"Students learn mathematics well only when they construct their own mathematical understanding."

This view of learning, called constructivism, is the premise upon which the reform movement in mathematics education is based. When students learn mathematics by doing mathematics, by exploring and discussing concepts in the context of physical situations, what emerges from these experiences are skills which are anchored in understanding and clarity. The students not only know the basic procedures, but also know how to apply them to new situations. Research supports the fact that students learn best by experiencing mathematics and thereby constructing understanding for themselves. Research also indicates that mathematics education will best serve societal needs when the curriculum is so conceptually focused.

The attitudes students form influence their thinking and performance, and, later, influence their decisions about studying mathematics. Students are active individuals who construct, modify, and integrate ideas by interacting with materials, the world around them, and their peers. Thus, the learning of mathematics must be an active process: exploring, justifying, representing, solving, constructing, discussing, using, investigating, describing, developing, and predicting. These actions require both the physical and mental involvement of students both hands on and minds on.

Such a curriculum has the following characteristics:

• students are actively involved in doing mathematics;
• problem solving, thinking, reasoning, and communicating are everyday activities;
• manipulatives are used to connect conceptual to procedural understanding;
• calculators and computers are used in appropriate ways;
• there is as much emphasis on application as on acquisition of knowledge and skills;
• a broad range of content is addressed; and
• central mathematical concepts are understood.

taken from : www.nheon.org/frameworks/math/learn.php