What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (2 page)

The Common Core math curriculum is not the curriculum I would have designed if I had had the chance. It still has far too much content that is not relevant for the modern world and that turns students off mathematics, particularly in the high school years, but it is a step in the right direction—for a number of reasons. The most important improvement is the inclusion of a set of standards called the “mathematical practices.” The practice standards do not set out knowledge to be learned, as the other standards do, but ways of
being mathematical.
They describe aspects of mathematics such as problem solving, sense making, persevering, and reasoning. It is critically important that students work in these ways; these actions have been part of curricula in other countries for many years. Now that these methods of thinking are part of the US curriculum, students should be spending time in classrooms using mathematics in these ways.

The inclusion of these practices means that the tasks students work on will change. Students will be given more challenging tasks and spoon-fed less. Instead of being told a method and then practicing it, they will need to learn to choose, adapt, and use methods. Students need to learn to problem solve and persist when tasks are longer or more challenging. This is really important work for teachers and students. My main problem with the Common Core standards is that they require teachers to engage students in thinking about what makes sense and problem solving; but such activities, which involve going deeper into the mathematics, take more time. In the elementary and middle grades, the content has been reduced so that teachers and students can take the time to work in these productive ways, but the high school standards are as packed as ever with obsolete content that works against teachers being able to go into depth and give students the experiences they need. For more information on the potential impact of the Common Core go to http://youcubed.org/parents/2014/why-we-need-common-core-math.

Many people think that countries such as China, who top the world in mathematics achievement, do so by drilling students in content, but this is far from the truth. In Shanghai, the highest scoring region of China, I watched numerous high school lessons, and in no lesson did the teachers work on more than three questions in an hour. What was staggering was the depth to which teachers and students delved into each question, exploring every aspect of the mathematics. In all of the lessons, the students talked more than the teacher as they discussed what they were learning. We recorded one of the lessons, and it can be seen on YouCubed. This is a model of mathematics teaching that we need in the United States.

Currently, more than half of all US students fail mathematics, and mathematics is a harshly inequitable subject.
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,
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When our classrooms change—when students are encouraged to believe that they can be successful in mathematics and are taught using the high-quality teaching methods we know work—the landscape of mathematics teaching and learning in the United States will change forever. This book gives readers—whether teachers, administrators, or parents—the knowledge needed to make the important changes required for our students in the United States and for the future of our society. I hope you enjoy it, whether you are a new reader or one of the many who read the original
What’s Math Got to Do with It?
, and are looking to be reenergized by the new ideas shared within this updated edition.

Understanding the Urgency

A
number of years ago in California, I attended a math lesson that I will never forget. Several people had recommended that I visit the class to see an amazing and unusual teacher, and as I climbed the steps of the classroom I was excited. I knocked on the door. Nobody answered, so I pushed open the door and stepped inside. Emily Moskam’s class was not as quiet as most math classes I have visited. A group of tall adolescent boys stood at the front, smiling and laughing, as they worked on a math problem. One of the boys spoke excitedly as he jumped around explaining his ideas. Sunlight streamed through the windows, giving the front of the room a stagelike quality. I moved quietly among the rows of students to take a seat at the side of the room.

In recognition of my arrival, Emily nodded briefly in my direction. All eyes were on the front, and I realized that the students had not heard the door because they were deeply engaged in a problem Emily had sketched on the board. They were
working out the time it would take a skateboarder to crash into a padded wall after holding on to a spinning merry-go-round and letting go at a certain point. The problem was complicated, involving high-level mathematics. Nobody had the solution, but various students were offering ideas. After the boys sat down, three girls went to the board and added to the boys’ work, taking their ideas further. Ryan, a tall boy sporting a large football championship ring, was sitting at the back and he asked them, “What was your goal for the end product?” The three girls explained that they were first finding the rate that the skateboarder was traveling. After that, they would try to find the distance from the merry-go-round to the wall. From there things moved quickly and animatedly in the class. Different students went to the board, sometimes in pairs or groups, sometimes alone, to share their ideas. Within ten minutes, the class had solved the problem by drawing from trigonometry and geometry, using similar triangles and tangent lines. The students had worked together like a well-oiled machine, connecting different mathematical ideas as they worked toward a solution. The math was hard and I was impressed. (The full question and the solution for this math problem, as well as the other puzzles in this book, are in
appendix A
.)

Unusually for a math class it was the students, not the teacher, who had solved the problem. Most students in the class had contributed something, and they had been excited about their work. As the students shared ideas, others listened carefully and built upon them. Heated debates have raged between those who believe that mathematics should be taught traditionally—with the teacher explaining methods and the students watching and then practicing them, in silence—and those who believe that students should be more involved—discussing ideas and solving applied problems. Those in the “traditional” camp have worried that student-centered teaching approaches sacrifice standard methods, mathematical correctness, or high-level work. But this class was a perfect example of one that would please people on both sides of the debate, as the students fluently made use of high-level mathematics, which they applied with precision. At the same time, the students were actively involved in their learning and were able to offer their own thoughts in solving problems. This class worked so well because students were given problems that interested and challenged them and, also, they were allowed to spend part of each lesson working alone and part of each lesson talking with one another and sharing ideas about math. As the students filed out of the room at the end of class, one of the boys sighed, “I love this class.” His friend agreed.

Unfortunately, very few math classes are like Emily Moskam’s, and their scarcity is part of the problem with American math education. Instead of actively engaging students in mathematical problem solving, most American math classes have them sitting in rows and listening to a teacher demonstrate methods that students neither understand nor care about. Far too many students in America
hate
math and for many it is a source of anxiety and fear. American students do not achieve well and they do not choose to study mathematics beyond basic courses, a situation that presents serious risks to the future medical, scientific, and technological advancement of society. Consider, for example, these chilling facts:

• In a recent international assessment of mathematics performance conducted in sixty-four countries across the world, the United States ranked a lowly thirty-six.
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When levels of spending in education were taken into account, the United States dropped to the bottom of all the tested countries.

• Currently, only 1 percent of undergraduates major in math,
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and the last ten years have shown a 5 percent decline in women math majors.
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• In a survey of middle school students, more than half said they would rather eat broccoli than do math, and 44 percent would rather take out the trash.
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• Approximately 50 percent of students in the United States attend two-year colleges. About 70 percent of those students are placed into remedial math courses repeating the math they took in high school. Only one in ten of the students passes the course. The rest leave or fail.
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For about fifteen million students in the United States, math ends their college career.

In September 1989, the nation’s governors gathered in Charlottesville, Virginia, and set a challenge for the new millennium: American children should top the world in mathematics and science by the year 2000. Now, fifteen years after that time goal, the United States sits near the bottom of international rankings of mathematics achievement.

Achievement and interest among children is low, but the problem does not stop there. Mathematics is widely hated among adults because of their school experiences, and most adults avoid mathematics at all costs. Yet the advent of new technologies means that all adults now need to be able to reason mathematically in order to work and live in today’s society. What’s more, mathematics could be a source of great interest and pleasure for Americans, if only they could forget their past experiences and see mathematics for what it is rather than the distorted image that was presented to them in school. When I tell people that I am a professor of mathematics education, they often shriek in horror, saying that they cannot do math to save their lives. This always makes me sad because I know that they must have experienced bad math teaching. I recently interviewed a group of young adults who had hated math in school and were surprised at how interesting math was in their work; many of them had even started working on math puzzles in their spare time. They could not understand why school had misrepresented the subject so badly.

This aversion to math is reflected in our popular culture as well: in an episode of
The Simpsons,
Bart Simpson returns school textbooks to his teacher at the end of the year, noting that they are all in perfect shape—and in the case of his math book, “still in their original wrapping!” Bart’s disinclination to open his math book probably resonated with many of his school-age viewers. Barbie’s first words may have done the same with her young owners. When she finally started speaking, her first words were “Math class is tough”—a feature that the manufacturers quickly and correctly withdrew. But Barbie and Bart are not alone—an Associated Press–America Online (AOL) news poll showed that a staggering four out of ten adults said that they
hated
math in school. Twice as many people hated math as any other subject.

Then again, amid this picture of widespread disdain there is evidence that mathematics may have the potential to be quite appealing. The mathematical TV show
NUMB3RS
developed a cult following during its first season. Sudoku, the ancient Japanese number puzzle, has gripped America. Sudoku involves filling nine 3 × 3 squares so that the numbers 1 to 9 appear only once in each row or column. Americans everywhere can be seen hunched over their number grids before, during, and after work, engaging in the most mathematical of acts—logical thinking. These trends suggest something interesting: school math is widely hated, but the mathematics of life, work, and leisure is intriguing and much more enjoyable. There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms, and an interesting set of ideas that is the math of the world and is curiously different and surprisingly engaging. Our task is to introduce this
second version to today’s students, get them excited about math, and prepare them for the future.

The Mathematics of Work and Life

What sort of mathematics will young people need in the future? Ray Peacock, a respected employer who was the research director of Phillips Laboratories in the UK, reflected upon the qualities needed in the high-tech workplace:

Lots of people think knowledge is what we want, and I don’t believe that, because knowledge is astonishingly transitory. We don’t employ people as knowledge bases, we employ people to actually do things or solve things. . . . Knowledge bases come out of books. So I want flexibility and continuous learning. . . . [A]nd I need teamworking. And part of teamworking is communications. . . . When you are out doing any job, in any business . . . the tasks are not 45 minutes max, they’re usually 3-week dollops or one-day dollops, or something, and the guy who gives up, oh sod it, you don’t want him. So the things therefore are the flexibility, the teamworking, communications, and the sheer persistence.

Dr. Peacock is not alone in valuing problem solving and flexibility. Surveys of American employers from manufacturing, information technology, and the skilled trades tell us that employers want young people who can use “statistics and three-dimensional geometry, systems thinking, and estimation skills. Even more important, they need the disposition to think through problems that blend quantitative work with verbal, visual, and mechanical information; the capacity to interpret and present technical information; and the ability to deal with situations when something goes wrong.”
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The mathematics that people need is not the sort of math learned in most classrooms. People do not need to regurgitate hundreds of standard methods. They need to reason and problem solve, flexibly applying methods in new situations. Mathematics is now so critical to American citizens that some have labeled it the “new civil right.”
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If young people are to become powerful citizens with full control over their lives, then they need to be able to reason mathematically—to think logically, compare numbers, analyze evidence, and reason with numbers.
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Businessweek
declared that “the world is moving into a new age of numbers.” Mathematics classrooms need to catch up—not only to help future employers and employees, or even to give students a taste of authentic mathematics, but to prepare young people for their lives.

Engineering is one of the most mathematical of jobs, and entrants to the profession need to be proficient in high levels of math in order to be considered. Julie Gainsburg studied structural engineers at work for more than seventy hours and found that although they used mathematics extensively in their work, they rarely used standard methods and procedures. Typically the engineers needed to interpret the problems they were asked to solve (such as the design of a parking lot or the support of a wall) and form a simplified model to which they could apply mathematical methods. They would then select and adapt methods that could be applied to their models, run calculations (using various representations—graphs, words, equations, pictures, and tables—as they worked), and justify and communicate their methods and results. The engineers engaged in flexible problem solving, adapting and using mathematics. Although they occasionally faced situations when they could simply use standard mathematical formulas, this was rare and the problems they worked on were “usually ill-structured and open-ended.” As Gainsburg writes, “Recognizing and defining the problem and wrangling it into a solvable shape are often part of the work;
methods for solving have to be chosen or adapted from multiple possibilities, or even invented; multiple solutions are usually possible; and identifying the ‘best’ route is rarely a clear-cut determination.”
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Gainsburg’s findings echo those of other studies of high-level mathematics in use in such areas as design, technology, and medicine.
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Gainsburg’s conclusion is definitive and damning: “The traditional K–12 mathematics curriculum, with its focus on performing computational manipulations, is unlikely to prepare students for the problem-solving demands of the high-tech workplace.”
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Conrad Wolfram agrees. He is one of the directors of Wolfram/ Alpha, one of the biggest mathematical companies in the world, which also owns Mathematica. Conrad is heading a movement to stop mathematics from being reduced to calculating. In his TED talk watched by more than one million people, he describes mathematical work as a four-step process: first posing a question, then constructing a model to help answer the question, next performing a calculation, and finally converting the model back to the real-world situation by thinking about whether it answered the question (see http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers).

He then makes an important point. Teachers spend 80 percent of the time teaching students the calculation step when they should be using computers for that part and spending more time helping students to ask questions and to set up and interpret models. Sebastian Thrun, the CEO of Udacity, appears in my online course making an important point for teachers and parents: we do not and cannot know what mathematics students will need in the future, but the best preparation we can give them is to teach them to be quantitatively literate, think flexibly and creatively, problem solve, and use intuition as they develop mathematical ideas.
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The chapters that follow will explain and illustrate how this happens in classrooms.