I just spent an hour or so attempting to master a method for factoring quadratic functions that made me more and more livid as I attempted to understand the purpose behind the exercise. I’ve been teaching Algebra I and Algebra II for years and I have developed ways for helping my students to understand both the purpose for doing so and how and why certain methods work. The one that was baffling the student whom I tutor is the so called tic tac toe method.
I don’t have any problem finding a sure fire way for students to do mathematics in an easier manner but it really has to make more sense that just repeating a set of rules to reach the answer. Sadly the tic tac toe way of doing things was more confusing than helpful based on the materials that the teacher gave to the student. It had little to do with understanding the art of factoring compared to other methods.
The real difficulty came about because the original teacher of the Algebra II class left the school after only working there for a week. She was young and perhaps not aware of the challenges of teaching math can be so she just left.
It took until November for a full time teacher to be hired while a series of substitutes kept the class going. Sadly most of them had little or no experience teaching higher level mathematics so they were not particularly gifted in explaining how and why things work. The result is a large number of very confused students who have so much catch up work to do in a short amount of time.
There is always more than one way to perform different calculations and processes so there is nothing innately wrong with using a method that is less complicated than guessing and checking but it has to be presented in a manner that makes sense. While surfing the Internet to learn how to use tic tac toe I found other ways of factoring that were explained so well that I picked up on the whys and wherefores of them in less than five minutes. Little was present for tic tac toe until I finally found a slide presentation that at least clarified the methodology even if it never bothered to explain why it works. Soon I was tic tac toeing my way to factor heaven but I knew that many other ways of doing so are available and most of them make way more sense.
One of the problems with mathematics in general is that one will always hit a wall if he or she has only memorized an algorithm. Sooner or later the difficulty level will rise to a point where even the slightest change will send the person into a panic of confusion. I decry so-called shortcuts that don’t take to time to demonstrate the logic and beauty of mathematics.
One of the things that I love most about how most modern day math teachers provide knowledge is that they use words, examples, visuals and physical manipulatives that literally show in concrete manners what the different concepts are. They bring in real life examples of how math is used and why it matters the know that the slope of a line represents a constant rate of change, not just a slanted line on a paper.
Some students figure out such things on their own but all too many people report in adulthood that they always hated math and felt confused and frustrated most of the time. I often wonder how many folks who might have proven to be excellent in mathematics gave up on themselves early in the game because a teacher or teachers were unable to show them the wonderful connections between mathematical ideas.
I’m picking up the pieces with the student that I am presently tutoring. He has also taken the initiative to meet with an experienced teacher dury study hall time at school. He is a very bright young man who is frustrated right now and anxious to master what he has missed. I have taught him before and know that he usually catches on to new information very quickly. The fact that he is showing papers with half of the problems blank tells me that he is in a very bad place mentally and it may take a great deal of effort on his part. the new teacher, and me to help him fell one hundred percent confident again.
I don’t think that there would be as many problems finding good teachers for every school if we valued educators as a society. Sadly many Americans have totally unreal beliefs about the lives of teachers. They imagine teachers lolling around swimming pools once the clock strikes three and having no more work to do until maybe nine the next morning. They speak of all the holidays that teachers have and the long summer vacations. The truth is that the average teacher brings home work every single night and works long after most people have gone to bed.
School hours are not just compacted into an eight hour day and those summers are much shorter than most people imagine. Many teachers are lucky to have six weeks of vacation time once all of the demands for new learning and preparations for the coming school year are met. Sadly their salaries are based on a ridiculous belief that they don’t really work as long and as hard as others and so they are still grossly underpaid for the skills that they have to offer. Add to that the audacity of advice from so called experts whose only connection with schools has been going to them as a children. It is not to difficult to understand why so many teachers are leaving he profession.
I’ll be going in a few minutes to pick of the pieces of destruction that have rattled the student that I sometimes tutor. I will do my best to help him understand that most of this was not a reflection on his intellect. Our society is neglecting and insulting our schools these days and it really is a shame. In the meantime if you find yourself needing help understanding how to factor with a tic tac toe grid just call me. I have figured it out even as I am not so sure that it is as helpful as it was meant to be.
All It Takes Is A Little Love 