1. ACTIVE INVOLVEMENT
The more students are actively engaged with their own learning, the more they learn. Students learn better when they are presented with problems that interest them and when they are provided the support and encouragement to discover relevant knowledge and strategies for solving those problems. Well designed group activities require students to develop problem solving strategies, articulate their mathematical ideas in words and in writing and to argue with peers about which strategies to employ.
2. CONFRONTING MISCONCEPTIONS
New ideas and knowledge are largely constructed out of existing ideas. If the existing ideas contain misconceptions, chances are the new knowledge too will be flawed. For this reason students should be urged to consciously identify and confront their own misconceptions. Learning activities should be designed to help identify and correct these misconceptions. For example, students could be asked to make predictions and to compare these to the actual results. By consciously addressing the difference between prediction and reality the learner would have the opportunity to make necessary adjustments to their accumulated understanding.
3. MULTIPLE REPRESENTATIONS
Learning is enhanced when mathematical ideas are presented with a mixture of representations. These include analytic, numerical, graphical, verbal, and written. Well designed activities both convey mathematical information and ask the student to respond in multiple modes.
Student learning is improved when students are required to express ideas and get timely feedback on them. Well designed activities allow students the opportunity to reflect on the critiques they receive, make adjustments, and try again.
5. APPROPRIATE USE OF TECHNOLOGY
Calculators and computers should be used to help students visualize and explore data and relationships, not just to follow algorithms to predetermined ends. Well designed activities with technology help students learn by providing a tool to explore different ways to represent the same information.
Theodore J. Marchese, 2002 . The New Conversations About Learning: Insights From Neuroscience and Anthropology, Cognitive Science and Workplace Studies
David L. Potter, 1998 . Powerful Partnerships: A Shared Responsibility for Learning
NRC, 2000 . How People Learn: Brain, Mind, Experience, and School