Effective teachers are those who can stimulate students to learn mathematics. Unfortunately, many educators are focusing on alterations in content rather than the reports' recommendations for fundamental changes in instructional practices. Many of these instructional changes can best be understood from a constructivist perspective. Although references to constructivist approaches are pervasive, practical descriptions of such approaches have not been readily accessible. Most traditional mathematics instruction and curricula are based on the transmission, or absorption, view of teaching and learning.
Teaching consists of transmitting sets of established facts, skills, and concepts to students.
Constructivism offers a sharp contrast to this view. Knowledge is actively created or invented by the child, not passively received from the environment. It is a relation that the child superimposes on a set of objects. This relation is constructed by the child by reflecting on actions performed on numerous sets of objects, such as contrasting the counting of sets having four units with the counting of sets having three and five units. Rather they invent new ways of thinking about the world.