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Math Power: Who, What, Why, and How
Average students in other countries often learn as much mathematics as the best students learn in the United States. Data from the Second International Mathematics Study (1982) show that the performance of the top 5 percent of U.S. students is matched by the top SO percent of students in Japan. Our very best students—the top 1 percent—scored lowest of the top 1 percent in all participating countries. All U.S. students —whether below, at, or above average—can and must learn more mathematics.
Mathematical joy! What a gift for your child!
Math power is the ability to use and enjoy mathematics. Math power gives a feeling of control, both over ourselves and our environment. It is a valid feeling. If we understand math well enough to use it spontaneously, we do have greater control both over our inner life and over society's decisions.
Children are born with enthusiasm for math. Think of how much your preschool child enjoys counting! It enlivens humdrum activities like stair climbing, toothbrushing, and toy-sharing. Or watch your child arrange toys in a pattern; that too is exploring math.
Every parent and caretaker can help preserve young children's innate enthusiasm. You don't have to be trained, or certified, or rich, despite rumors to the contrary. You can do it, whether you are an upwardly mobile professional, a struggling single parent, a home-schooler, an environmentalist retreating to the simple life, or Aunt Gertrude, whose family just dumped the kids on your doorstep.
A supportive family is the single most important factor in the intellectual success of their offspring, even if the parents have only a fourth grade education and regardless of whether they remained married throughout the youngster's childhood. Mathematical competence is helped by parental enthusiasm for learning, easily available books of all types (not just math), and habits of family conversation. Most of these require remarkably little money, especially in a community with a public library.
Although I do not believe support can be measured, I do believe it is worth writing a book about how to provide it. The most important things in life can't be measured. Mathematics has its limits.
Studies repeatedly show that the greatest measurable predictor of a child's academic success is the parents' socioeconomic status. Without doubting the conclusion of these expensive studies, we can be skeptical about their meaning and application. We all know of high socioeconomic parents with a shiftless offspring. Conversely, I know of a minority single mother waitress whose female child grew up to be a college mathematics professor. Measurable correlations cannot be legitimately used to predict individuals' fates.
Black mathematicians of New Jersey: In the mid-1980s I surveyed African Americans in New Jersey with degrees in math. There were 75 responses. All had professional careers.
* Only 4 had two parents who were college graduates.
* The majority, 44, did not have two parents who finished high school.
* Almost a third, 23, had no parent who had finished high school.
* Almost a quarter, 18, had no parent who had begun high school.
Obviously, formal education is not necessary for raising a professional. There is much more involved than formal education, social status, and economics. Most of these parents were near the bottom of the socioeconomic ladder. Indeed the most mathematically successful parent that I have ever heard of was the daughter of two slaves.
A Slave's Daughter: In 1912 Susie Johnson McAfee took the examination for Texas teachers' certification. She passed every part except that her spelling paper was mysteriously lost. Her father was told that if he paid $50, the paper could be found. He said he was outraged and refused to pay, so his daughter couldn't become a teacher.
She married a carpenter-farmer and had nine children. "She taught us," said one son, Dr. Walter McAfee. Five of her children received degrees in mathematics itself. Another successfully completed two years as a math major and then became an electrician, later obtaining a degree in his chosen math-related field. Two others earned degrees in chemistry.
That makes eight. The youngest rebelled and earned his undergraduate degree in physical education. In middle age, however, he took more courses and became a mathematics teacher.
Susie Johnson McAfee was not high in socioeconomic class, but she is a superb example for the skeptical or discouraged. Admittedly, she may have had some unusual intellectual resources, but she obviously also had serious obstacles.
Our country seems mired in destructive teaching techniques. As the opening quote indicates, a top U.S. high school student at the 95th percentile has learned mathematics comparable to a Japanese youngster in dead center. One reason is our structural bias against real mathematics. Twenty-four states have no math requirements whatsoever for prospective elementary school teachers, and the others require passing only a minimal test or course. Yet all non-handicapped children can learn, regardless of sex or ethnicity. Until states require elementary school teachers to learn more math, parents are their children's major hope.
In other times and places it was assumed that people would learn if taught. Plato's Meno, written over 2,300 years ago, relates how a slave boy learned mathematics merely by being asked questions. Plato argued that we all knew math from our previous life and that it need only be recalled. His theology is debatable, but his conclusion of human teachability has been verified again and again.
Mathematical power is in jeopardy in our culture because the popular assumption is "that even with hard work some children are doomed to low levels of achievement." Harold Stevenson and James Stigler, who compared classes in Minneapolis and Chicago to classes in Japan and China, claim that, despite U.S. rhetoric about equality, our educational system assumes that math power depends more on innate ability than work. They argue that parent involvement through high school is critical and that although school reform is necessary, it will not succeed unless parents "become more involved in their children's education and develop appropriate expectations."
Fortunately, parents can help their children without a great deal of formal background themselves. It takes some work, of course, but usually it will be fun, and parenting is not always easy. Keeping your child from mathematical misery may prevent serious difficulty in the long run.
Our children need courage to tackle complex ideas. If you follow the guidelines of this book, I can't promise that your child will be outstanding, but I am quite sure that he or she will be comfortable with math. Unless you insist upon A's (or your child falls into one of the scholastic traps that I will describe), you and your youngster will be satisfied with her or his grades. If you welcome more math into your home life, your entire family will be glad that you did.
What Is Mathematics?
Mathematics is the study of patterns and the use of patterns to solve problems. Mathematics is a language. Mathematics is a spirit. It is shared most effectively as a journey with love, joy, and wonder.
Math power evolves from a combination of knowledge, ability, and attitudes. These are closely related. Without knowledge, we can't develop ability. Without ability, we can't use knowledge. Without a hopeful attitude we won't acquire either math knowledge or ability.
Computation (routine calculation) is to mathematics as spelling is to literature. It has value in itself, but it is no substitute for the real thing. Just as good literature entices young children to read, real mathematics should be provided at the earliest stages of mathematical involvement. If it is not, children get a mistaken belief about what math is. Too often this belief haunts them for a lifetime.
As real mathematics struggles for survival in our culture, it becomes increasingly urgent that parents share real mathematics with their own children. Patterns are everywhere. You can enjoy showing your child relationships between patterns in one place and those in another. If you are alert, as you will be after reading this book, you can find many ways to make mathematics come alive in your child's life—and your own.
What are patterns? Patterns involve relationships, resemblances, and rearrangements—noticing what is the same and what is different in various contexts. Patterns occur in geometry, in music, and in human behavior. Numbers may measure these patterns, but math includes much more than just numbers.
We must use patterns to cope with the overwhelming details in our lives. Nobody can process all the data we experience daily. Math power helps us resist being crushed under the onslaught. It is frightening how often mathematical nonsense creeps into public discussion.
* A politician attacks his opponent for raising taxes more times although the number of times that a person supported a tax increase does not affect our pocketbook. The total size of the increases, along with how the taxes and the services they buy are distributed among the taxpayers, determine how they affect our family spending power.
* An insurance company refuses to renew a customer because of the number of times the customer has collected from the company, even though each collection is tiny. Just one collection from a typical customer costs the company far more.
* Some states have passed laws requiring additives in fuels to decrease the percentage of pollutants in the emissions. However, since the additives also lower the fuel mileage, the amount of pollutants remains constant. Consumer prices rise and the emissions with additives appear to be more harmful medically.
* Some campuses and municipalities have needlessly frustrating traffic patterns. Some applied mathematical analysis could enable vehicles to travel much more efficiently.
Mathematics is one way of understanding the world. It is not the only way, and I wouldn't claim it is the best way. But without it, our perceptions are incomplete.
Why Is Mathematics Important?
Why focus specific attention on children's mathematical growth? There are personal, interpersonal, career, and civic reasons.
Mathematics was meant to bring understanding and joy. Most mathematicians are enviable people. Their ability to "center" affects the rest of their lives. Only one of the 75 black mathematicians in the New Jersey study wasn't enthusiastic about his or her career. (She made over $60,000 in the mid-1980s; one suspects she could have made changes if she was really unhappy.)
Intellectual growth gives inner freedom. If I really believe that nobody can fetter my mind, then there is no limit on what I can think or do. Some people can cultivate such freedom in amazing circumstances. Harriet Tubman and Dietrich Bonhoeffer are two memorable examples from the horrors of U.S. slavery and German Nazism, respectively. We can wonder how they managed to maintain their independent perspective and courage under such circumstances. But most of us are not so inwardly strong, especially as children.
The usefulness of mathematics in everyday life is undeniable, but overemphasized. "What if literacy were taught only by means of parking tickets, job applications, tax forms, and other material that people will need to read? That would be an accurate analogy to much of the traditional curriculum in mathematics." Thus mathematician Dr. Neal Koblitz and computer scientist Dr. Michael Fellows argue for including entertaining, enticing math topics in the primary grades. People who don't do math quickly too often fall prey to the vultures of society, but there are happier reasons for learning math.
In this culture, math comfort strongly affects an individual's identity. Mathematical confidence generates self-esteem useful in many facets of life. Conversely, feeling mathematically crushed curtails both private and public options. It goes far beyond competence while cooking, driving, making things, and managing finances. The sense of defeat felt by people uncomfortable with mathematics is hard to overestimate.
Even if you have been a victim of an anti-mathematics system, your child need not have a similar fate. Parents and teachers can unfetter talent in their little ones that was stifled in themselves. As they do so, the adults also grow, but usually not as fast or as far as their children.
Mathematics, like most interesting activities, builds bridges between people. The international mathematics community extends remarkable trust and caring among its own. For years my best insight into what was happening in the Soviet Union was via the Notices of the American Mathematical Society. When Canadian mathematician Lee Lorch arrived for his first scientific visit to the Soviet Union in 1966, he was warned by a Canadian diplomat in Moscow that he would have a very lonely four months because Soviet mathematicians would be afraid to have Western ties. Dr. Lorch went directly from the embassy to his hotel room, where there were already several invitations from Soviet mathematicians to their homes. In each Soviet city it was the same, and the political views of his hosts varied widely. Mathematics was enough to begin deep friendships.
People connect through specific mathematical enthusiasms. For example, people who enjoy chess, bridge, fantasy games, and computer hacking have created their own subcultures. More broadly, the ability to perceive and organize patterns enhances the speaking and writing skills that are so valuable for connecting with others.
Parents and children can develop a wonderful bond through math. You can establish collaborative problem-solving habits. When your child is a successful adult, you will feel a sense of satisfaction as you reflect upon your mathematical sharing long ago when she or he was a child
As our world becomes ever more complex, career opportunities increasingly depend upon mathematical enthusiasm. Surveys consistently indicate that four of the most promising careers are mathematical—actuary (and other types of financial analysts), accountant, computer specialist, and statistician. Other mathematical careers include telephone networks, drug research, and scheduling. Environmental jobs include setting standards, helping industry comply with them, helping governments enforce them, and testifying during litigation. New York City saved a great deal of money by hiring mathematicians to plan where to place its fire stations and how different teams should respond to fires in specified locations.
Careers in science, engineering, and finance do not require a math major but expect comfort and competence in mathematics. Majors not requiring math tend to lead to low-paying jobs. Secure jobs with decent pay usually require mathematical competence.
Even traditionally female careers require math for top positions. It is not just that credentials for leadership in nursing, social work, and elementary education require mathematics and statistics courses. Also, the actual job requirements of analyzing information, allocating resources, planning schedules, and controlling budgets draw upon the information and skills learned in these courses. Furthermore, leaders in any field need to contemplate overview patterns and to solve problems analytically, abilities developed by "real" mathematics.
Mathematics helps unmask false prophets who continually try to deceive the math-anxious. To make intelligent communal decisions, people need to know math. For over two thousand years all educated people studied mathematics because it empowered the mind and was considered essential for wise citizenship.
Now that we all may be voting citizens, we all need mathematics. Just understanding a newspaper requires math knowledge.
The success of a modern democracy depends upon the ability of many citizens to analyze complex social and economic patterns. Such analysis requires not just numbers but sophisticated mathematics.
Excerpted from Math Power by Patricia Clark Kenschaft. Copyright © 2006 Patricia Clark Kenschaft. Excerpted by permission of Dover Publications, Inc..
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