Teaching Philosophy
My approach to teaching stems from two beliefs: the first is that learning is a shared responsibility between student and teacher- both parties have to actively participate in the educational process; and the second is that different students have different mentalities and hence different perceptions of what a teacher has to say. In any field of study it stands true that no matter how lucid a teacher’s explanation is, some students will not grasp the concept forthwith. Mathematics is no different, in fact it is more so.
I see mathematics as a discipline that holds a plethora of problem solving techniques. To optimally use these techniques to understand and see the beauty of the subject, and to actively engage the students in the educational process I believe that traditional teaching methods, a variety of applications, and modern technology should be blended in the classroom. The intermingling of these three approaches gives the student a solid theoretical foundation, a perception of the practical uses of mathematics, and the aid of a powerful tool in mathematical problem solving.
I believe that students should have a solid foundation in theory- embedded within the basic theory is the core understanding of mathematics. A solid understanding of the basic theory facilitates for the student the derivation of solutions from first principles rather than tediously memorizing an array of formulas and rules. Within the theory lies the climactic beauty of mathematics which I attempt to reflect to my students and strive to give them an appreciation of.
I find that exposing the students to the practical applications of the theory at hand makes the theoretical more tangible. During my graduate matriculation I have taken part in various areas of research (Data assimilation, physical oceanography, computational neuroscience, mathematical neuroscience) and I have been exposed to numerous applications and examples of dynamical systems (geometric singular perturbation theory applied to the bursting of neurons, the simple pendulum, synchrony of fireflies and Strogatz’s chapter section on love affairs). In my undergraduate calculus classes we solved problems in, to state a few, physics, chemistry, and optimization. Having had such exposure to applications of mathematics, I am comfortable tailoring examples from different application areas as well as trying to intellectually stimulate the students and arouse their inherent curiosity. For example when talking to students with interest in the medical sciences, an example that I give them is of the ‘BCM’ theory of Bienenstock Cooper and Monroe. The BCM theory describes the synaptic plasticity of the visual cortex, i.e. how the brain learns to see.
As for technology, I believe that it can provide an undeniable means of bridging the gap between the theoretical and applied. Software such as MATLAB can be a robust tool in Calculus, Differential Equations, and Numerical Methods courses to name a few. It can provide solutions to multiple values of a variable in linear algebra which can be tedious to calculate by hand or on a calculator, act as a visual aid to an ordinary differential equation in phase space (such as the simple pendulum), or provide a geometric solution to partial differential equations that have no analytic solution (such as the Navier-Stokes equations).
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