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. 

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