Mathematician Siméon Poisson once said "Life is good for only two things, discovering mathematics and teaching mathematics." Over the course of my education, I developed a passion for discovering mathematics. Beginning in high school, I had the fortune of having several teachers who encouraged me to cultivate my passion for mathematics. During my undergraduate and graduate careers, several professors inspired me to continue to discover new methods and ideas within the field of mathematics. This rewarding experience demonstrated for me the important exchange of thoughts and ideas that constitute effecting learning. Reflecting on the critical role that teachers played in my discovery of mathematics, I developed a desire and enthusiasm for the other thing life is good for: teaching mathematics.

My objectives in teaching are two-fold: to help make students aware of the value of mathematics and statistics in their day-to-day lives and for students to leave the class having learned something useful. I believe that when students understand the practical value of course topics, they become more interested in learning new concepts in mathematics. I recognize that many students have developed a dislike for mathematics and, as a result, often fail to see the importance of the subject. To help demonstrate the relevance of mathematics to my students, I often give them problems that relate to real-life scenarios. I find that using applied problems to first introduce new topics gives students a frame of reference that enables them to more readily comprehend the underlying theory. As a means of doing this, I incorporate news stories or issues of general interest to students (such as college life and crime) into motivating examples and applications.

While I make a point to have my courses well laid out, I believe that it is important to maintain flexibility in teaching. I make an effort to be flexible in the pacing of the course in order to allow for more in-depth coverage of some material if necessary.  The classes I have taught have consisted of students with a wide variety of mathematics backgrounds, so leaving some freedom in scheduling can be helpful for some students who may not grasp concepts as quickly as others. I also strive to maintain flexibility in problem solving approaches in my courses. I understand that people think about and understand things differently, and my thought process may not work for some students. Often, I will allow students to work through problems on their own in class and call on individual students to explain their solutions. This allows students to be exposed to different ways of thinking through problems, and allows students to learn from one another.

A primary means I use to gauge success in accomplishing my objectives is student participation in class. I will often introduce topics by having an intuition-building discussion to give students the basic idea of  a new concept. Often, when posing a problem that will require a specific method to solve, I first have students offer initial thoughts about what the answer will be and have them explain their reasoning. I can then use their explanations and thought processes to connect to the intuition behind problem-solving methods. After discussing a topic and working through some related exercises, I often ask students to give me examples related to the topic. In giving examples, students simultaneously demonstrate an understanding of concepts while relating those same concepts to something with which they are familiar (see sample student evaluations).

A second, more rigorous measure of how effectively I have accomplished my objectives is through a comprehensive project. This gives students the opportunity to apply course material to their field of study or an area that interest them. I feel that this assessment tool, as opposed to a traditional written exam, emphasizes the relevance of the material to students’ lives and allows students to demonstrate a broad understanding of the course topics.

I recognize the increasing importance of technology in the classroom and have worked to integrate technology into my courses. Teaching statistics, I utilized JMP software for in-class data analysis and visualization. This was helpful in allowing me to perform in-class demonstrations to help illustrate certain topics and enabled students to gain a better understanding of the process of data analysis. In a College Algebra course I taught, students’ homework and quizzes were to be completed online using MyMathLab. This online medium allowed students to get immediate feedback on their assignments, as well as providing extra explanation of concepts that may not have been immediately clear during class. MyMathLab also had the advantage of providing me with useful data such as how students performed on certain problems and how long it took them to complete assignments. This information was helpful in my decisions to review some topics in the course and ensure students’ thoroughly understood the material.

I believe that teaching is an art that one should constantly work to develop. To this end, I have participated in two Certificate in College Teaching programs, one through the Reinert Center for Teaching Excellence at St. Louis University and the other through the Graduate School at Duke University. Both programs gave me an opportunity to seriously reflect not only on my methods inside the classroom, but also on my philosophy on the importance of teaching mathematics. In the future, I plan to find a faculty mentor and draw from their experience as a valuable resource in my development as a teacher. I plan to be involved in teaching throughout my career and, as such, I know that my methods and philosophy will evolve to enable me to better facilitate the learning of my students.