Multiple Methods

Do you remember watching your math teacher solve a problem on the blackboard and then diligently trying to copy her technique to solve the other problems on your worksheet? That’s the way many of us learned math. The problem is, we absorbed some counterproductive messages in the process. As it turns out, there isn’t always one best way to solve a given problem.

In his research, Associate Professor Jon Star is pushing hard to craft some new messages, by showing students how important it is to use multiple strategies when solving math problems.

“Math problems can be approached in many different ways,” says Star, an educational psychologist and former math teacher. “When a teacher insists that there is only one way, or only one best way, to solve a problem, students are missing out. There is great value in allowing them to explore and contrast many different ways to solve problems.”

Star and colleague Bethany Rittle-Johnson of Vanderbilt University have conducted a number of studies over the past decade that demonstrate the benefits of comparing a variety of problem-solving approaches for learning math, especially algebra. And their work has paid off: the US Department of Education’s Institute of Education Sciences echoed their findings in two recent publications by the What Works Clearinghouse: a new problem-solving guide for grades 4-8 and a new algebra practice guide for middle and high school students.

Building on this work, Star, Rittle-Johnson, and colleague Kristie Newton of Temple University developed a set of curriculum materials designed to be used in middle and high school algebra classrooms. The goal is to expose students to multiple problem-solving strategies and to build deep and flexible mathematical knowledge.

“In math class, you should have opportunities to talk about different approaches, and comparison helps us to think not only about what works in mathematics, but also about how and why things work,” says Star. “Our materials are designed to be used by algebra teachers to supplement their regular curriculum, to provide a stronger focus on the learning of multiple strategies.“ The curriculum materials were developed with middle and high schoolers in mind, but there are some applications for elementary schoolers as well. Educators can access the curriculum online at no cost.

In several recent studies, Star and his colleagues have studied the impact of teachers’ use of these materials on their students’ learning. He calls the results quite promising.

“Our research suggests that using our curriculum materials was not especially difficult for teachers, and that students enjoyed and benefited from the emphasis on multiple strategies,” says Star. “Many teachers already include multiple strategies for certain topics that they teach; our materials are designed to expand this focus across all topics in algebra.”

Additional Resources

• Read "Developing Flexibility in Math Problem Solving."
• Visit the Contrasting Cases website.
• Use the Contrasting Cases curriculum.
• Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students

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