Teaching Philosophy

In the classroom, I expect students to work toward reaching goals, and I welcome them to come to me for help in attaining those goals. I found that stating clear connections between a current lesson and a previous lesson provides the student with a direction of where the material in the course is headed. Stating the goals for individual lessons informs the student of what is important and what the students should learn, at the minimum. Although goals help indicate important topics and course direction, students will need help. I reassure students that I am there by often asking whether they have questions and by constantly reminding them when I have office hours. Goals are less daunting when there is steady support.

I have objectives for myself and for my students. As a teacher, I am responsible for the education of youth. It is important that I effectively teach my students. I believe students need a little push to do the work themselves. However, I am also willing to try something new if something old isn't working. To maximize a student's learning, I have three main objectives.

1. Give mathematical Yoda answers.

It is important to cultivate confidence. The biggest reason for the disconnect between students and the understanding of mathematics is the lack of confidence in their ability to understand. It is the instructor's job to reassure students that they can practice mathematics, and to provide support when they cannot quickly do so. The confidence level is different when considering non-mathematics students and mathematics student, but I believe the establishment is the same.

To practice this belief, I emphasize the importance of understanding how we get to a result rather than the actual result. If a student learns the road map to the treasure, then they will always be able to reach the "X" without the map right in front of their face. This cultivates autonomy in mathematics as well as critical thinking skills. These traits create confidence. These are also traits that will last throughout a student's mathematical career. I hope these skills will also prepare students to tackle problems in other areas of study and life. Another method I use is what I call "Yoda" answers. It is often better to give answers which provoke thought than to give a straight answer. Even if a student cannot reach the correct answer, this person has struggled with the problem. This yields mental growth.

However, if I expect the student to academically grow, I must be willing to do so myself.

2. Be willing to learn, practice, and evolve my teaching strategy.

Hence, refreshing workshops and new workshops for teaching strategies are events I am more than willing to attend. I have attended several workshops, and I have already tried different methods I have learned. For example, the first time I taught calculus, I used the white board completely, employing a practice I observed. However, the second time I taught the course, I created skeletal notes, a tool suggested in a Learning Styles workshop. Students expressed opinions favoring the skeletal notes. The notes allow students to listen to what I said rather than only write, and there were positive results in scores that followed. Of course, I am aware that not every experiment in teaching strategies will be as positive. You cannot earn positives without first encountering a few negatives.

An area of teaching that I enjoy working on is attention to each learning style. There are eight different styles: active and reflective, sensing and intuitive, visual and verbal, sequential and global. However, mathematics classes can deter students' education if an instructor favors a specific set of learning styles. I've learned that instructors often favor their own learning styles, and this can be harmful to students who do not fall into even one of those styles. While I am fairly balanced in the first three areas, I heavily favor sequential learning, which explains my emphasis on learning the route to the result. However, I try to balance the scale by stating objectives and pointing the students in the direction we want to go.

While growing academically is beneficial to students, they must also be trained to be productive adults as well. While this is not an instructor's direct responsibility, leading by example lends to learning.

3. Failure is nothing to be ashamed of as long as you get back up and try again.

Everyone makes mistakes. Because students may lack confidence, they are afraid to participate in class. They are afraid to display the lack of understanding (or misunderstandings) to others. They must learn that mistakes are okay as long as you learn from them. If I make a mistake on the board and a student catches it, I turn to them and say "Thank you so much for catching that." In this way, I've made the mistake and I show them that I can move on without shame. Of course... instructors are perfect, and these mistakes are intentional. This teaches students that even professionals make mistakes, but they should not be ashamed. In return, when a student comes to me for help, I patiently point out what they misunderstood and I try to explain the thought process they should use.

My experience in graduate education has increased my awareness of what is important for students of mathematics to know. Applied Mathematics is an ever growing field, and there are topics and tools that many undergraduate programs do not cover. I would be willing and excited to teach classes dealing with scientific computing. Matlab and Maple are useful tools students in mathematics (and related areas of study) should be able to use. It is also important for students to understand how methods and algorithms in scientific computing work, not just the fact that they work. I believe that all mathematics students should at least be exposed to these concepts and methods.