Professor Stresses the Language of Math

by Susan Gaidos, University News Service

Professor Justin J. Price Imagine asking for directions and being told, "I know how to get there, but I can't describe it." Award-winning mathematics professor Justin J. Price found a similar situation in his classroom when he asked students to describe various mathematical processes. For many, the task of interpreting mathematical language was next to impossible.

"There's a lot of truth in saying, 'If you can't explain it, you don't understand it,'" Professor Price says. He devised a course to boost students' mathematics and language skills by requiring them to write explanations for mathematical operations. Price says that writing forces students to think deeply about mathematical processes and express themselves precisely.

Asking students to write about mathematics seemed only logical, Professor Price says, noting that in all other disciplines of study, writing is required in some form, such as term papers or lab reports.

"Can you imagine a student who has taken eight years of French and still cannot write or speak a simple sentence?" he says. "We have simply neglected an important part of students' education. We pay the penalty in frustration when we find our students practically illiterate in the language of mathematics. If my students parachuted into Algebraland, most of them would starve because they could not speak the language."

Professor Price notes that the language of mathematics includes not only numbers and symbols, but also words that describe with precision the types of procedures used to solve mathematical problems. "Using words such as 'multiply' rather than 'times' or 'inverse' rather than 'opposite' helps students focus more clearly on what they are doing," he says. In his class, Professor Price instructs students to describe solutions so that readers who are not familiar with mathematics can learn from their explanations. He also requires students to follow the rules of grammar and punctuation, and encourages them to strike a balance between words and mathematical symbols. "This process initially requires more thought and time on the part of the students, but it helps make them think more clearly," Professor Price says.

He has used his mathematical-writing approach in a wide range of mathematics courses at Purdue, from freshman calculus to graduate courses in real analysis, and particularly, in a course he developed for prospective teachers. In recent years, Professor Price has become involved in teacher training, working to help school teachers nationwide adopt his approach for their classrooms.

One of the benefits of the method is that it can be used to increase mathematical performance at all grade levels and for all students, according to department head Leonard Lipshitz. "Teachers often adopt new teaching approaches to reach students who are having trouble learning new concepts or procedures," he says. "This approach, however, has proven to be beneficial to top students as well, as it helps them to think in a logical manner, thus increasing their understanding of the process."

His attentive attitude toward teaching has not gone unnoticed. After being named by students as one of the top 10 teachers in the School of Science in 1978, 1980 and 1982, Price was named Outstanding Teacher in the School in 1986. In the fall of 1993, Professor Price was selected by the Mathematical Association of America to receive the organization's 1993 award for distinguished college or university teaching.

"I am very grateful to the Association for this award," says Professor Price. "It is a particular honor to be one of three chosen from such a distinguished field of sectional awardees. I have had many satisfactions in teaching: seeing a student's eyes suddenly light up with understanding, imparting enthusiasm for the subject and a desire to learn more, convincing future teachers that math is more than a collection of rules. But these were private awards; to be cited publicly is truly wonderful."

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