How science and mathematics should be taught is much more than a question of what a teacher should he doing in class. What students learn is fundamentally connected with how they learn. [10] According to the Curriculum and Evaluation Standards for School Mathematics of the National Council of Teachers of Mathematics (1989)

Serious mathematical thinking takes time as well as intellectual courage. A learning environment that supports problem solving must allow students time to puzzle, to be stuck, to try alternatives and to confer with one another . . . Students' learning of mathematics is enhanced in a learning environment that is built as a community of people collaborating to make sense of mathematical ideas. [11]

All of the recent national efforts to redefine priorities in science and mathematics education have common elements. They reflect similar views on how individuals learn. They focus on what happens in effective classrooms and what makes these classrooms effective. In order to describe settings that enable people to learn, the Learning Framework will first describe how students learn, and then focus on four aspects of teaching:

• The kinds of tasks in which students are engaged,
• the kinds of discourse present in classrooms,
• the environment for learning, and
• the analysis of instruction - keeping track of progress in achieving mathematical and scientific literacy. [12]

HOW DO PEOPLE LEARN NEW IDEAS?

Students come to school with varying experiences with, ideas about, and explanations of the natural world. The scope of these ideas are as diverse as the students' backgrounds and they are often different from those of scientists and mathematicians. For example, most sixth graders believe that a heavy metal ball will fall to the ground faster than a light wooden one of the same size.

These ideas have grown over a long period of time, supported by observations that paper (light) falls more slowly than a rock (heavy). However, these ideas may be contradicted by scientific observations about falling objects. Students will have to become dissatisfied with their old idea and abandon it before they can construct the new idea that gravity accelerates all objects at the same rate and that their experience with the rock and paper demonstrates something else. Students can't learn by adding new information to old misconceptions. They have to change their conceptions.

While the process varies from individual to individual, changing a conception involves a series of occurrences:

1. Students become dissatisfied with their existing conception. Therefore, teachers must know what misconceptions are likely and create an environment in which the students become aware of the misconceptions and have a need for new conceptions. In this environment, students must consider and talk about what they think, and teachers must listen in order to hear the students' conceptions.

2. Students achieve a minimal understanding of the new scientific or mathematical conception.

3. The new conception appears plausible to students.

4. Students see the new conception as fruitful and useful to understanding in a variety of settings.

Teaching procedures that build on students constructing their own under standing include:

• Seeking out and using student questions and ideas to guide lessons and whole instructional units.

• Accepting and encouraging student initiation of ideas.

• Promoting student leadership, collaboration, location of information, and taking actions as a result of the learning process.

• Using student thinking, experiences, and interests to drive lessons (this means frequently altering teachers' plans).

• Encouraging the use of alternative sources of information both from written materials and from experts.

• Using open-ended questions and encouraging students to elaborate on their questions and their responses.

• Encouraging students to suggest causes for events and situations, and encouraging them to predict consequences.

• Encouraging students to test their own ideas, i.e., answering their own questions, their own guesses as to causes, and their own predictions of certain consequences.

• Seeking out student ideas before presenting teacher ideas or before studying ideas from textbooks or other sources.

• Encouraging students to challenge each other's conceptualizations and ideas.

• Using cooperative learning strategies that emphasize collaboration, respect individuality, and use division-of-labor tactics.

• Encouraging adequate time for reflection and analysis; respecting and using all ideas that students generate.

• Encouraging self-analysis, collection of real evidence to support ideas, and reformulation of ideas in light of new experiences and evidence. (Yager, 1991). [13]

Understanding learning affects what happens in teaching. Understanding learning also helps us understand the process by which adults change their conceptions and it helps us realize why change is so difficult.