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Teaching Philosophy

Most of the students I have taught in my career have been students struggling with mathematics.  These students require a special kind of patience to help them work through the deficits they bring to the study of mathematics.  Sometimes their biggest handicap is just fear.  Perhaps they believe they can't do math, or that it's pointless, but ultimately, I believe these attitudes stem from fear.  My goal as their teacher is to help them overcome theirs fears about math--that it's too hard for them, that they are lacking basic skills that they need to make it easier, that they experience test anxiety or that they will never use the material again.

There fears are best addressed in small, personal classes, but this is not something I typically have control of.  I attempt to address these fears in a number of other ways.  The first is to be as approachable as possible and to eliminate as much sense of intimidation from the situation as I can.  I dress in a manner which is casual intentionally to help them feel at ease, and my classroom style is laid back--they don't need to be constantly reminded who's in charge.  On the rare occasion when one of the students crosses the line, they are reminded where that line is.  In teaching particularly developmental classes, I attempt to strip away as much mathematical "theory" as possible when it doesn't aid in understanding, and leave the students with just the information that will help them comprehend how to use what they are learning and when to use it.  I encourage a strong give-and-take atmosphere, so that students are encouraged to try challenging problems, and to ask questions.  I feel that examples are important, but I prefer to let the students guide their learning process as much as possible.

I also address their fears, particularly of exams, by de-emphasizing exams to whatever extent is possible.  I try to maximize the opportunities for students to make up for disastrous test scores through emphasis on homework problems.  I try to make these assignments as challenging as possible, but since the students can take whatever time they need on them and get help when needed, I believe that these are better representative of their real-world abilities than is an artificial testing situation.  However, homework assignments and other out-of-class work typically represents no more than 20% of their total grade in run-of-the-mill developmental mathematics classes,  Certain courses may justify shifting that when either projects make more sense or classes have students with a stronger mathematical ability.

I take special care to encourage students in all things, to remind them constantly that they CAN do math, and that if there is something they do not understand that they should seek help for it immediately--since math is such a cumulative subject, this is especially crucial.  Students are strongly encouraged--or required--to attend every class, to prevent falling behind.

I attempt to break down my thought processes on particularly hard topics as much as possible.  Not only to help students develop their own problem solving routines, but also to spot key words or phrases--particularly in word problems--that point to the kind of question that is being asked, and how to set up the problem as an equation.  The more clearly I can articulate the way I do it, the better students are at matching their own behaviour to a process that works for them.  Mastering word problems really is the key to being able to apply what is learned in class to life--and thus making it useful to them.

Motivating students to care about the subject can be challenging at times.  Most, I believe, are strongly motivated at the beginning of the term to succeed and do well.  Older students are better able to maintain this sense of motivation when they begin struggling, but my goal always is to help students succeed so that they don't require special encouragement.  Success is its own motivation.

Teaching students that are better prepared and better at the subject, I have learned, requires a different sort of focus.  They want to be challenged as much as possible, and it's extremely important for the instructor to be prepared and one step ahead (or more) of the best students.  These students require less kid-glove treatment, but still I strive for a good, relaxing relationship with the students, and prefer to emphasize challenging homework problems rather than the artificial testing situation.  Here keeping students interested is the real test, rather than keeping them motivated.  In teaching more advanced classes, there is also more emphasis on the theory, and applications in physics and engineering problems.