Philosophy of Teaching Statement

Teaching Statement Sofia Ortega Castillo October 2013
I have experienced teaching mathematics to very diverse audiences, teens and adults
alike, budding mathematicians as well as general students, and what I have learnt is
that transmitting the ideas behind mathematics requires approaching the class with a
large bag of teaching tools. Over the years I have sharpened some that have helped me
in my journey of learning to teach, like showing the intuition behind mathematical
theories, keeping the big picture of mathematical ideas developed over the course,
reasoning through finding key words, developing critical thinking by adapting to
new material presentations, correcting and comparing solutions, seeking feedback,
connecting with the audience through enthusiastic and thoughtful problem design,
and in general expanding the insight into the world of mathematics.
I show my students in class that the methods and techniques in mathematics all
reduce to understand simple intuitive ideas, and that knowing and handling them
is only a matter of developing their intuition and trusting it. I accomplish this by
starting new topics with solving a problem intuitively and then developing the theory
behind, like the definitions and the notation. I believe that repeated expositions
of intuitive ideas, through simple pictures, tables, diagrams, graphs, etc., paves the
way to eventually move to solve problems symbolically, with geometric, algebraic or
quantitative approaches.
I plan each class making sure all new concepts are not only well explained, but also
put in a wider context, by showing how such concepts relate to other mathematical
theories besides the one being developed. I pay particular attention to relations
to topics developed previously in the course. For example, after having taught the
fundamentals of logic, I teach set theory by relating the union symbol ∪ to ∨, the
logic symbol or and relating the intersection symbol ∩ to ∧, the logic symbol and.
To keep a global perspective during the course, I summarize the main ideas of the
previous classes, like concepts, methods and results, at the beginning of each class,
and describe intuitively how it relates to the day’s topic.
I frequently upload notes to my class’ website with important points to be covered in
class and statements of the examples to be solved in the classroom. In a nutshell, I
plan my classes well in advance to be able to solve problems in class without notes,
because that enables me to focus on showing how to translate words into mathematical
expressions. I also bring solved notes as a backup and I take a lot of input from the
students to check solutions are making sense for the audience.
When I teach, I aim to cover the material as clearly as possible. With that in mind,
I consistently go over common mistakes in quizzes and exams, to make sure those get
straightened out. I also pay a lot of attention to my pace during class to give enough
time to my students to digest new material and ask related questions. I take care of
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Teaching Statement Sofia Ortega Castillo October 2013
making my students comfortable to ask questions by being very respectful, open and
friendly, and by thanking their participation.
Since I care about my classes being well understood, I also give review lessons, and
change the notation over those to test if the ideas behind are grasped well enough to
handle different presentations of the same material, or otherwise I give more examples.
I seek to develop some critical thinking in my students, therefore my exams usually
include a number of work out problems to test it.
Seeking to meet my students’ needs also outside of the classroom, I publish online all
solutions to exams, quizzes and problems worked in class, so that they may be able
to work them out on their own if necessary, and may be able to compare solutions. I
also make sure to answer all questions in class and through email, and I make myself
available for office hours.
Teaching adequately is challenging, thus I seek feedback from my students on teaching
performance through a mid-semester anonymous survey to adjust my teaching
methods to their needs. I also communicate with fellow teachers to find solutions to
challenges in teaching.
During my undergraduate years, I engaged in weekly sessions of informal instruction
for the Mexican Mathematical Olympiad, teaching students from elementary school
to high school, and with diverse levels of interest in mathematics. What I have learnt,
is that I want my general students to take from my classes a broad understanding and
insight into the mathematics we encounter every day, and I want to provide them with
the knowledge of the tools that help solve such basic math problems. To audiences
of mathematicians, I want to transmit a desire for learning a language of abstract
thinking and an art of abstract problem-solving.
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