Daunting

main-content-management-imageBecause I grew up in a single parent family led by a strong and confident woman I am strong willed and independent. Had my husband, Mike, not been nurtured by a mother who was an equal to mine in her commanding presence he might have struggled with my personality after we married forty eight years ago today. I suppose that the real me may have been a bit of a surprise to him. I was a month shy from being twenty years old on that Friday when I walked down the aisle to exchange vows. We were still in that tingly romantic stage of our relationship. Both of us were on our best behavior. As so often happens our true selves ultimately revealed themselves in the day to day routines that evolved and Mike noticed that I was not exactly the person that he thought I was.

I’m a daunting competitor who likes to win. Since nobody ever mentioned to me that women are expected to fulfill certain roles and that we are supposed to struggle in a man’s world, as a young bride I simply threw myself full force into handling the household and preparing for a career. I was not held back by beliefs that there were glass ceilings above me or that I wouldn’t get as fair a shake as the men with whom I interacted. I carried on the way my mother did after my father died, unafraid to try almost anything. Of course Mike had unwittingly provided me with the last bit of courage that I needed to emulate the confidence that I had always seen in my mom. I had been socially shy and uncomfortable around men before I met him mostly because I had not been around males very much. Mike taught me that I could hold my own with a man and he admitted at every turn that he was my biggest fan. With him in my corner I felt able to tackle any problem that came my way, which was fortunate because I would have to muster great courage to become a lifelong advocate for my mom when she began to show signs of her bipolar disorder.

As I evolved in my marriage and my role as a woman I had perhaps the two best role models possible in my mother and my mother-in-law. I witnessed both of them walking without fear into the fray of what was at that time a truly male dominated world. They encouraged me to follow my dreams no matter where they might lead. My mother-in-law in particular gave me the priceless gift of her time, often rescuing me when one of my children was sick by coming to babysit while I went to work. When I had a job that kept me at work until late in the evening she faithfully came to my home each afternoon so that my youngsters would not have to be latchkey kids. She prepared dinner to give me a break when I arrived home exhausted. While these may sound like very traditional womanly duties they came accompanied with profound advice that kept me feeling that I was doing the right thing in pouring myself so totally into my work.

Then there was Mike who never complained when I became absorbed in the many time consuming aspects of being a successful educator. My days and nights and weekends were filled with planning, grading, attending seminars, and working toward an advanced degree. I often spent more time with my students and our daughters than I did with him but he understood my need to perfect my craft and to give my all to the work that I thought to be so important. He took pride in my accomplishments and supported me without question even as he sometimes sacrificed his own needs. To this very day when I become involved in new pursuits his only bit of caution is that I do what makes me happy, not what I think that other people may want.

I suppose that the key to the success that Mike and I have achieved in our marriage is that we are truly best friends in every sense of the word. Neither of us has ever felt that one is superior to the other. We equally value the contributions that each of us has made to the partnership. While I compete with the world at large, neither of us feel compelled to outrank the other. We are truly coequals, each with different skill sets that are important to the family. There are no jealousies or fears. We can be ourselves and feel completely safe. Nothing in forty eight years has given either of us reason to believe that we cannot trust the other without reservation. Ours is a union of mutual respect and admiration.

I suppose that my circumstances have been fortunate in that my brand of feminism is a bit different from most. I did not grow up around domineering men, instead I watched a widow woman earn a college degree, work as a teacher and researcher, purchase and pay for a home, raise three well adjusted children and lead a profoundly happy existence all without assistance from a man, while also battling the horrifically debilitating symptoms of mental illness. I married a man who gave me total freedom in determining how I wanted to use my own talents and then became my most devoted cheerleader. As if that wasn’t enough to encourage me to be formidable in my interaction with the world, my mother-in-law became a source of limitless wisdom as I drew upon her experiences as the manager of a family electrical business, the chief financial officer of a mega church, and a well read student of history and politics. Based on the complaints that I hear from women today I suppose that I was too blessed and too ignorant to realize that I was not supposed to feel as equal to men as I always have.

I grew up in what is defined as a classically dysfunctional family. We were poor and had no father. Because of my mom’s optimism and strength, somehow the situation never felt that terrible. I married a man when I was too young to have enough sense to make things work but our love and respect for one another carried us through both triumph and tragedy year after wonderful year. My incredible mother-in-law served as a sounding board and a sterling example of what a determined woman might accomplish even when all of the world is telling her that she may not have the right stuff. These are the people that I knew and the privileges that I had that made me the woman that I am. As daunting as the world may sometimes be I have always been able to tackle it. The real key to my success as a woman has not been in having some kind of special sources of influence, because I have never had any, but in being valued and loved.

Breakthrough

frustrated6-e1461345600746She was a brilliant young woman who excelled in virtually every arena of life with the exception of her mathematics classes. She had learned to excuse her missteps in Algebra with a tilt of her head and the classic excuse, “I’m just no good in math.” Somewhere along her educational way she had decided to accept mediocrity when dealing with formulas and algorithms because it had secretly bothered her competitive spirit that questions of trains meeting at a station seemed both meaningless and confusing. Little of it made sense and she had it on good authority that she would rarely use any of the information again in “real” life. She approached mathematics with disdain and longed for the day when required courses would no longer stalk her. One day she would proclaim to her family and friends that she had done well without being a mathematical whiz and that her genes were evidently unfit for ciphering.

As a long time mathematics teacher I heard all of the negative commentaries and phobias associated with fears and misunderstandings about the subject that I taught. In conferences parents often explained away their children’s low grades with familial anecdotes outlining a long history of ancestors who shied away from arithmetic and all of its components. Students often masked their own confusion with difficult concepts by feigning laziness or bad behavior. In general a significant proportion of the populace is frightened by the mere thought of mathematics and runs from its grasp as soon as the educational system allows them to do so.

As with so many things in this world we are saddled with a necessity to approach the teaching of numerical skills with a one size fits all approach. The natural born mathematicians reveal themselves rather quickly. They possess a keen understanding and of how numbers work and what they truly represent. They manipulate them easily and are able to explain why we need numbers both whole and rational. They are innately fascinated by the beauty of mathematics and its ability to explain how most of the universe works. These students only need be guided by their teachers as they master one concept after another. As educators we know how to accelerate their progress so that they remain inspired by the world of numbers. It is a joy to teach them and to realize that they carry the future of inventiveness in their minds. Sadly, the journey through mathematics is not so easy for the vast majority of the children that we encounter but we nonetheless persist in teaching it in pre-dispensed doses, insisting that everyone keep up with the pace even as we witness many stopping on the sidelines.

The fact is that anyone may learn mathematics and learn it well but whenever we insist that they master concepts within a narrowly defined timeline we are asking for trouble. The brain is quite complex and each of us interact with the physical world in different manners. We have clearly proven that some people excel more at linguistic tasks than those requiring the centers of their brains that decipher mathematics. There are students who learn through movement and repetition and those who need to hear the information that is sending signals to their minds. Some, like me, have to see and visualize what is happening before they are able to solve problems. In our large classrooms crammed with individuals of every sort we often attempt to serve each type of learner but our efforts often fall short due to a lack of time and pressing pacing requirements. We generally paint a large swath of information through the middle and hope for the best. Of course again and again there are students who become lost and those who become bored. Unfortunately they mistake their feelings as a sign that they are somehow unfit for the world of mathematics and begin the process of reinforcing negative feelings about numbers. We lose them and they lose possibilities that they might otherwise have had.

I have met countless adults who have confessed that they harbored great fear of mathematics all the way through high school. They purposely avoided college majors and jobs that were intensely mathematical because they worried that they might somehow become failures if they reached beyond their perceived capabilities. They noted that somewhere along their evolutions as adults they began to feel more and more comfortable with all things mathematical as they realized its patterns and its rationale. They developed number sense and learned to calculate mentally. They wondered why it had taken them so long to feel as competent with math as they eventually did. 

My answer for everyone who struggles with mathematics at some point in time is that we have to begin to teach the critical skills of numbers at a pace that allows the learner to thoroughly understand and appreciate what is actually happening in the process. That means that children will be learning along a wide spectrum that is not defined by parameters associated with a particular grade. There must be flexibility and teaching for mastery and breakthroughs that often don’t occur. Far too many students memorize processes without ever being able to explain why those processes work. They derive answers but can’t tell if those answers are within the realm of reality. Because they are merely parroting ideas they eventually hit a wall and begin to doubt their own abilities.

There is an old platitude that all children can learn, which is generally true, but it masks the reality that the pace and style of learning is different for each of us. Unless we are moving through concepts appropriately we will falter and therein lies the rub for all of education and especially for mathematics. We need to somehow design a system that allows for differences so that more people will experience the breakthroughs in understanding that so often daunt all but our most gifted students. It may require employing more manpower and technology in our classrooms to accommodate each individual. Instead of simply teaching a topic, giving a general test and then moving to the next concept we need to reteach those who failed to grasp the ideas in the first go around. This might require before or after school tutoring that includes methodologies that were not initially employed. We need to also provide our students with a new kind of mindset in which they understand that the goal is not to meet certain requirements by a certain date but to achieve ultimate mastery at the pace that works for them. Failing grades should only be interim markers with the final score being a replacement of low scores with the ones that indicate student success. Time, patience, inventiveness and a different mindset can and will produce more and more individuals who not only do well mathematically but actually enjoy the beauty of this incredible subject.

Such breakthroughs are within the realm of possibility. In some ways they return us to the world of the one room schoolhouse in which a gathering of students represented many different levels of progress. It is a challenging idea to even consider. We have become accustomed to a clearly defined process of sequencing and pacing from one grade to the next. Our teachers are mostly trained to do direct instruction to a whole class and then to attempt to provide one on one guidance in an exceedingly short span of time. They buzz through concepts like bullet trains leaving behind those not quick enough to jump onboard, not so much because the teachers think that what they are doing is right, but because the packed curriculum for each grade requires them to work faster than they should. Common sense and our own educational experiences tell us that far too many of our students are being left behind. It truly is time to view our methods through a more critical eye. We need to consider the research of countless experts that has shown the need for teaching in ways that address our differences. Society must find the willingness to expend the time and resources necessary to make educational breakthroughs that will change minds and lives for the better.