A university calculus course taught in an interactive laboratory format

At New Mexico State University, Las Cruces, NM USA, we are offering a mathematics course in calculus for prospective and practicing teachers which is taught in an interactive laboratory format. Students, working in groups, design and construct physical objects, where the planning stage requires using calculus techniques. For example, students are given a golf ball and poster board, and the task is to design and build a cone that the ball just fits into, with the cone having the smallest volume possible. Lectures are very brief or non-existent. There is no textbook assigned, but students get extensive handouts that contain detailed lesson plans, which can be used in high school classrooms. The material is organized into units built around tasks such as the one above, and not around mathematical topics. So one unit may require some knowledge of trigonometry, basic geometric theorems, and both derivatives and integrals (for example, in computing the length of a curve). Graphing calculators are used extensively. A typical unit takes from ½ to three classroom periods in high school. Because the calculus concepts are used in a large variety of concrete situations, the concepts are introduced in a more abstract way than in other calculus courses, in order to avoid misconceptions such as, “An integral is (always) the area under a curve.” This approach covers some mathematical topics in minute detail in a variety of contexts (for example, the meaning and uses of integrals), and it completely omits others (for example, the Mean Value Theorem). After teaching the course for the fourth time in 2008, we plan to make the materials available on our website, http://www.math.nmsu.edu/~breakingaway/. The poster will present a selection of units; it will briefly summarize how the main concepts are introduced, and which parts are most difficult for students. It will also describe how student work is assessed and will give a small selection of students’ comments from anonymous questionnaires they filled out about the course.

This poster is in alighment with TSG 17.