Math for Life: Crucial Ideas You Didnt Learn in School

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The law that replaced No Child Left Behind—the Every Student Succeeds Act, enacted in —has eased the consequences but has hardly weakened the emphasis on testing. Since , the curriculum in many elementary schools has narrowed to little more than a steady diet of reading and math. And when test scores fail to rise after third grade—as they often do, especially in high-poverty schools—subjects like history and science may continue to be relegated to the far back burner through middle school.

To some extent, it does make sense to focus on reading skills in the early years.

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One component of reading is, like math, primarily a set of skills: the part that involves decoding, or making connections between sounds and the letters that represent them. But educators have also treated the other component of reading—comprehension—as a set of skills, when in fact it depends primarily on what readers already know. What inferences can you make? Rarely do the topics connect: Students might read a book about bridges one day, zebras the next, and clouds the day after that. One of those cognitive scientists spoke on the Tuesday panel: Daniel Willingham, a psychology professor at the University of Virginia who writes about the science behind reading comprehension.

If they put all the information in, their writing would be tedious. Students from less educated families are usually the ones who are most handicapped by gaps in knowledge. Another panelist—Ian Rowe, who heads a network of charter schools serving low-income students in New York—provided a real-life example during his remarks. The unfamiliar word made it hard for her to understand the passage. When Rowe asked her to spell the word, it turned out to be rugby. The implication is clear.

Not to mention that learning content like this can be a lot more engaging for both students and teachers than the endless practice of illusory skills. According to Shanahan, no evidence backs up that practice. In fact, Shanahan said, recent research indicates that students actually learn more from reading texts that are considered too difficult for them —in other words, those with more than a handful of words and concepts a student doesn't understand.

What struggling students need is guidance from a teacher in how to make sense of texts designed for kids at their respective grade levels—the kinds of texts those kids may otherwise see only on standardized tests, when they have to grapple with them on their own. That view was endorsed by Marilyn Jager Adams, a cognitive and developmental psychologist who is a visiting scholar at Brown University. We have a major problem with our education systems, not just in America, but in many of the old, industrialized countries. With that amount of waste, there's something wrong with the system— with impersonal forms of education, with people sitting in rows and not discovering the things that impassion them or invigorate them or turn them on.

That's increasingly the case with this culture of standardized testing. It's totally counterproductive. Looking back at our own education, we came alive in certain sorts of lessons with certain teachers when we were given an opportunity to do things that invigorated us. And when you find things you're good at, you tend to get better at everything because your confidence is up and your attitude is different.

Too often now we are systematically alienating people from their own talents and, therefore, from the whole process of education. This isn't, to me, a whimsical argument, like, "Wouldn't it be nice if we all did something we liked.

For some people, it's gymnastics; for some people, it's playing the blues; and for some people, it's doing calculus. We know this because human culture is so diverse and rich—and our education system is becoming increasingly dreary and monotonous. It's no surprise to me that so many kids are pulling out of it. Even the ones who stay are often detached. Only a few people benefit from this process. But it's far too few to justify the waste. People often associate creativity with the individual. But is there a social dimension to creativity that's particularly relevant in the 21st century?

Most original thinking comes through collaboration and through the stimulation of other people's ideas. Nobody lives in a vacuum. Even people who live on their own—like the solitary poets or solo inventors in their garages—draw from the cultures they're a part of, from the influence of other people's minds and achievements.

In practical terms, most creative processes benefit enormously from collaboration. The great scientific breakthroughs have almost always come through some form of fierce collaboration among people with common interests but with very different ways of thinking. This is one of the great skills we have to promote and teach—collaborating and benefiting from diversity rather than promoting homogeneity.

We have a big problem at the moment—education is becoming so dominated by this culture of standardized testing, by a particular view of intelligence and a narrow curriculum and education system, that we're flattening and stifling some of the basic skills and processes that creative achievement depends on. Look at Thomas Edison. He was one of the most prolific inventors in American history.

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He had over 1, patents in the U. Patent Office. But actually, Edison's great talent was mobilizing other people. He had teams of cross-disciplinary groups working with him. They gave themselves clear objectives and tight deadlines and pulled out every stop to work collaboratively. So there's no doubt in my mind that collaboration, diversity, the exchange of ideas, and building on other people's achievements are at the heart of the creative process. An education that focuses only on the individual in isolation is bound to frustrate some of those possibilities. But people think they can't teach it because they don't understand it themselves.

They say, "Well, I'm not very creative, so I can't do it. But there are actually two ways of thinking about teaching creativity. First of all, we can teach generic skills of creative thinking, just in the way we can teach people to read, write, and do math. Some basic skills can free up the way people approach problems—skills of divergent thinking, for example, which encourage creativity through the use of analogies, metaphors, and visual thinking. I worked a while ago with an executive group of a Native American community. They wanted me to talk to them about how they could promote innovation across their tribe.

We sat around a boardroom table for the first hour, and I guess they were expecting me to get some flip charts out and show them some techniques. We did a little of that, but what I actually got them to do was to get into groups and draw pictures of some of the challenges they're facing as a community. Well, the minute you get people to think visually—to draw pictures or move rather than sit and write bullet points—something different happens in the room.


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Breaking them up so they aren't sitting at the same desk and getting them to work with people they wouldn't normally sit with creates a different type of dynamic. So you can teach people particular skills to free up their own thinking, of valuing diversity of opinion in a room. But in addition to teaching those skills, there's also personal creativity. People often achieve their own best work at a personal level when they connect with a particular medium or set of materials or processes that excites them.

My new book, The Element , is about finding your passion. I talked to many people—gymnasts, musicians, scientists, an amazing woman who was a pool player. Whether it was music or jazz or the triple jump, each of them found something that they resonated with, that they had a personal aptitude for. If you combine a personal aptitude with a passion for that same thing, then you go into a different place creatively. You know, Eric Clapton was given his first guitar about the same time I was. Well, it worked out for Eric in a way it didn't quite work out for me.

He got the hang of it, but also combined it with tremendous passion. You can't assess people—in general—for being creative because you have to be doing something to be creative.


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  • If you're working in math class and the teaching is encouraging you to look for new approaches, to try new ways of thinking, then of course you can begin to judge the level of creativity and imaginativeness within the framework of mathematics as you would within the framework of music or dance or literature. I make a distinction between teaching creatively and teaching for creativity. Teaching creatively means that teachers use their own creative skills to make ideas and content more interesting.

    Some of the great teachers we know are the most creative teachers because they find a way of connecting what they're teaching to student interests. But you can also talk about teaching for creativity, where the pedagogy is designed to encourage other people to think creatively.

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    You encourage kids to experiment, to innovate, not giving them all the answers but giving them the tools they need to find out what the answers might be or to explore new avenues. Within particular domains, it's perfectly appropriate to say, "We're interested in new and original ways you can approach these issues. Whether there would be an individual grade for creativity, that's a larger question.

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    Certainly giving people credit for originality, encouraging it, and giving kids some way of reflecting on whether these new ideas are more effective than existing ideas is a powerful part of pedagogy. But you can't reduce everything to a number in the end, and I don't think we should. That's part of the problem. The regime of standardized testing has led us all to believe that if you can't count it, it doesn't count. Actually, in every creative approach some of the things we're looking for are hard, if not impossible, to quantify.