What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success Read Free Page B

because they lecture and they have students work individually, but they also ask students great questions, engage them in interesting mathematical inquiries, and give students opportunities to solveproblems, not just rehearse standard methods. Such teachers are wonderful and I wish there were many more of them. The type of traditional teaching that concerns me greatly and that I have identified from decades of research as highly ineffective is a version that encourages passive learning. In many mathematics classrooms across America the same ritual unfolds: teachers stand at the front of class demonstrating methods for twenty to thirty minutes of class time each day while students copy the methods down in their books, then students work through sets of near-identical questions, practicing the methods. Students in such classrooms quickly learn that thought is not required in math class and that the way to be successful is to watch the teachers carefully and copy what they do. In interviews with hundreds of students from such classes, I have asked them what it takes to be successful in math class, and they almost always give the exact same answer: pay careful attention. As one of the girls I interviewed told me, “In math you have to remember; in other subjects you can think about it.”
    Students taught through passive approaches follow and memorize methods instead of learning to inquire, ask questions, and solve problems. I have interviewed hundreds of students taught in such ways and they usually reflect on their experiences saying such things as “I’m just not interested in, just, you give me a formula, I’m supposed to memorize the answer, apply it, and that’s it,” and “You have to be willing to accept that sometimes things don’t look like—they don’t seem that you should do them. Like they have a point. But you have to accept them.” Students who are taught using passive approaches do not engage in sense making, reasoning, or thought (acts that are critical to an effective use of mathematics), and they do not view themselves as active problem solvers. This passive approach, which characterizes math teaching in America, is widespread and ineffective.
    When students try to memorize hundreds of methods, as students do in classes that use a passive approach, they find it extremely hard to use the methods in any new situations, often resulting in failure on exams as well as in life. The secret that good mathematics users know is that only a few methods need to be memorized and that most mathematics problems can be tackled through the understanding of mathematical concepts and active problem solving. I am now working with the PISA (Programme for International Student Assessment) team, based in the OECD (Organisation for Economic Co-operation and Development) in Paris. The PISA team not only collects data on students’ math achievements, but it also collects data on the strategies students use in mathematics and relate these to performance. 15 One of the strategies the PISA team has identified is “memorization.” Some students think their role in math classrooms is to memorize all the steps and methods. Other students think their role is to connect ideas. These different strategies link, unsurprisingly, to achievement, and the students who memorize are the lowest achieving in the world. The highest-achieving students are the ones who think about the big ideas in mathematics. Unfortunately, in most US classrooms mathematics is presented as a set of procedures, leading students to think that their role in learning mathematics is to memorize. This PISA result gives us an interesting insight into the low performance of students in the United States, relative to the other countries tested.
    I have spent my research career conducting unusual studies of learning. They are unusual because, instead of dropping in on students to see what they are doing in math classes, I have followed students through years of middle