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New Mexico State University

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NMSU professors help students, teachers appreciate math

What do you get when you put high school math teachers, future teachers and non-math majors in the same college math appreciation class? An innovative way to teach math to non-majors in both college and high school, according to David Finston and Doug Kurtz, New Mexico State University math professors.

NMSU math professors Dave Finston, left, and Doug Kurtz demonstrate the mathematical concepts for distinguishing surfaces for a course they taught together this spring.

Math appreciation, a course taught for students not majoring in math, is designed to demonstrate the mathematical concepts underlying things we see in everyday life, said Finston, who heads the mathematical sciences department at NMSU. When he began teaching math appreciation several years ago, he disliked the textbooks that were available.

"They included neat topics," he said, "but they would begin to explain the mathematics and then just stop. I thought it insulted students to imply they couldn't understand it.";; So Finston started from scratch, evolving topics, examples and demonstrations for his class. The topics included symmetry, probability, acoustics, encoding and surfaces.

"I tried to find instances of serious math in the real world that we take for granted," he said. For example, a UPC code is not a random number. The number itself has error-detecting traits, he said. Many students don't realize the deep, yet understandable mathematics involved.

Recently it was suggested that local high schools might be interested in the course. As a result of the high schools' block scheduling, students may finish their required math credits in three years, Finston said. He envisioned offering math appreciation as a fourth class option.

Armed with a $22,000 Eisenhower Foundation grant administered by the New Mexico Commission on Higher Education, Finston developed a course to prepare current high school teachers and secondary math education majors for teaching math appreciation to high-schoolers.

"We have a long history of working with the teachers here," said Kurtz. "Many of them are willing to try something new, but they need materials first. They will get involved, but they don't have time to start from scratch."

Finston and Kurtz teamed up in the spring to teach a unique course, with students including NMSU non-math majors and secondary math education majors, as well as area high school math teachers. They followed many of Finston's topics, often using advanced technology, such as interactive Internet sites to explore symmetry and software to analyze musical tones, developed by John Pierce, the department's computer operations manager. The class met once a week, alternating between lecture periods and discussion times.

On discussion weeks the class split into six groups, each including a high school teacher, a future teacher and a handful of math appreciation students. Finston and Kurtz circulated around the room, answering questions and explaining concepts as the groups worked to understand the previous week's lecture.

The idea was for the non-math majors to better understand the concepts and for the teachers and future teachers to better understand how to explain the concepts, Finston said. The math appreciation students wrote reports showing their grasp on the lessons. At the same time the teachers, with input from the math appreciation students, developed lessons for teaching high-schoolers. Each group received college or continuing education credits for passing the course.

"The most pleasantly surprising part was watching a math appreciation student going to the board to explain something to a high school teacher," Finston said. "They all respected, worked with and learned from each other."

"This is not a typical math class," said Paula Mabrey, a Mayfield High School algebra and geometry teacher. "They try to teach us how math applies to things. It's a critical thinking math class."

The others in her group agreed more classes should be taught this way, with team-teaching and group discussion opportunities. Finston and Kurtz worked with each other to keep it from being just a lecture, they said. Then the group sections let them share ideas with each other.

Even the teachers were "learning, rather than teaching," said Mabrey and Valerie Lopez, a secondary math education major. "It makes you realize math should be made applicable."

"This course gave me a chance to practice teaching, but also to learn from Paula as she explained things," Lopez said. "I think it should be required for all secondary education majors."

This summer, as part of the grant, Finston plans to put together a resource book containing the lessons and demonstrations developed by the class participants. He hopes this resource will encourage other teachers to adopt math appreciation at the high school level.