ABSTRACT
This paper explores aspects of mathematical “understanding” that extend beyond the mastery of routine facts and procedures. It deals with three aspects of such understanding, summarized in the following three assertions:
Metacognitive skills and a “mathematical epistemology” are essential components of competent mathematical performance.
Most students do not develop very many metacognitive skills or a mathematical epistemology to any degree, largely because mathematical instruction focuses almost exclusively on mastery of facts and procedures rather than “understanding”; these are basic causes of students’ mathematical difficulties.
It is possible, although difficult, to develop such skills in students.
