Real MATH

Everyone is born with “an affinity for mathematics,” according to EDC’s Wayne Harvey. “But people typically underestimate their mathematical abilities,” he says. What turns many of us off is not mathematics itself, but what Harvey calls “school mathematics” or “textbook mathematics,” which he feels amounts to little more than learning the results of someone else’s work.

As director of EDC’s Division of Mathematics Learning and Teaching, Harvey has been working to shift the culture of mathematics education in this country. His goal: move away from traditional textbook instruction toward teaching that engages children in doing mathematics.

What are the shortcomings of traditional mathematics teaching?

It focuses too much on teaching students the results of mathematics. But this is not the same as teaching students to do mathematics. Real mathematics is not only, or even primarily, the facts in the textbook. Real mathematics is what you do when you are challenged by something mathematical, when you find the tools to act on it, when you make progress toward a solution, when you gain insight on something new. That kind of reasoning is useful to people in all walks of life. It isn’t that knowing basic mathematical facts and skills is not important; it’s critical actually. But those facts are only useful when used as a tool for doing something much more powerful—thinking mathematically.

Are all students capable of “thinking mathematically”?

Absolutely. Mathematics is a way of understanding the world that is relevant to all of us. But often in the early grades, certain students are identified as having an interest or an affinity for mathematics and others are not. That can have a lifelong impact on the way they see mathematics.

One of our goals is to have all students acquire knowledge of mathematics that is useful to them, that empowers them, that isn’t just for those who are going on to careers in science and mathematics. In the early grades there is no reason why all students can’t become very proficient in mathematical thinking. It has to do with how we empower our teachers and what curriculum we choose.

What can be done to change the way teachers teach mathematics?

We’re very excited about our programs that allow mathematics teachers to work with mathematicians. For example, our Focus on Math project brings mathematicians together with middle and high school teachers in order to give teachers an immersion experience in mathematics. They work together, regularly and as part of their profession, on challenging problems. Dozens of teachers in five districts are involved along with a number of partners, including Boston University. The program was originally funded by the National Science Foundation for five years, but our numbers have been growing astronomically and the superintendents want to keep it going.

Teachers come away with a different perspective on what they can do in their classrooms. Teachers often tell us that they look at their struggling students differently as a result. When one of their students has a wrong answer, they don’t just discard it. They think, the student’s answer is incorrect, but I see his mathematical ideas—how can I use this information to help redirect his thinking?

What happens when you get mathematicians and teachers together?

You see a lot of different talents come together, and the mixture is very powerful. The mathematicians and teachers work together as partners. The teachers have a certain kind of knowledge that mathematicians don’t have, which is how students come to learn new ideas and what they need to do in their classrooms to help them learn. The mathematicians bring a particular expertise, which is how to use the mathematics they know to engage in a problem and move it forward to a solution.

Your new elementary school curriculum, Think Math!, focuses on teacher learning as well as student learning. Tell me more about that.

As a group, elementary school teachers do not enter the profession with a strong mathematical background. In fact, many of them carry an aversion to mathematics, like the general public. The goal of Think Math! is not only for students to learn mathematics, but for the teachers, while teaching it, to acquire new mathematical understanding as well. Teachers learn how the particular piece of mathematics they’re engaging in with their first graders relates to what students will be doing in third grade, fifth grade, middle school, and high school, so they can experience the thread of mathematical understanding that grows over time.

What makes you feel optimistic about the future of mathematics education?

Every year we sponsor a Math Expo where more than six thousand middle and high school students develop and display original mathematics projects. These are typical kids from diverse districts who are spending their time on weekends and evenings on a mathematics project that interests them. For many of these kids, it’s their first experience doing something hard in school that they enjoy doing. You can see that they have a sense of accomplishment and pride. When you meet them, they can’t stop talking about the mathematics. That makes me feel optimistic.