One of my favorite methods of introducing a new topic is to set out a logical sequence of questions and exercises for students to work on at their own pace. They can work together or alone, depending on their preferences. Usually they do this during class time when they can ask individual questions and hear my preliminary introduction and closing summary.
This is one version of "discovery learning," where the student takes an active role in structuring his learning environment, asking questions, and finding answers. Another version, the Moore Method, is particularly suited to mathematics. For more information, see the University of Texas' site on discovery learning and the Moore Method.
I have had the pleasure of teaching a differential equations course in which I did almost no lecturing at all! The initial motivation was an opportunity to meet in a classroom equipped with computers. My previous experience had indicated that it is difficult for students to listen when they have a computer in front of them. So I designed an environment in which students did not have to listen in order to learn. Each day they completed a worksheet in class, then reinforced their discoveries with homework. The course was well-recieved, and a workbook resulted:
A Guided Tour of Differential Equations Using Computer Technology
co-authored with Alexandra Skidmore
published by Prentice Hall (ISBN 0-13-592767-6)
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