ABSTRACT
For about two decades beginning in the late 1950s, conceptual approaches to mathematics education made increasing inroads on traditional computational approaches. Special projects 1 were launched both in the United States and internationally for the express purpose of determining how best to teach children the basic concepts and principles that give coherence to the subject matter of mathematics (i.e., the structures of mathematics). The mathematics curriculum was expanded; in schools, young children were exposed to relatively “advanced” concepts like inequalities, the properties of sets, the use of zero as a number, and the principles underlying decimal notation. Educators grappled with the problem of upgrading teacher training to handle the increased demand for expertise in mathematics ( Goals for Mathematical Education, 1967). New materials appeared, and some old ones were rediscovered, that were especially designed for teaching the mathematical structures underlying computational procedures. Meanwhile, psychological research sought to explain how children come to understand and use complex mathematical concepts.
