As a mathematics teacher I often observed students who were in a state of deep distress before, during, and after a test. Some of them had not paid attention during the lessons, nor had they taken advantage of the many tutoring opportunities that I provided. Others were just the anxious sort who fell apart emotionally at the mere mention of a challenge to regurgitate what they had learned. Many had simply struggled to master the concepts in spite of their Herculean efforts and mine. They needed more time and attention than the crowded curriculum driven by high stakes testing allowed. I felt for those who were not seemingly born with a mathematical gene that insured that they would rarely find the ideas that I presented to be problematic. It almost seemed unfair the way the normal curve of learning was so unfairly distributed among my pupils. I desperately desired to bring understanding to as many of my charges as possible but there were always a few who so earnestly tried but still failed. I realized that our society has carved out a cookie cutter sequence of learning that is all too often ill fitting for the majority of individuals.
We often praise those who demonstrate brilliance in the classroom. We select them for honors and place them on a track to success. The truth is that many of them have done very little to earn the glory other than to be born with abilities that place them at the head of their peers. Particularly with regard to mathematics they have an innate sense of numbers and what they mean. They operate with fluency and quick comprehension. They would most probably learn even with a mediocre or even sub par teacher. I always enjoyed having them in my classroom because they had exciting minds and they somehow made me feel that I had indeed been quite successful in my instruction. Deep down inside I also understood how little effort I had to expend to keep them interested and moving quickly forward. They were already gifted and all I had to do is make the class exciting enough to maintain their attention.
The most difficult aspect of teaching mathematics came with those who often appeared to be clueless regarding the most basic foundations of the subject. Numbers were a mystery to them and they had moved from grade to grade hoping to hide the deep dark secret that they really did not understand the beauty and the harmony of mathematics the way the superstars did. An hour long class designed to acquaint them with the latest concept was never enough to break through the fears, mental blocks, and missing links that plagued them. They always needed more of my time. The frustration for me was that I had to live and breathe under rather rigid time constraints dictated by the overly crowded scope and sequence of the state mandated curriculum. I knew that if I had been allowed to craft individual learning plans for each of my students everyone would be doing well but they would all be in very different places along the mathematical continuum.
I rarely heard students say, “I’m no good in social studies, or science.” but I often heard them complain that they just could not do math. They literally believed that something was wrong with them with regard to an understanding of the way numbers and algorithms and theorems work. If given the opportunity they would have run far away from any kind of mathematics class. It grieved me to see them so frustrated and convinced that something was wrong with them.
I once told one of my principals that I felt more like a cowboy on a cattle drive than an educator. I was always playing a game of hurry up, hurry up. I had to outline the course of the entire school year to be certain that I covered every single skill and concept. I built in days here and there for review but those were few and far between. I used spiraling in my warm ups, tests, quizzes, and even within the main lessons but I still felt hard pressed to keep moving forward even as I knew that some of my students were losing ground. There were common assessments looming at the end of each grading period and the big daddy state tests at the end of the school year. Both my students and I would be judged on success or failure. I had to keep pushing forward even as I saw some of my kids lying exhausted in a ditch of despair. It was depressing to see them that way and to know in my heart that if only I had more time with them I would be more than able to provide them with the extra push that they so needed.
From my tutoring I have become convinced that the majority of students need targeted and personal attention beyond the confines of the classroom if they are to enjoy mastery of mathematics. After a lesson on a particular concept they are still somewhat confused. There are gaps in their comprehension and questions that need answers. If the construction of the school day provides them with the time to process the information and to interact with a tutor they will generally achieve a level of comfort and understanding. Without such accommodations they lack the foundations needed to continue building upon prior learning.
Since retiring I have been tutoring individuals who have fallen through the mathematical cracks one way or another. I helped a woman in her seventies to learn concepts that had eluded her when she was in high school. With literally hundreds of hours of work on her part she ultimately managed to achieve the knowledge that had kept her from earning a diploma so long ago. It took patience on both her part and mine to slowly but surely walk her through the typical high school mathematics curriculum. She began to realize that she was not “dumb” but merely someone who learned things differently. Once the concepts were firmly anchored inside her brain she was able to meet virtually any challenge. She felt good about herself as never before.
Far too many of the students with whom I presently work have given up on themselves. They are convinced that they are somehow defective. The truth is that they have different learning difficulties but they are far from being unable to learn. I see those who become so anxious that they literally become ill at testing time. I notice how disorganized some of my kids are. They have a mess of papers spilling out of binders that appear to have been tossed randomly inside a wind storm. They have fallen so far behind that they feel that it is impossible to catch up with their peers. Others lack a skill here and a skill there. They are missing just enough knowledge that they are unable to effectively use new information. Still more process ideas very slowly. They need to ask dozens of questions and try multiple examples before feeling confident of their understanding. Some are so easily distracted that even the slightest noise or movement inside the room suddenly disconnects their brains from the task at hand. Unfortunately the average teacher and classroom is poorly equipped to handle the needs of such students. Instead they have to keep up with the crowd or be left behind.
I often wonder how many incredibly bright souls have stumbled through life believing that they are not as intelligent as their peers simply because nobody ever acknowledged the true fact that we all learn differently and at different rates. I am convinced that all kids can indeed learn anything if we provide them with the time and the learning modalities that they need. We are not herds of cattle. We are unique individuals each of whom see the world in slightly different ways. Education should not be a race and yet given the nature of universal instruction it often ends up being that way. We group and assess and compare everyone at the same time and then wonder why so many have fallen short. We don’t expect all babies to stand up and walk at exactly the same date but we demand that our students roll along an assembly line that takes little consideration of their specific needs. The truth is that the onus for learning is on the student. Those with talents and work ethics manage to navigate well. Those who are not ready or who suffer from learning disorders too often end up mangled and confused.
My most powerful mathematic memory comes from a time when I was retaking Calculus because it had been decades since I had learned it in college. Since I never used it I had forgotten many of the concepts. I was in a very small class at San Jacinto Junior College and among my fellow students was a man who appeared to be a mathematical genius. He and the professor often engaged in esoteric discussions that were far above the level of most of the students. I wondered why this man was enrolled in a course that he didn’t appear to need. In talking with him I learned that he had hated mathematics in his high school days because he had not been able to master any of the concepts. He failed and failed again and ultimately dropped out of school. He somehow managed to earn a GED and entered the military. While there he became quite interested in ballistics and excelled at the mathematical ideas related to determining targets and so forth. An officer noted his exceptional mathematical abilities and encouraged him to further his knowledge. Somehow concepts that had once eluded him began to make perfect sense. He saw the beauty of mathematics and how geometry and algebra fit so neatly together. He felt as though some kind of miracle had happened but I realized that his military experience had unlocked the key to his personal learning style. I marveled that he was reclaiming his life.
I suppose that it is unrealistic to believe that we might one day develop personalized learning for each and every student. It would be so grand to allow our children to develop at a pace that is right for them rather than one dictated by a calendar. If we desire more people to embark on STEM careers then perhaps we need to be scientific enough to admit that we can’t possibly expect everyone to be successful in a one size fits all form of learning. We have to allow for differences. We ask our teachers to craft thirty different plans for the same lesson but then we tell them that everyone will be tested on the same day and time. We are not serious yet and because of that our children will continue to suffer and there will be those who admit defeat when they proclaim, “I’m not good at math!” It doesn’t have to be that way!