s regular teacher when my S came up with a different way of solving a problem. Hers was straight from the textbook"s teacher’s manual; she had memorized the solution, but I do not know whether she truly understood it.</p>