Invention
and Investigation in Mathematics
Many students associate
math instruction with being taught a trick to finding the right answer to problems.
I was lost in this trick-wielding arithmetic I learned as a child until later
when I understood how to think critically and reason about the structure of
mathematical systems. In fact, as a high-school student, I often came home from
school wondering why the geometry or calculus methods I was learning in school
worked, and I would methodically reason out and prove them to myself. It wasn’t
until I received college-level coursework that I discovered the intriguing
world of logic and abstract ideas behind the arithmetic we use, and it thrilled
me. While I was working with the Educational Program for Gifted Youth at
Stanford University, I discovered that their curriculum introduced students to
logic and reasoning in the 2nd grade, and I found that what I
suspected was true: math facts and tricks stick better with students when they
better understand the basis for their usage. I enjoyed watching students catch
onto the excitement I have for math at a younger age as well.
Due to my personal
experience in learning and teaching online, I believe students will gain more
from their mathematics instruction with a more investigative approach than the
usual lecture and homework problems. I will rethink the traditional instruction
I’ve received before I pass it on to students in order to ensure that they
learn how to think critically and mathematically about a problem. The key to a
mathematical problem is not the answer but the thinking process that produces
the answer. I must draw on the methods of teachers in other content areas and
then ask myself, “That was a literature course, but how can I apply the same
fervor to mathematics?” “What is it specifically in mathematics that I find
inspiring?” “How do you teach the beauty of abstract reasoning to students?” “How
do I create adeep, investigative learning to motivate their minds?”
A key to teaching
students a new method of understanding mathematics is an open environment, a
place where no question is unwelcome; rather, curiosity is encouraged. Students
are too familiar with fact-regurgitation mathematics in which they are “right “
or “wrong” which stifles many students’ ingenuity. I see my role as a teacher
to retrain students to explore mathematics and help them hone their thinking
skills and creativity so that they can experience the excitement of discovery,
that fabulous “Eureka!” moment of an epiphany when they feel they truly own a
new concept. I will create a motivating classroom environment by introducing
new material with enthusiasm, encouraging students to explore the familiar
material by asking them diverse questions, requiring them to write about their
thinking processes as they work problems, and answering their inquiries by
modeling the sort of openness and investigative spirit I hope to see from them.
I was brought into
teaching because I am myself always hungry to learn more, and I would like to
help my students to continue to grow and explore as they mature through
adolescence. I will exemplify the professionalism (timeliness, respectfulness,
organization and planning, integrity) that students will need to succeed in their
academic, work, and personal life. Throughout my teaching career, I will remain
open to learning and correction and continue to grow professionally. I want to
continue to take courses to remain up-to-date in relevant topics and discoveries
in mathematics and education and to keep myself exploring and creative in my
instructional techniques.
