Teaching the Structures of Mathematics
DOI link for Teaching the Structures of Mathematics
Teaching the Structures of Mathematics book
In this chapter, we look at the beginnings of this period of widespread interest in conceptual approaches to mathematics teaching. Our focus is on the shared interest of mathematicians, psychologists, and educators in extending the range of topics covered in school mathematics and in developing new teaching methods to make mathematics learning "meaningful." Researchers and curriculum developers oriented toward conceptual approaches seem to agree on the importance
of fostering in children a strong intuitive understanding of the underlying structures of mathematics. We look at several converging lines of thought suggesting that an understanding of mathematical structures is fundamental to meaningful learning. We also describe some structure-oriented teaching methods and materials designed to promote meaningful concept development. We discuss a developmental theory of thinking that suggests how teaching can respond to children's capacity to build mental representations of the subject matter, and present instructional principles developed by a mathematician/educator who used concrete materials to teach mathematical structures to young children. Finally, we pose a number of questions that the structure-oriented approach raises for a psychology of mathematics.