Modern civilization is increasingly dependent on technology which rests solidly on a mathematical foundation. We can be consumers of technology without an understanding of this foundation but we can never be its designer. In an increasingly global economy, it is the inventors and designers of technology who will command the highest standards of living. It is quite conceivable that we face a global role reversal between "third world" and "first world" countries. The quality of mathematics education is a major determinative factor in how this plays out.
Improvement in this area continues to be hampered in the U.S. by our industrialized approach to education, which leads us to commit two serious errors which leave many, if not most, of our children without a genuine appreciation of mathematics. The first is that we teach mathematical algorithms as a substitute for true understanding of concepts. This is in fact partially caused by the second error, which is that we rush our children through the process of education. Math is an abstract pursuit which many children find themselves unable to satisfactorily process until they mature well beyond what we think of as appropriate. This process produces graduates who hate math because they are functionally innumerate.
The goal of elementary mathematics should be numeracy: the corollary of literacy. Merriam Webster defines it as the capacity for quantitative thought and expression. However, true numeracy is developed constructively in the minds of students via concrete constructions and modeling, which requires huge chunks of time. Also, numeracy is accomplished at widely differing times for children, which runs counter to our basic model for education. We don't seem to have the patience for it.
Complete systemic reform is required if we are to meet this challenge and time is not our friend.
