Equation for Excellence: How to Make Your Child Excel at Math First Chapter
Why Study Math?
(You might want to share this with your children.)
When students are told why they need to study math, the answer usually has something to do with either day to day life or applications to science and technology. The problem with the first type of explanation is that it is an obvious and transparent lie. The second type of explanation actually tends to turn many students away from mathematics.
The “day to day” explanation tells students that they will need math for their daily activities. For example, they will need to calculate the tip at a restaurant, or determine how much they should pay for their groceries. Most students are quick to point out that this problem can be solved by carrying around a calculator. And anyone who is worried about running out of batteries can carry around a spare set of batteries, or even two calculators. Even cell phones have built-in calculators.
The arguments against the “day to day” explanation continue. In daily life, you never need to do more than add, subtract, multiply, or divide. Why learn trigonometry? Why study calculus? Why do anything beyond arithmetic? Even math-oriented jobs rarely require any advanced math. When I worked as an actuary, the only math I used on the job was multiplication and the occasional exponent (the actuarial profession is one of the most math-oriented professions in the world.)
The other argument focuses on science and technology. We need math to design space-shuttles and satellites, to work in laboratories, and to build the newest computers. In one way this argument makes sense. Much of that work requires intensive use of advanced math. But very few people work in those areas, and those that do are usually motivated more by internal passion than by external factors.
In fact, from the perspective of most students, there is very little external motivation to be a scientist. The strongest external motivators for most teenagers are money, fame, power, popularity, and sex. Scientists tend not to embody any of those. For every million dollars a scientist makes, the businessmen for whom he works make a billion. For every famous scientist, there are a thousand famous musicians and actors. The scientists who made the nuclear bomb were not the ones to use it; that power belonged to politicians. And in American culture, scientists have no more popularity or sex appeal than anyone else.
Thus, this argument not only fails to motivate students, but it actually does the reverse. A student with no interest in being a scientist who hears the technology argument now thinks that advanced math is useful only for scientists. Thus, he does not need to learn it. If his goal is personal gain, his time is better spent doing almost anything else – studying politics, learning to play the guitar, spending time with friends, working out, or thinking of ways to make himself rich. Math becomes just an annoying requirement.
So then why should a student learn math at all?
Kings used to play chess to learn military strategy. When I first heard this at age ten, the idea struck me as unbelievably stupid. In chess the bishop can move only diagonally. The knight can move in an L shape. A real soldier, on the other hand, can move in any direction. How would studying chess help in any real war?
I had, of course, completely missed the point. Strategy has nothing to do with L shapes or diagonals. A chess player learns to anticipate his opponent. He learns to look for strong positions, rather than short-term gains. He learns to make intelligent sacrifices, and be wary of the strategic ploys of his opponent. He learns to predict his opponent’s future responses to his actions, rather than focusing on the immediate gains. This mental discipline makes his mind sharper, and he becomes a much more capable strategist.
Similarly, math is not important because it teaches a student how to use trigonometry to measure the height of a building, or because it lets a student find the area of a triangle. It is important because it develops a student’s ability to analyze and solve unfamiliar problems. Math develops concrete reasoning, spatial reasoning, and logical reasoning. Math does not just develop skills that can be applied to science and technology; when math is taught right, it develops the student’s fundamental cognitive architecture, increasing his intelligence. The student will develop the logical reasoning skills that allow a lawyer to analyze a legal situation and to present a coherent and convincing argument. He will develop the ability, essential to any businessperson, to isolate the key components of a system. He will develop mental skills that can be applied to any type of problem. His mind will become faster, sharper, and more precise.
What lifting weights does for muscles, math does for the mind. In no sport will an athlete suddenly lie down on his back and lift a weight 10 times. However, the vast majority of athletes do the bench press. Why? It makes them stronger, and thus prepares them for athletic endeavors in general.
When you teach a child math in the right way, you are giving him the gift of a sharper and more powerful intelligence. You are helping him actually develop his mind. You are making him smarter. You are giving him the ultimate ability to succeed in the world, and to build a happier life for himself. You are not just making him better at math; you are making him better at thinking.
This book will show you how to make any student excel at math, even a student who is extremely lazy or innately bad at math. You will learn how to motivate any student and what to teach. Whether you are great at math or barely able to do algebra, there are techniques in this book that you can use to make your child excel.
There are a few things you need to know before continuing. The first is that the methods in this book are designed to be effective. They are not designed to be easy, nor are they designed to be fun.
On the flip side, this book does not advocate a “beat your kids to make them strong” type of approach. I never yell at any student, and I obviously do not use any physical punishment. If you do your part right, you will never need to raise your voice to effectively teach math.
Similarly, the techniques here are not ones designed to cause antagonism. Many of my students spend a good portion of their tutoring sessions frustrated with a math problem, begging for an answer, or literally groaning. And yet the ones who complain the most are the ones who seem to appreciate my training the most. In fact, many of those students pay for part of their tutoring fees with money received from allowances, jobs, and internships, rather than switch to a more moderately priced tutoring service. Money that they could spend on entertainment they voluntarily spend to learn math.
Why would a teenager actually spend his own money to learn math? I believe that it is because at some level every person desires ability more than entertainment. Although we often believe the opposite, most teenagers would rather gain intelligence than momentary enjoyment. I may make my students struggle more than another educator would. But my methods bring out their very best, and they can see it.
About half of this book focuses on motivation. Right now, some of the finest minds in the country are using every advertising trick they know of to persuade your child to act in certain ways. Alcohol and tobacco companies spend millions of dollars per year on advertising, as do hundreds of junk food, clothing, and entertainment companies. Thus, in today’s world, weak motivational methods simply cannot compete. Parents and educators who want to be effective must use motivational methods as powerful as those used by today’s professional persuasion artists.
In fact, you will have to be even more persuasive. Unlike an advertiser promoting entertainment or recreation, to effectively teach your children math, you will have to persuade your child to take the more difficult and rewarding path.
For example, many schools allow students to use calculators. As this book explains, chronic calculator use can dramatically weaken a child’s math abilities. Thus, you may be the one persuading your child to not use his calculator, even though his teacher encourages calculator use.
While that task might seem impossible, the methods in this book will show you what to do. Once students understand the damage that calculator use causes, most of them voluntarily stop using calculators completely. Several of my students have even taken the SAT, the most important test of their lives, without calculators. Almost all of them returned with perfect SAT math scores.
The fact that you will be working to fundamentally improve your child’s life will make motivation a bit easier. Even when kids complain, they know what benefits them. And over time, as they see themselves becoming more intelligent and more successful, motivation will become easier.
The rest of this book explains what to teach, and how to teach it. It explores the most effective methods for teaching math, including the legendary Asian system and the methods that underlie the success of my company, Arvin Vohra Education.