On Teaching
Interacting with students is my favorite part of being in
academia.
My thoughts as I walk around campus often drift to ways in which
I could explain a concept more clearly or make a lesson come alive.
My goal as a teacher is to keep students engaged, thinking and
communicating so that they obtain a solid understanding of the
mathematics. The best days are when all the students interact
with
me and with each other, as they discover ideas and take questions
to the next level.
My enthusiasm for teaching comes through in my classroom style. I
keep lectures interactive by asking frequent questions. I use
pictures, models, silly examples (a smiley face is my favorite group
element) and stories to keep things interesting. To get everyone
involved I sometimes ask the class to vote on the answer to a question
I've posed. This requires them to all consider the question and
commit
to an answer. My students can tell that I care about their
success and
this encourages them to take risks and ask questions in and out of
class.
Students often present homework problems on the board
at the
beginning of class. These presentations serve as springboards for
discussions of methods and pitfalls.
To change the pace and check the students' understanding I stop the
lecture part way through and present a problem for the students to
work at their desks, and discuss with their neighbor. This break
gives students an opportunity to reflect on the material, try their
hand at a problem and ask questions they might not otherwise have
thought to ask. By walking around the room I can check on their
progress and address individual stumbling blocks. Furthermore,
they approach their homework with more confidence having solved
similar problems on their own. I am especially excited during
these
problem breaks to hear my students discuss their ideas with one
another.
Together they are more likely to find creative solutions. In
addition,
explaining concepts to others deepens one's own understanding.
Because of these mutual benefits I encourage students to work together
in class and on homework. At times my optional, weekly group-
homework session for a proof writing course saw 3/4 of the class in
attendance.
While teaching a graph theory mini-course to elementary students I
saw how hands-on activities can make sophisticated mathematics more
immediate and concrete. To take advantage of this, I use
discovery-
oriented group activities in my classes. For example in an
introductory
statistics course students captured a sample of fish from a goldfish
cracker pond, tagged and replaced them (with pretzel goldfish) and
recaptured a sample to estimate the population of the pond. In my
``geometry for teachers'' course, students drew triangles on tennis
balls and made conjectures about the properties of straight lines and
triangles on spheres. Since it is especially important for future
teachers
to communicate clearly, students explore the ``whys'' of mathematics
through writing assignments as a follow-up to group activities. I
have
also had the opportunity to teach using graphing calculators and
computer
labs (Maple and Data Desk). The technology offers students
another way
to visualize mathematics. By using the zoom on a graphing
calculator
students can work with the epsilon-delta definition of a limit, and get
a
feel for linear approximations and derivatives. In addition,
computer
simulations and sampling of real data sets make statistical analysis
relevant.
At the end of the week I incorporate something lighter into my
lessons.
With my finite math class this was in the form of logic puzzles (which
often required the students to cleverly save mathematicians from
cannibals).
In the geometry course each student gave a mini demonstration of a math
teaching tip or technique that they especially enjoyed. During
one class
I even assigned each row a note and together we performed a song (some
of my songs actually involve math, but they're terrible, so please
don't ask
me to sing them!).
I am constantly trying to find better ways to challenge my students and
make
the mathematics more engaging. I have thoroughly enjoyed my
teaching
experiences thus far, and am excited about finding new methods to make
my
teaching even more effective in the years to come.