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Constructivism and Guided Discovery
By Norman Labush

Constructivism

Constructivism is a philosophy of learning founded on the premise that, by reflecting on our experiences, we construct our own understanding of the world we live in. Each of us generates our own "rules" and "mental models," which we use to make sense of our experiences. Learning, therefore, is simply the process of adjusting our mental models to accommodate new experiences.

The purpose of learning is for an individual to construct his or her own meaning, not just memorize the "right" answers and regurgitate someone else's meaning.

In order for students to construct their own meaning, they must be allowed to independently discover the concepts and knowledge, and then make this understanding their own. This method of discovery is well suited for mathematics learning.

Guided Discovery

Guided discovery, an approach to instruction and learning, will help students personalize the concepts under study, creating an understanding that cannot be matched using any other method of instruction. The teacher must guide the students toward the discovery. This can be accomplished by providing appropriate materials, a conducive environment, and allotting time for students to discover.

Guided discovery greatly impacts instruction. It is the responsibility of the teacher to 'set' the student up to make the desired discovery. The teacher must provide all the necessary background knowledge to lead the student to the discovery. The student must realize the method(s) to be used to make the discovery. To assure this, the teacher may demonstrate what the students are expected to do. Thus, guided discovery becomes the goal of the lesson.

(from http://www.mylinkstolearning.com/math.htm)