NOT LONG AGO I BROKE UP A FIGHT AT A SCHOOL WHERE I WAS tutoring by telling the boy who started the fight to apologize or I wouldn’t give him his bonus question. Perhaps the most surprising thing about this incident was not that the boy was willing to apologize to receive extra work, but that the work itself was in mathematics.
In my experience, children want two things in order to be happy at school: to exercise their minds and to show off. Mathematics may well be the subject in which children can most easily satisfy both of these desires.
Before children can read, they must acquire an extraordinary number of visual, auditory, and cognitive skills. But children can master a great deal of mathematics simply by counting on their fingers (something we have evolved to excel at).
As I am not a psychologist, I can’t say why the method of teaching used in JUMP has such a remarkable effect on children who have trouble learning. Perhaps the thrill of success and the intense mental effort required to remember complex rules and carry out long chains of computation and inference develops parts of their minds they normally are incapable of using. (Lately I have even observed growth in motor and perceptual abilities in children who have completed the fractions unit.) I suspect that a remedial reading program would be more successful if preceded by or coupled with a JUMP-style math program. I also suspect that JUMP could significantly help children who have trouble with socialization: I have witnessed children diagnosed as autistic or selective mutes regularly call out answers in class after only a month or two of lessons.
If math is the subject in which students can succeed most easily (and thereby can develop the cognitive abilities and the confidence they need to succeed in other subjects), then our failure to teach math to the majority of students is all the more deplorable.
I would be extremely disappointed, however, if this book caused even one parent to pester their child’s teacher with unreasonable demands. Teachers are largely responsible for the success of JUMP: they have welcomed the program into their classes because they are dedicated to helping their students. Rather than harassing a teacher (who is likely overworked, underpaid, and on the verge of quitting), a parent who wishes to improve our schools should consider volunteering in a class or pressuring governments to provide training for teachers as well as tutors for students who need extra help. (This is not as costly as it sounds: one or two full-time tutors, assisting trained teachers, could take care of an entire school.)
Teachers, on the other hand, must open their minds to the fact that, with proper teaching, all children can learn math. I recently worked with a teacher who told me I shouldn’t waste my time with his weakest students as they had mild intellectual delays. After I had tutored those children for several months, the teacher changed his mind: he is now one of the most enthusiastic supporters of the program.
Historically, societies have always been divided by myths of difference: between peasants and nobility, slaves and slave owners, or minorities and majorities. Today, the most pervasive and enduring of those myths — the myth of ability — is being challenged. People who traditionally would not work together have found common cause in JUMP. Our volunteers include vice-presidents of banks and social activists. Regardless of their political beliefs, people who have seen children flourish in JUMP find it easy to agree that children are more alike intellectually then they seem.
I am not advocating a society without challenges, where exceptional achievement goes unnoticed. But the tests a society offers its members, particularly when they are young, should be designed to elevate the human spirit, not crush it.
Recently I gave a lesson in mathematics to class of students at the York Detention Centre in Toronto. I was rather nervous before the lesson started, not only because the members of the class were all awaiting trial, but also because I had no idea how teenagers would respond to a method of teaching I had only tried with children. It didn’t help when I heard a girl mutter, “I’m not doing this,” or when a guard stopped me from lending a boy my pencil because it hadn’t been counted and might be smuggled out of the class as a weapon.
After an hour, the students had all completed ten pages of work. The girl I had heard complaining called me over to her table. I told her she shouldn’t expect me to mark all ten pages: I could tell, from the questions I had checked during the lesson, that she had gotten everything right. But she insisted that I put a check mark beside every one of her answers. When I had 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.
As the guards gathered and counted the pencils, and the students were escorted to their cells, it seemed to me that we were all involved in an absurd mistake: the teenagers had spent the hour calling for the instructors to mark their answers and demanding more challenging work. They had responded exactly as I have seen children respond to the promise that they would succeed.
When I was a child, I believed that one day I would travel in time. But time escorted me, quickly and irreversibly, into a life I could scarcely have imagined. I had hoped I would grow up to be a great mathematician, or the author of a book better than this. But I have come to believe in my abilities rather late.
We all have abilities that were neglected in the past and that we now are unlikely to develop. But we might still accomplish more as a society than all the towering geniuses of the past. For if we were merely to educate our children, we would be the last generation whose promise was lost.