Joseph P. Previte

My teaching style is based on the premise that students learn mathematics by doing mathematics. To master a topic, students need to supplement the lecture by working problems. After introducing new material, I allow class time for students to work sample problems. This ensures that each student leaves class with a working knowledge of the topic, and is prepared for the homework assignment.

In 1994, the mathematics department initiated a pilot program called ``Close-Contact Calculus'' where the traditional lecture-style recitations were replaced with sessions that consisted entirely of students working in groups on worksheets. As a teaching assistant for Close-Contact Calculus, I was encouraged by the success of the program. The classroom environment was less rigid, students learned from one another, and I was able to give more attention to those who needed it. As the instructor for the

course, Mathematics for Elementary Education Majors II, I used the methods I had learned in Close-Contact Calculus by augmenting the lecture with class time spent in a group-oriented workshop setting. Later, I was given the opportunity to teach an experimental section of the course, Elementary Mathematical Models. There I combined a concise lecture with in-class group work and regular homework assignments. Student enthusiasm, performance, and final grades far exceeded those in any course that I had previously taught.

Although these teaching methods were successful for me in three different courses, I feel that traditional lecture methods are probably more appropriate in a higher level mathematics course. In such courses, students are more motivated and better able to think abstractly. However, no matter the level of the course, the regular collection and grading of homework is crucial. The material in a mathematics course is cumulative, so a student who falls behind is immediately at a great disadvantage. Regularly graded homework assignments keep students from falling behind, give immediate feedback, and show the instructor where common errors arise so that they may be addressed.

Occasionally, courses should be reviewed and restructured, if necessary. I served on the textbook and curriculum committees for the course, Elementary Mathematical Models. The curriculum committee decided to consolidate the syllabus into an in-depth study of four main topics. The textbook committee found a book which covered three of the four topics. A fellow graduate student and I created a text supplement for the fourth topic, data analysis. The text was designed to accomodate instructors who use either a group workshop setting or traditional lecture methods. I was asked to teach the pilot section of the course. Seeing that the course went extremely well, the mathematics department decided to use the text and accompanying materials in all sections of Elementary Mathematical Models at the University of Maryland.

Technological tools such as Maple, Mathematica, and graphing calculators are powerful tools in the classroom. Using Mathematica in the course, Differential Equations at the University of Maryland, computational techniques are paired with deep qualitative concepts. As a Mathematica teaching assistant for this course, I found it commonplace for my students to further experiment with Mathematica and ask probing analytical questions, long after their assignments were completed. The graphing calculator made the data analysis section of the course, Elementary Mathematical Models, much more enjoyable by allowing for the analysis of real data sets which would have been impractical to analyze by hand.