Angela is a good student; she's also lovely to look at - auburn hair that falls in waves, just so, smooth skin, and bright eyes that smile, but say something more, a depth, a curiosity, a hunger for life. She's also forgotten fractions. Now in the scheme of things, she's way beyond fractions: second year algebra to be exact. And she's perturbed to discover that she's forgotten how to add them.

I ask Angela to consider what might happen if she were to ask 100 random people on the subway one weekday morning if they would be kind enough to take a short little quiz on fractions to help her with, say, a little research project. It's a long commute, and there are a lot of professionals on the train into work, but I suspect her responses would include some fear and trembling, some rude "no's," and possibly one or two death threats, despite her smiling eyes.

Why do we hate math so much? After all, it's supposed to open doors, earn us more money, help us in everyday life, right? So what's wrong? Why would the average person rather clean all the toilets in a high-rise than ponder a question with fractions or do a few little factoring problems?

There are many reasons, most of them good, I'm afraid, but few of them have anything to do with the nature and beauty and essence of the subject itself. But it wasn't the essence of math that you learned in the classroom. It is among the greatest ironies of education that a subject so graceful and elegant, so able to inspire and bolster confidence, and so useful for living a joyous and effective life, should be presented in a manner that strips it of its substance and glory, and leaves students feeling bludgeoned and inept, convinced they "stink at math", unaware of its beauty, or their own precious abilities.

And they are there. Most people are convinced they are awful at math. They're wrong. Mathematics is vast; mathematical strengths and abilities come in many forms. If our view is so limited that we present math as a mere collection of techniques, then only those who can perform these techniques will see themselves as successes. But we can change our view of mathematics. And through this, change our students' view of themselves.

Jared is an athletic 14 year-old who's had his share of troubles. Discarded by his parents, he's known the inside of drug treatment centers, special schools, and psychiatric hospitals, and has witnessed shooting, violence, and drug use from an early age. I was assigned to teach him mathematics, a subject he had little use for, and could tell me in detail why not. He was bold and defiant, but when he thought no one was looking, he was also curious.

We struggled. Patience and consistency were not things Jared had learned in his short life. He wanted to fly, and the steady, sure pace of skill acquisition was not to his liking. He and the small group of students in his class didn't want to learn fractions; they wanted to learn trigonometry and calculus.

Now, between you and me, ratios are fractions, but trigonometric ratios have an aura about them that fractions don't have.

"I could teach you guys the first month of trig in a few days," I told them with some truth, and a bit of bravado, "but you'd have to stop talking long enough to let me." They let me. And they learned. Not because they are brilliant, or because I am brilliant, but because they wanted to. They tried on the image of that competency and liked what they saw and how it felt. They reasoned, and figured, and grappled with problems and found their way to solutions, on their own. There was a toughness to it that they liked, and a sense of mastery they could feel, and they could see themselves fitting into that world. In Jared's world before, the big guys had done drugs and guns. Jared can see a world now where the big guys do trigonometry and calculus.

People hate math because over and over we tell them they're not good at it. We do this through frequent testing that puts a big red mark through every "wrong" answer, as if doing math means getting right answers. We do this by teaching math as a collection of arcane manipulations that few see the reason for, or the connections between.

This erodes the confidence and self-concept of our children, but our current system fails them in an even more fundamental way. Mathematics requires thinking and reasoning, pulling together ideas and information, and then problem-solving toward a solution - without a road map or delineated instructions. This is rather like what life will ask of them. In mathematics, we have the best opportunity to praise, nurture and development these tremendously valuable skills. There are few experiences we can give them in their childhood years more valuable than that sense of their own competency and ability to find their own way, using their own strengths and skills. But we miss the chance.

Consider basketball. To watch Michael Jordan sail through the air with the greatest of ease and then describe the game as a sport of dribbling would be absurd. Yet what we have done in presenting mathematics to students is akin to taking the flight out of the sport of basketball and leaving only the dribble. Maneuvering free, soaring up and making a basket must leave the athlete with a rather good sense of himself, probably better than he feels after dribbling practice. Few kids have the equivalent experience in mathematics: maneuvering past obstacles, seeing the way clear to the goal, soaring up, and making it. Maybe this is the biggest failing of our system, because a child who accomplishes this in math - and it is available to all students, not just the 'whizzes' - knows, deep down, that if he can do that, he can do anything.

What life asks of us, mathematics prepares us for. We have all heard that, and we accept it in some vague way, thinking it refers to measurement or finances or velocity. "The true value of mathematics lies outside commonplace activity," says Jerry P. King, author of The Art of Mathematics.

Reconsider what math is. Expand your view of the subject. Challenge the stereotype that math is only about numbers, figuring, or manipulations of symbols to get a 'right' answer. Ask yourself, or your child, what is being sought, and why. Try to glimpse the bigger picture. Surprisingly, your child's textbook, in the textual material and in the colorful sidebars, will give a view of this. And don't neglect your public library. Both the children's and adult sections have a wonderful selection of books that go beyond the drudgery to give you a new view of what math is all about.

Encourage the process of discovery and reasoning. Mathematicians wonder, and seek to discover. Conclusions are derived logically, from premises clearly laid out before. This rigor of thinking and reasoning is an invaluable asset to all of us far beyond math class. Help your child see the connection between reasoning and finding the right answer. This will help you and your child see math as more than a haphazard series of manipulations and techniques, as you connect thinking to problem solving.

Permit exploration. Don't require a clear path. Accept the struggle as normal. Let your children know that mathematicians struggle just as they do. Our frequent testing and assigning grades to these tests gives students and parents the idea that the goal is to know the answer or the technique fast, right away, without errors. But this is not how mathematics is done, nor is it what math is about. Give your child permission to try a variety of paths toward a solution. The schools won't stop testing or grading, but you can de-emphasize their importance, and positively reinforce your child's wondering, exploration, and struggling.