· Use “common sense” vernacular to explain complicated mathematical statements and theories.
One of the corner stones of my teaching philosophy and one of my best teaching attributes is my ability to explain mathematics in a language that my students have less trouble comprehending. Of course mathematics is a rigorous subject, in which definitions and notation are crucial. As such, I strive to have my students learn (and more importantly really understand) the formalities of the subject by explaining with a language that is more familiar with the student base population. Of course, as most good philosophies are ever changing, I often have to adapt the language to my audience. During lecturers, I try to use the language I feel the majority of the class will understand. During office hours (or private meetings) I can alter the words used to explain the material and tailor the explanation for the individual. As a teacher I try to be very aware of the diversity of my students from learning styles to culture and mold my lectures accordingly.
· Persistence is just as good as Brilliance.
This component of my teaching philosophy comes from a lesson I learned during one of my very first educational experiences. At the beginning of my college career, I started taking classes at Palomar Community College. My first math course was Math 140 - Calculus with Analytic Geometry, in which I scratched, clawed, and fought to earn a ‘B’. Naturally, the next semester, I enrolled in Math 141 – Calculus II with Analytic Geometry, but I quickly found that I was lacking sufficient knowledge of Trigonometry (my algebra skills needed to be honed as well) to continue the course and I was forced to withdraw. I did not let this discourage me however, and I enrolled in Math 135 – Pre-Calculus. With the mindset that I would eventually conquer the Calculus II “mountain”, I worked very diligently (filling in the “holes” in my math education). I then returned to Calculus II and indeed worked very hard to earn a ‘B’. What I learned at that early stage in my mathematical growth was that “Persistence is just as good as Brilliance”. Many of my fellow students at the time had the wonderful gift of “seeing” the solutions to complicated problems that would take me all afternoon to solve, but I would still get the correct solution in time. Many in this field are what I call “naturals”. They have some innate ability or natural talent for mathematics like the genetics of athletes. I, on the other hand, worked very hard for my knowledge. This makes my education and my skills as an instructor even more valuable to me, since I worked so hard for them. As a teacher, I hope to instill this type of diligence in my students. Never give up and take the time to understand the material not just memorize it.
· Mathematics is not a spectator sport (it takes practice).
This saying is a favorite of one of my mentors, Dr. Brooks Reid. Like anything else worth doing, mathematics can only be learned through practice. This practice most frequently comes in the form of homework exercises. I often tell my students, “If you could learn mathematics by simply listening to me lecture, I would get paid a lot more”. Of course, what I mean by that is, even if a student could listen every day to the greatest mathematics lecturer in the world, this would not be sufficient to truly learn the material. While lectures alone are insufficient, they are still a vital part of the learning process. Lectures provide an overview and introduction of the material to be covered. My lecturers are often designed to motivate the “why” behind the material by demonstrating its usefulness in another discipline or as a connective topic leading to higher material. However, learning mathematics takes time and the active learning most frequently occurs, away from the classroom, while doing homework. Most students will struggle with some exercises and will often make mistakes. This is not a bad thing. In fact, this is an essential part of the learning process. Correcting and learning from our mistakes in life and mathematics is how we avoid making them in the future. As such, I encourage my students to take charge and become active learners by attempting all homework exercises. I reassure them that the learning process is not often linear, but to make progress they must make a valiant effort in their work.
· Technology is a mathematical tool (not a crutch).
Very recently I taught two different courses that utilized technology in the classroom (basic algebra and business calculus). By this I mean the technology was a tool for the real learning of mathematics. At the basic algebra level, I used a self-paced program titled “ALEKS” to provide students with a continuous supply of exercises to practice, as well as clear explanations, for each topic that the students were currently working on. This program fit into my teaching philosophy in two major areas. First, the on-line explanations were another way (besides my lecture or office hour explanations) of clarifying the material. Second, the virtually endless sample problems provided my students with plenty of practice so they could become active learners and continue to remain persistent. This does not mean the program was flawless. On the contrary, I found my students did not fully understand the proper way to present solutions especially as it pertained to correct mathematical notation. After collaboration with fellow instructors and the technical support crew working for the ALEKS Corporation, I suggested modifications (hand written solutions as well as computer entered ones for homework, quizzes, and exams) for the upcoming semester that will hopefully alleviate this problem. For the business calculus course, the tool was the Texas Instruments TI-83 graphing calculator. Its ability to draw complicated graphs and find certain irrational roots that were out of the scope of the class, was just one way this tool provided the students with insight and understanding without bogging them down. However, I have in the past instituted a no calculator policy if I felt the students were using the tool as a crutch. In one of my teaching evaluations I read, “You should let us use calculators, not everyone can do fractions without them”. I was shocked (especially since this was a college algebra course) that this student needed to use a calculator for fractions. As such, I believe that the standard for technology in mathematics should be this: a student should be taught to employ a technological device - be it a computer, a calculator, or whatever else - to accomplish tasks only after he or she has demonstrated the ability to perform that same task (albeit far more slowly) without the use of that device. This ensures that the student will learn to rely on his or her own abilities, and will use technology as a tool - not as a crutch.
· Be humble, approachable and respectful
In my life, as in my teaching techniques, I endeavor to always remain simply, a good person. I consider my knowledge a hard earned reward that I am very proud of, but I know enough to know how much I don’t know. I am definitely a life long learner and I remain receptive to learning new mathematics as well as new teaching techniques. As such my student evaluations reflect my high marks in approachability and availability. As the saying goes, “Do unto others as you would have them do unto you”. Respect is a simple thing, but it truly creates a wonderful learning atmosphere. This may sound a bit silly, but my mother raised me right. I address every person (peers and students alike) as sir or madam or by their appropriate title. This simple demonstration is but one way I show my respect, and it has worked well in the past. I have developed great relationships with my students and have had the opportunity to see them progress both in mathematics and in the career. As an example, one of my former students (see David New on reference list), has used his knowledge of mathematics to obtain my old position as a tutor in the Math Learning Center at California State University San Marcos (I am rather proud of him). It is because of these types of lasting relationships fostered in the classroom that allows me to witness the fruits of my labor. In other words, if David and I did not remain in contact, I would not have known of his new job working for my old supervisor.
In conclusion, my comfortable classroom setting, developed from my respect and understating of the student perspective, has allowed me to frequently observe my students grasping concepts at the moment the understanding takes place. This is the best part of teaching and I like to call it seeing the moment of “ah-hah”. The look on a students face when they truly comprehend material that they otherwise found difficult is priceless.
The following two quotes eloquently exemplify a few of my previous points.
"Treat an individual as he is and he will remain as he is. But if you treat him as if he were what he ought to be and could be, he will become what he ought to be and could be." Gauss
"...I am convinced that life is 10% what happens to me and 90% how I react to it. And so it is with you... we are in charge of our attitude." Charles Swindoll