If we accept the centrality of Concept-Rich Instruction as highlighted in the national standard (National Council of Teachers of Mathematics [NCTM], 1989), then it is important that we develop facility in delivering that instruction. Whether we follow the most prevalent theory and research in cognitive psychology today or examine the current research emanating from mathematics educators, we will learn that teachers must play a key role in developing students' concepts and their ability to apply these concepts.
The constructivist theory that springs from Immanuel Kant's teaching tells us that the mind is an active organ and postulates that it is the teacher's responsibility to organize experiences into concepts that determine subsequent learning. Research in the field of mathematics education indicates that the teacher indeed plays a key role in meaningful learning of concepts. Without the teacher's mediation, most students do not understand the fundamental concepts, cannot make connections among the different strands within mathematics, and cannot transfer what they know beyond very particular problem situations they practiced in the classroom. Good teaching capitalizes upon the learning of core concepts. Therefore, it is important that we examine what theory and research say about the “best practices” for helping students develop new mathematical concepts.