Despite efforts from Washington, math education is still in trouble in the U.S. We are now experiencing the so called “math wars”. Educators are competing with policy makers, and mathematicians are challenging both. The argument is that educators are focused on the mission and purity of education as a whole. Education is the basis for lifelong learning and free thought. When mathematics is concerned there is a wedge between mechanical learning and reasoning. University mathematicians believe that teaching reasoning before standard algorithms is crippling student‘s abilities to learn the more advanced concepts in college level mathematics. It is argued that before learning mathematical and numerical reasoning students must understand the standards of math.
The dangers of sticking to a mechanical standard algorithm approach are flexibility, intellectual growth, and individual ability. Flexibility refers to having a standard such as right to left based calculation. This concept alone can prove very confusing especially in younger students who are still honing their reading skills. In most languages, specifically English, students are learning to read from left to right. Every time they are exposed to any form of writing they are taught that it should be understood from left to right. When children begin learning math they are taught to read math in contradiction to all the other reading that they learn. In essence this can cause confusion in both subjects for most students. Not only is the left to right approach quicker and easier, it also flows logically with the way we are taught to read.
Another issue is that when teachers are grounded with this single algorithm method, students who understand it differently are often punished with bad grades. Some teachers are so set in the standard right to left and carry method, that if a student chooses to use a different method they are given a bad grade. The stigma put on outside the norm computation will stunt the students drive and understanding of math. It places in them the “why am I wrong when I got the same answer?” argument. I had a personal experience with this receiving a failing grade on a test because on the page where you “show your work” I did all multiplication from left to right. The teacher of the class I was in had no clue how that method worked and therefore failed me on my exam “for cheating”. The reason given was that the only way to multiply is the standard right to left so the work shown was an attempt to cover up cheating. Now this is a specific individual example that does not reflect all teachers, but there are still some that are so set in the standard that “out of box” thinking is “out the window”.
Aside from flexibility, we have the issue of intellectual growth. Intellectual growth is arguably the central idea of education. The ability to think and reason is devastatingly uncommon among many adults and children. Most educators wish to remedy this situation, by trying to step outside of the memorize and regurgitate on the test paradigm. Standardized testing is standardizing thinking and learning which is destroying innovation and lifelong learning. While most agree that some concepts should be tested and retained to be successful in college, the ways by which we test and use these concepts need to be modified.
The last issue is individual ability. Going back to the personal example of being labeled a cheater for utilizing a method that was easiest to me was a stab at my individual abilities. That failure caused me to have to take a much lower level math class then I should have been in twice. Luckily, the next time around I had a better informed teacher that removed me from that class put me into pre-calculus instead where I aced the exams. The point is that no matter how you try to standardize people, we are all individuals with individual ability to understand the world around us.