The nature of mathematics is a
tricky subject to write on. I avoided it (outside of my first blogpost) because
of this. Since I am going to be a teacher, I wanted to write about the nature
of math in today’s culture. It won’t so much delve into the nature of higher
math, but will deal with the anxiety that exists in our culture today.
Societies view on math is just as relevant to the nature of mathematics as a professor’s
papers on the subject. All kinds of buzz populate our media and social
networks; buzz filled with judgments on the common core and the plethora of standardized
tests. The weird difference about this topic is that everyone seems to think
that they are an expert in it. Most everyone agrees that they didn’t like the
way they learned math, yet they all seem to want to keep it the same.
I was very gifted in math at an
early age and was always told that I was smart in math. (Obviously this isn’t
exactly a great practice for teachers.) Early on in my school career, I began
getting pulled a few days a week to work on more advanced math with a small
group. My teachers used Everyday Math,
that is more of a reformed set of math books, but the teachers were not trained
in how to use them. Instead of having rich mathematical discussion in which we
could share our reasoning, we answered questions that always always always
always always ended in “Explain your reasoning;” one could hear the groan each
time a student got to this part of a problem. The ideas behind Everyday Math were strong, but the
implementation was week. This continued till I rejoined the class in algebra in
eighth grade. Algebra and on was a more traditional method that lacked the
explanations that Everyday Math had
asked for. It wasn’t until I reached a level beyond calculus that I got to a
mathematical problem that I couldn’t answer quickly. The mathematical practices
in the common core that ask for perseverance in solving mathematics did not
exist within me. It wasn’t until I went back and studied math pedagogy that I
understood my own strengths and weaknesses, and those in the program I had gone
through.
Teaching alternative methods are is
part of the common core. Everyday Math
is a big one for teaching multiple ways to solve a problem. Looking back I can
understand the pedagogical decisions behind this. Many of today’s curriculums
ask for an environment in which many of these methods are discovered or taught
to clarify a concept. But they don’t demand that the quickest, rote, way of
solving a problem be perceived as the best. Instead it asks for methods that
are tied to the concepts. I love this idea. Everyday
Math attempted to present this same idea by teaching multiple ways to solve
problems that have a traditional method i.e. division. In the end it didn’t
demand a method be chosen above the others and many teachers either
supplemented the book with traditional methods or lacked the understanding to
demand that students find, and stick, to one method. This led to a lot of
confusion in my childhood development of mathematical methods and to this day I
can’t perform division or multiplication with ease. Thus, I understand and
agree with the ideas behind today’s more reformed curriculum, but I can see how
the ideas alone don’t make a good math curriculum; it is the teacher’s
determination to create a rich mathematical environment in the classroom that
makes math come alive.
Alternative methods didn’t always
provide a natural progression to a more efficient way of solving problems for
me. There were more concept based methods that lent themselves to understanding
better; I even remember learning methods like these. But these methods weren’t
always the most efficient and the most efficient can be useful when variables
are added into the mix. When I was in a calculus course we needed to know how
to do long division with variables. Without a strong understanding of the
traditional method this became much more difficult. Instead of leaving a child
with a method that is less efficient, I prefer to move the child to a more
efficient method once the concepts are thoroughly understood. I do understand
that without a strong foundation these methods can prove difficult but the
methods are useful and deserve a place in the curriculum. An understanding in
the concepts and most efficient methods seems like a happy median. I was
blessed with an ability to understand numbers and I have always tested well. I
tend to find myself dismissing alternative methods since I never struggled in
these areas. But honest reflection demands that I learn how all types of
students work, so that I can empathize with their unique situations. This will
be a system of trial and error for me. I hope that I have the ability to create
a rich mathematical environment that is accommodating to all students, despite
my personal hurdles.
Text anxiety is a huge issue. In
order to deal with this many schools have elaborate systems in place to support
students. The weeks of preparation, the letters home, the relaxation methods,
all seems over the top. The success of the students on this test matters, I’m
not denying that these can be helpful, but not to the extent that our society
suggests. It distracts students and takes away from valuable teaching time. But
many teachers give up at this point and say “if you can’t beat ‘em, join ‘em”
and proceed to teach one how to operate in the world we live in. The weeks
preceding the test are given a significant amount of weight though. Why? This
creates stress by giving the test weight. Being the best teacher I can be is
important to me. I will not waste several weeks preparing my students for a
test that I don’t give a damn about. Instead, I will explain to them the
situation like they are adults, and expect them to perform well. Teaching to a
test is obviously something that society would discourage, but the mathematical
environment they create is still bound by the shackles of the test looming in
the spring. A rich mathematical environment will allow for the creativity of
the students to come out and go in directions that support all students’
mathematical creativity. I argue for creating a rich environment and to make
this an exception day where there is a test taken.
So the nature of mathematics in
today’s society is a grim one. It is laden with debates on reformed vs.
traditional methods and test anxiety. I only briefly talked about these two
issues, but there is hope. Classrooms can create rich mathematical environments
that are not bound by standardized tests. I will do my best to never back down
from a belief in a culture that can support children in their mathematical
journeys.
