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UI Researchers Use Proof and Argument to Help Teachers, Students in Mathematics

September 20, 2016

University of Idaho mathematics and education researchers will work with teachers across the Northwest beginning this fall to explore the success of a method for improving mathematics learning in eighth grade. The four-year project examines teaching and learning math with and through viable argumentation.

The National Science Foundation awarded a nearly $3 million grant to the project, which is led by David Yopp, a mathematics professor with a joint appointment in UI’s College of Science and College of Education. Rob Ely, an associate professor of math, and Anne Adams, an associate professor of curriculum and instruction, also are part of the project, along with analytical experts RMS Research.

The researchers will work with 60 teachers and up to 2,000 students across Idaho, Washington and Montana to implement a method that uses proof, reasoning and argumentation to help students improve their mathematical thinking and understanding. The project’s goal is to demonstrate that when students learn mathematics through high-level reasoning, their entire mathematical proficiency improves.

Yopp said that teaching and learning with and through viable argumentation, including proofs, helps students understand what math really is: developing ideas and addressing whether they are mathematically valid. Just as students learn the scientific method or how to write a persuasive essay, they can learn the rules for reasoning in math.

“As students solve problems, they make claims about what they think is true, then they focus on the structure of the mathematics to either prove or refute their claims,” Yopp said. “This focuses students on how the mathematics works and gives them access to understanding the mathematics.”

This project follows a 2014-15 pilot project in which Yopp and his research team tested the argumentation method for teaching algebra in several northern Idaho classrooms. They found participating students not only improved their skills in using proof and reasoning, but also improved their mathematical skills across the board.

The researchers also found in the pilot project that students who may have been uncomfortable in math class in the past began speaking up, because the method gave them a clear structure for talking about math, Yopp said.

“When students learn to prove mathematical claims, what they are really learning is how to establish truth without appealing to power or authority,” Ely added. “Learning to show for yourself that something is irrefutably true, not just because the teacher said so — what could be more empowering than that?”

Yopp emphasized that the argumentation method enhances traditional approaches to teaching and learning mathematics.

“We’re not displacing the role of practice and skill development,” Yopp said. “We’re making the mathematical notions and ideas that students develop richer and more meaningful to them, which makes mathematics easier to apply and use in other contexts.”

The researchers will begin working with an initial group of 30 classrooms later this month, helping teachers adapt their existing lesson plans or implement a set of lessons developed by the researchers. These teachers also will attend a summer professional development course at UI.

“It can be very challenging to make big changes in one’s teaching practices,” Adams said. “Ongoing professional development embedded in teachers’ own practice has been shown to be effective in helping teachers make changes. We will support them in many ways, including understanding argumentation in mathematics, developing mathematics lessons using argumentation, and supporting implementation of those lessons.”

During the project’s first two years, a second group of 30 classrooms will not implement the argumentation method, but will serve as a comparison to the classrooms that do.

In the project’s third year, the researchers will introduce the argumentation method to the second group of teachers and step away from the first group. They will observe how effective the method continues to be in the first group of classrooms once support from the researchers has ended.

Yopp said the National Science Foundation hopes the project not only will provide valuable information about using argumentation in mathematics education, but also will influence how universities train teachers to teach math.

Media Contact: 
Tara Roberts
University Communications

About the University of Idaho

The University of Idaho, home of the Vandals, is Idaho’s land-grant, national research university. From its residential campus in Moscow, U of I serves the state of Idaho through educational centers in Boise, Coeur d’Alene and Idaho Falls, nine research and Extension centers, plus Extension offices in 42 counties. Home to nearly 12,000 students statewide, U of I is a leader in student-centered learning and excels at interdisciplinary research, service to businesses and communities, and in advancing diversity, citizenship and global outreach. U of I competes in the Big Sky and Western Athletic conferences. Learn more at