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My TEACHING PHILOSOPHY

I believe that teaching mathematics well requires a good understanding of how students learn mathematics. When I first started instructing students I was under the impression that if you just told students the “rules” of math, then they would understand. In the beginning, I would spend my lectures with my back to the students writing on the board. In contrast, my experiences in graduate school at the University made me realize that teaching, as well as learning, is not a passive activity. As a teacher, I must constantly observe the student in order to be aware of their presuppositions and state of understanding. One of the first things I realized while teaching was that students come to the first day of class with different levels of knowledge and backgrounds. Because of this, I dedicate one class within the first week to a problem session over the necessary presupposed material. For example, while teaching a calculus I course,  I gave students problems dealing with factoring and manipulating expressions. During these sessions, the student is encouraged to talk to their neighbor as well as to me as I am walking around the room. This time of discussion with the students helps me understand what they know mathematically while at the same time creating a welcoming environment in the classroom. For the majority of students, the lecture is the first time they are introduced to a mathematical concept. Because of this, every talk should be well thought out and organized with precise board work. Working for many years has helped me hone my organizational skills; being underprepared in classroom is not an enjoyable experience. For example, in order to keep the middle students’ attention I would quickly address the main concept by asking the students questions. I implement similar techniques in my classrooms. I believe students of all ages respond well to directed questions overlaid with exposition. , the questions direct the students attention to the main concept of the exposition. It is my goal in every class to use these types of techniques to deliver a well organize message to the students. The use of technology can be very helpful in presenting the material as well. . I have noticed the students become engaged; not just with me, but with the ideas that are being discussed. This environment is great for learning and overall growth of the student. Examples are fundamental in both teaching and research for illustrating the concept of abstract ideas. Mathematics is a precise language used to articulate these ideas; therefore, in teaching one should use precise language. However, the information must be displayed to the student in an accessible way. Examples help find the common ground between precision and analogy; between using the exacting language of mathematics and communicating this language with students. I believe that examples are pivotal in helping the student understand the material. During lecture I prefer to take my time and talk through important examples; this gives the student plenty of time to think about the concept as well as time to formulate a question. Discussions centered around good examples help the student process the information. While I enjoy lecturing over mathematical material, I welcome class discussions as well. This type of exchange is beneficial to the student as the class conversation is guided with their own questions. My primary goal is to actively participate in the students learning and to help establish a firm foundation of the basics from which more complex ideas may be explored, providing a solid purpose for learning, and allowing for open discussion and discovery, all of which are important elements for student success.