T EACHING S TATEMENT
TATCHAI T ITICHETRAKUN
What is our expectation to students after they have completed a mathematics course? Someone
may say that we want them to acquire knowledge and skills listed in the syllabus. This is already
hard to accomplish even if we delivered the best lesson to students. Teaching is a multidimensional
task. I believe that a good math teacher should be a person who does some math (at some level),
who has good reasons of doing it, who has experience and enthusiasm to share. On the other hand,
a teacher should understand the students as well as the subject. What kind of things could students
perceive? How should we talk to them? Teachers have to show that mathematics is something
that worth doing. Students need motivation to be engaged in the course. The only way one can
learn mathematics is to think actively then roll up sleeves a little and does it by oneself. Students
also need leadership and support from teachers to go through their challenging missions. Today,
mathematics and quantitative skill are indeed important in many professionals and everyday life.
Mathematics is a subject of absolute truth. We deduce results from given set of axioms by pure
logical reasoning. This could sound a bit dry at first, but mathematics is a way we describe the
nature which is beautiful and sometimes unimaginable. Mathematics is then an art. Mathematics
is like a mysterious language that ideas and imaginations are hidden in the equations. It would be
exciting for the novices if they could decipher this language. Students in the first year may have
to encounter some abstract terrifying concepts and notations in their very first time. These abstract
things actually originate from endeavors to explain everyday life phenomena around us. From this,
I would digest difficult concepts, emphasize to students important messages that this concept is
trying to say. I link abstract concepts to students’ experiences and intuitions. Go to informal discussion before the rigorous statement. From this, students will be easier to be engaged, participate
and think actively about the class material. Indeed, this does not mean that I make it agree with
students’ intuitions and oftentimes it is going to contradict them. I teach them the importance of
logical reasoning, why it is important to be cautious and rigorous? How to check fallacy and not
to rely on intuition. Mathematics is a pair of glasses to see the world.
Mathematics is studied by human, it’s a human story. It’s also a cultural heritage received from
our ancestors. We still study geometry textbooks written by Euclid 2000 years ago. I like to put
history anecdotes in a lesson because, as human beings, students will see more lives in math. Why
did Newton invent Calculus? What was he thinking about ? What were common beliefs and how
people thought at that time? How were they different from ours? Mathematics indeed appeared
in many cultural activities. Origami paper folding that are not only used as a cultural activity and
hobby but also has real applications in real life from map folding to industrial applications (folding
products to take less space) or even in heart surgery. So it’s not just a history but it’s also about the
future. How we used linear algebra to design Google algorithm that we use everyday. I try to link
math with students’ lives.
I want my students to have a feeling of accomplishment even on very small things. These small
feelings will eventually lead to acceptance of mathematics. I give motivations to students to work.
They may get lost, get frustrated but engaged enough to struggle diligently until they got it. Aha
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moment, that we cry out loud, the moment that we can feel the ideas we learn synchronizing in
harmony with our thoughts or experiences and we won’t forget it. It takes time to learn new things.
I value on patience and struggling more than speed as it is much more rewarding. Mistakes are
inevitable, we have to know how to accept and learn from them. It is the only way to learn and
students will have to face this. Thus from learning math, students will learn many other working
skills as well. Teachers have to constantly give appropriate supports and feedbacks to students.
Mathematics, when come to the right viewpoint, is not messy and should be as simple as possible
(this does not mean it is easy). It is a good lesson to teach students how to see things from the right
viewpoints. Solving mathematical problems is not about doing grammar, it is a story. Students
should not learn by remembering rules or methods or only following somebody’s ideas. Instead,
it should be a playground that we can play with ideas. Why would we define the derivative like
this? What happen if I change? Sometimes let them play with the ideas then guide them to the correct path, sometimes just let them struggle not expecting the answers. In short, math should be fun!
I emphasize students to talk with each other, present ideas to friends or teachers. From my
experience, beginning undergraduate students usually lack these skills (also they are too shy).
Sometimes even if they know how to solve a problem, they don’t know how to present or write
logically. I would still prefer a few written homework complementary to WeBWorK homework.
Practicing these skills will not only be useful for their future lives but one of the best ways to learn
the materials is to be able to convey their understandings to the others, like lighting other’s candles
from his or her own’s. Although a large lecture room may not be an ideal place to do such activities
(also due to time constraints), we can modify our lecture style or class activities to emphasize this,
making students realize its importance. If they have smaller group activities like workshops or labs
then this will be the opportunity to practice.
Students need leadership from a teacher. Leadership in a teacher that motivate students to do
things that they would not manage to do by themselves. I teach them how to leave one’s comfort
zone, overcome fear, laziness, weakness or fear of failures, step out to the stage. One of the most
important thing as a teacher is that I should be able to convey a message to my student that I do
really care of them. I make myself and the class atmosphere open. I link myself to students. I also
make them realize that I believe in their potential. I push students’ curiosity button and encouraged
them to ask questions, explain their own thoughts. They know that I am not perfect and oftentimes
I learn new ideas or viewpoints from these intelligent novice students. I show them as an example.
I also emphasize on life skills, priority setting, time managing, responsibility when living or working with others (and also the responsibility to one’s own study) and how to deal with unexpected
problems, how to accept one’s faults and accept different ideas from others, without losing selfesteem, how to ask for help, how to manage bad feelings. In summary, how to be professional.
Teaching is a dynamic activity, students from each year will be different and I always have to
learn and adjust my teaching. New ideas always come in. Go back to the question; what do we
want our students to gain after they finish math courses? For my answer, I want my students to
be a math learner. This means a person who realizes mathematics as a beautiful discipline that is
relevant to human society. They would know where and how to look for something in math that
may be useful or necessary in their professionals or their lives.
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