3 Thinking and Doing, Not Watching and Listening | Tom LoFaro

Since my promotion to Associate Professor in 2004 I have continued to innovate and grow as a teacher. I have modified techniques and developed new materials for familiar courses.  I have taken on new courses and challenges.  And I have developed new courses both singly and in collaboration with departmental colleagues.  My excellence as a teacher of mathematics does not come just from my mastery of the material, but rather from a continued concern of how best to engage and motivate my students.

Probably the most effective way to engage students is to be enthusiastic about the material.  I believe that I am exceptionally passionate about mathematics at all levels and this comes through in the classroom.

Of course passion is not enough; it must be complemented by preparedness and materials that allow the students to become engaged in the subject matter.  Students have a tendency to use a math textbook as a source of problems and worked examples and do not read the text before coming to class.  In the past we used a web-based program to assign what we called “prep problems.”  This system worked, but it was pretty inflexible because it took a significant amount of time to publish the questions and was cumbersome to adjust when the schedule inevitably varied.  To address these shortcomings, I have gone back to using a written “problem of the day” at the start of many class periods.  I find that this still prompts the students to read the material, but gives me the flexibility to prepare questions that address either the current topic or to review and reinforce previous ideas and techniques that will be needed during that class period.

In our department we try to emphasize that mathematics is best learned by “thinking and doing, not watching and listening.”  As a consequence, we try to mix traditional lecture with in-class problem solving sessions.  I have significantly increased the amount of time I devote to this more active approach, especially in 100 and 200 level courses.  As a consequence, I have also developed a larger repository of worksheets, activities, and projects for these classes.  This is especially true in MCS 118/119 “Calculus with Precalculus Review.”  Barbara Kaiser and I developed this course and we have small group classroom activities most every class period.  We think that this is especially important in a course that is designed for students who are under-prepared for a college level calculus course and are more prone to the anxieties that accompany this background deficiency.  Closely monitored classroom activities provide me with an opportunity to give one-on-one instruction to students who need additional direction and allow me to discover common misconceptions so that they can be addressed to the entire class.

I am also a strong believer in the importance of in-depth projects and have always used them in the applied mathematics courses that are my specialty (MCS 253, 357, 358 and PHY 230).  In this context, a project is much more than a word problem.  It is generally a guided mathematical modeling project that utilizes the mathematical ideas that have been recently covered.  These projects require students to model a physical phenomenon, analyze it mathematically, and then write (and sometimes present) a short report on the project.  In fact, this process is almost the entire content of MCS 358, Mathematical Model Building.   Last year, I began using projects in MCS 122 Calculus II and was very pleased with the outcome.  The students seemed to enjoy the projects and I think that they helped me demonstrate the value of the material and how it might be applied in their future studies and endeavors.

As mentioned previously, Barbara Kaiser and I together proposed and developed the two-semester sequence Calculus with Precalculus Review (MCS 118-119).  The department felt that a having traditional precalculus course (that did not fulfill a general education requirement) and then having these students take MCS 121 (Calculus I) might not be as successful as having an integrated course that focused on calculus but approached precalculus material in a “just in time” manner.  The course is structured so that every major calculus topic is revisited multiple times throughout the two semesters.  For example, when MCS 119 began in the spring semester we started the semester by discussing derivatives and their applications: topics that were first presented in MCS 118.  In this revisit, however, we introduce some applications that we did not discuss in MCS 118.  Derivatives will be discussed two additional times during the semester when we discuss exponential functions and again when we discuss trigonometry.  Moreover, we will review the precalculus concepts necessary to master these materials when we begin these topics.  We believe that this approach allows sufficient time and practice to master calculus concepts and techniques while at the same time reviews important precalculus ideas when they are needed.

In addition to classroom teaching responsibilities I have been active in advising and the direction of Honors Theses.  Honors Theses are not terribly common in the MCS Department and I have directed four of these since coming to Gustavus.  Of particular note is the thesis by Tim Dorn that led to the publication of a joint paper in the journal Genetics.

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