Chapter One
The Waste Ethic
Twenty-five years ago, when I was studying philosophy at McMaster University, I wanted to write a book called "The Waste Ethic," which I hoped would be the first attempt in the history of the social sciences to accurately measure the amount of time people waste at work. I wasn’t interested in simply tracking the time wasted by people who hate their jobs or who are totally unqualified for their positions. I wanted to find out what proportion of our work goes into producing, marketing and disposing of the vast array of products that, before the advent of mass media, nobody knew they needed or wanted. I never did find time to write that book, but having spent the past twenty years teaching mathematics to thousands of children and teenagers – both gifted and challenged, and from both affluent and impoverished homes – I think I have a better idea of why we as a society are so efficient at wasting time.

It seems to me that two kinds of ignorance are always at work in our society, one extremely destructive and the other healthy. My career in theatre was initially shaped by the first kind of ignorance, in ways I am only beginning to understand. I came to writing plays rather late in life because I grew up thinking that to be an artist you needed to be born with a special gift. It wasn’t until I read Sylvia Plath’s letters to her mother and saw how as a teenager she had learned her craft in small, determined steps, dismantling poems like motors to see how they worked and writing imitations of the things she loved, that I began to believe there was a path I could follow to develop a voice of my own.

The destructive form of ignorance has divided many societies: it is the ignorance that says there are fundamental, inborn differences between people, between peasants and nobility or minorities and majorities. It is this ignorance that leads us, even in this affluent age, to neglect the majority of children by educating them in schools in which only a small minority are expected to naturally love or excel at learning.

Two years ago, during a visit to the York Detention Centre, I saw the effects of this ignorance in its most devastating form. I had been asked to teach a lesson in mathematics to a group of teenagers who were awaiting trial and who were not thrilled to be spending their afternoon doing math. I told the students I had once struggled with mathematics myself and I promised to try to make the subject more interesting and easier than they might remember from school. I reassured them that if they didn’t understand something in my lesson it would be my fault for not explaining it properly, so they could ask me to explain it again. The teenagers responded to my promise exactly as I have seen young children respond: they raced through their worksheets and called for the tutors to give them extra work. One girl, whom I had heard complaining at the beginning of the lesson, made me put a check mark beside each of her answers. When I finished she said, "I've never had that in my life. I've only had this," and she wrote a large X across her page.

The letter X is a fitting symbol for our failure to care for those individuals who, like the girl at the detention centre, happen to struggle or fall behind in school or in life. The crossed lines evoke the barriers we place, out of ignorance and indifference, between the majority of children and their unrealized potential. But the letter X is also a universal sign for a different and potentially redeeming kind of ignorance: in the sciences and in mathematics, it is the letter most commonly used to stand for the unknown.

Einstein once wrote:

The most beautiful and deepest experience one can have is the sense of the mysterious . . . One who has never had this experience seems to me if not dead, then at least blind. To sense that behind anything that can be experienced there is something that our mind cannot grasp and whose beauty and sublimity reaches us only indirectly and as a feeble reflection, this is religiousness. In this sense I am religious.

The sense of the mysterious that Einstein described can define a person as much as their sense of courage or integrity or charity. People who experience the ineffable mystery of the world also tend to have a deep sense of humility, as Socrates demonstrated when he admitted how little he knew to the Athenians who put him on trial for his life. This sense of the mysterious drives such people to pull aside the veil or wipe away the fog that separates them from the mystery.

Every child who is well cared for naturally develops a sense of the mysterious. The feeling that behind every door another world is waiting can make a child’s world a paradise. But, once at school, children often begin to lose their sense of the hidden beauty of the world. By having to compete and be compared to their peers, many lose faith in their intelligence and their imagination; by having to struggle so hard to keep up, many come to believe that the world is beyond their understanding. The magical world that they once inhabited begins to recede until they can see no point in dreaming about or searching for anything beyond the world of their immediate needs and desires.

People are often surprised when I tell them that I am a mathematician as well as a playwright. Some people seem to believe that the brain can hold only one kind of information, or that when one side is working the other has to be left empty for storage. If they are lucky, students graduating from high school will likely believe that they have only one or two talents and that the majority of subjects offered at school are either uninteresting or beyond their grasp. As a society we are living under a vast spell or illusion. We have effectively hypnotized ourselves, but not in a single performance. It has taken twelve or thirteen years of school to put us in a suggestive state so that we all believe more in our limitations than in our potential, and it is difficult for anyone to snap their fingers to break the trance.

When I was a teenager I read a fair number of biographies of scientists and mathematicians. These biographies always gave me the impression that a person had to be born with a gift for mathematics and that someone who had this gift would never do badly on a test or struggle to learn a concept. This belief sank in very deeply; like many young people I would often give up on things because I was afraid of coming up against my limitations. It wasn’t until I was in my thirties that I had the courage to go back to school and study mathematics.

At university I had an enormous advantage over the other first-year students: I had been tutoring math for several years to supplement my income as a playwright, and I knew the high school material inside out. I had also learned some of the university material in advance. But occasionally I would do badly on a test and I would be paralyzed by insecurity. I remember lying in bed after I had failed one test, thinking that I had reached a threshold I couldn’t go beyond and that I would have to give up my ambitions. My work as a tutor had given me a great deal of perspective on the issue of ability, but I still couldn’t get over those fears. It took several years before I began to notice that the things I had found impossible on a particular test became trivial once I had a chance to practise and learn them properly. I began to wonder how many people have stopped themselves out of fear of failure from developing talents in things they found interesting when they were young.

Nine years ago I was looking for a way to give something back to my local community. It occurred to me that I should try to help kids who needed help with math. Mathematicians don’t always make the best teachers because mathematics has become obvious to them; they can have trouble seeing why their students are having trouble. But because I had struggled with math myself, I wasn't inclined to blame my students if they couldn’t move forward. If a student didn’t understand my explanation I assumed there was something wrong with the explanation, not with the student.

Many of my closest friends are actors. Actors often have a good deal of time on their hands and they will do anything for attention, so I was able to convince a group of my friends, even the ones who had dropped out of math, that they too could tutor math. We started an after-school tutoring program in my apartment called JUMP (Junior Undiscovered Math Prodigies).

The JUMP program was founded on a very lucky accident. I had asked the principal of a local school to send some kids to the program who were having trouble with math. She misunderstood me and delivered the most challenged kids in the school, including a number of kids in special education classes who were performing far below grade level.

Working with these children, and with the thousands of children I have taught since JUMP started, has been one of the most inspiring things I have done. I am now convinced that the brain can develop new abilities more readily than traditional theories of intelligence allow, and that children who face challenges at school are capable of far more than we expect of them. Many of the students from the first few years of JUMP had moved into academic classes by the time they entered high school. And thanks to the work of hundreds of teachers and volunteers, JUMP is now an in­class program that delivers the complete curriculum in mathematics from Grades 1 to 8. JUMP materials and methods are being used with encouraging results in several hundred schools in Canada, the United States, Australia, South Africa and Britain (which is home to the world’s largest single JUMP program, with five thousand children).

In this book I will describe the methods and results of the JUMP program, but this is not primarily a book about JUMP, or even about mathematics. The examples I give illustrate broader points about the way we educate children and about the expectations we have of weaker students. It is possible to apply the methods I describe to various subjects. Deep psychological principles, which are as important as the curriculum or the content of the course, must be taken into account in the teaching of any subject: including the way children perceive themselves in groups and the way cognitive abilities can be developed by playing with subtle variations on patterns. I argue that, because we have ignored these principles, our educational system is far from optimal and the means we have developed to educate children are extremely inefficient.

The philosopher Wittgenstein said that people get themselves into trouble when they fail to pay attention to the precise meanings of words. I argue that many inefficiencies in education stem from confusions over the meaning of some words used in educational theory. These confusions are not of academic or philosophical interest alone: they have had a profound effect in our schools.

It is not easy to describe the things I have seen in the educational system, or the ideas behind JUMP, without over-simplifying. I often return to the same idea several times to provide a different angle or perspective. It is almost impossible to say anything in education that is not both true and false at the same time. The things that children respond to are often surprising and counterintuitive, and words and categories can fail to capture the complexity of a child’s behaviour. It is easy to attach a label to a particular style or philosophy of teaching, but I hope that educators will wait until they have read the whole book before they try to classify or name the methods I describe in this book. One of the greatest threats to education is educational theory that does not take account of the extraordinary complexity of the mind or of the subtleties in what children find interesting and meaningful and in what motivates them to learn.

When I was growing up I often dreamed about becoming a good mathematician or a good writer, but never about becoming a good teacher. Given a choice, I prefer sitting alone in my office doing mathematics to teaching, giving talks about mathematics or writing workbooks for children. But over the past ten years I have effectively given up my careers in math and the theatre to work forty to fifty hours a week as a volunteer for JUMP. And there are several reasons why I have set aside my other work in order to teach and develop educational materials.

I think it is fair to say that there has been no great improvement in the state of education in the past thirty years. And over the same period, despite the substantial efforts of governments and charities, there has been no significant improvement in the condition of the world’s poor. At the same time, a succession of breakthroughs in productivity and in technology has transformed our society and created vast fortunes around the world. When so much has changed in contemporary society, how have the state of education and the level of poverty remained the same? I believe our lack of progress in these two areas is connected.