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Two years ago I implemented a basic outline of each class for my students to take notes on for Calculus II at the United States Military Academy. The outline provided students with a shell of the class material for each day of class. Their job was to fill in the shell as we went through the material. The outlines provided students an easy method to organize their own notes exactly how I organized the class. Space was provided to fill in pertinent definitions, label figures, or drawings that I provided, and to work step-by-step examples that I planned to go over in the class. The reason behind this approach was to help the student follow the flow of the class without having to think about what they should write down and what they should not write down. The things I wanted them to write down were on the outlines. Essentially the outlines represented the minimum material each student needed to take away from each class. Further, I chose difficult problems to include in the outline that were not in the text for students to work on their own. After executing this style of teaching for three semesters the following paper discusses my experience implementing this technique. [ABSTRACT FROM AUTHOR]

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and investigations which can be used with their future middle school classes. Their study of calculus gives them a broader understanding of the formulae developed in the investigations. [ABSTRACT FROM AUTHOR]

The reform movement, with its bold and innovative approaches that focus on student-centered learning, has been able to uncover the richness in undergraduate mathematics. The most outstanding pedagogical practices take into account the environment in which learning occurs as well as the background of the student body. Mathematics educators should be aware that what count as the finest practices are institution dependent. This paper reports on three such pedagogical practices, with cooperative learning at their core, that have worked with remarkable success and could be adopted at different institutions. Formatted Interactive Lecture Leaves highlight the need for active learning by creating an interactive learning environment. Student Projects showcase the relevancy of mathematics by making connections to the diverse majors prevalent in our classrooms. The Program for Excellence in Mathematics, based on collaborative learning, challenges motivated students to strive for excellence. Details of these pedagogical practices as well as appropriate evidence of success are presented. [ABSTRACT FROM AUTHOR]