Saturday, December 5, 2015

Nature of Math: Alternative Methods and Anxiety

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.


  1. I can remember the classic "Show ALL your work" from the younger days. I remember taking a math test to move up into the advanced class in like 5th or 6th grade, and almost the whole thing was showing the steps, even though the answers were simple and sometimes (dangerous word) trivial. I agree with the nature of mathematics being tough these days. I think thankfully more and more people are starting to see that standardized testing is about as useful as a high school GPA for a post college job interview.

  2. Two big issues, for sure. To me, misuse of the test results is a big problem. As long as we're comparing and funding schools by the results - schools which are not comparable in many ways - it's going to be a mess. Tying teacher job security and raises to them is doubling down on the unhealthy.

    Of course, I'm in favor of the inquiry type math. Calculators are really the most efficient method, and they continue to improve. All that's left for the humans is understanding and application. We're coming to grips so slowly with the post-computation age. (Cf. Conrad Wolfram division is a good example. There's no need to work by hand for an answer, but understanding what you're doing and the algebra of it is what's important. Always was, but especially now.