Some Suggestions for A Good Learning Experience:

  1. People learn best by doing and then reflecting on what they did. This is not a new observation, but can be found in the works of Papert, Piaget, Dewey, Montessori, and countless others. Notice that this is a two-fold statement. Doing is important, but the following reflection is critical. Reflecting is important, but having a basis of experience upon which to reflect is critical as well.
  2. Activities over Explanations. When preparing to teaching some non-trivial piece of mathematics, it is more important for mathematics teachers to think up some good activities rather than just good explanations.
  3. The Principle of Effective Minimal Help. A good rule of thumb when interacting with students as they have questions is that most of the talking should be done by the student and not by the teacher.
  4. The Principle of Successive Refinements. Complex concepts are not learned in one shot, but rather are learned through a sequence of successive refinements.
  5. Computer programming activities which treat functions as first class data types can help students construct appropriate understandings of advanced mathematical concepts.
  6. Reflection is an ultra important part of both learning and knowing, and is significantly enhanced in a social context.
-- Uri Leron of Technion