UW News

October 25, 2016

New NSF initiative to bring ‘real-world’ mathematics to elementary education

UW News

Julia Aguirre, associate professor of mathematics education at the University of Washington Tacoma.

Julia Aguirre, associate professor of mathematics education at the University of Washington Tacoma.Eric Wilson-Edge

The National Science Foundation will fund a three-year, $1.5 million research project to study teaching and learning of mathematical modeling in elementary education. Julia Aguirre, an associate professor of mathematics education at the University of Washington Tacoma, is one of four principal investigators leading the endeavor.

“Mathematical modeling is a process of using mathematics to analyze a ‘real-world’ problem, represent it using mathematical concepts, make predictions and take action,” said Aguirre. “It’s used widely in business, science, technology and engineering fields. But it’s not customarily been a part of elementary education.”

That may change as mathematical modeling plays an increasingly prominent role in education and employment sectors across the country. It forms a key part of Washington state’s Common Core secondary curriculum, which has in part prompted interest to introduce the principles of mathematical modeling earlier.

Mathematical modeling is an exploratory and quantitative process, utilizing graphs, equations and diagrams to decipher and illustrate the mathematical underpinnings of real-world phenomena and decision-making. The principles of mathematical modeling play a role in everything from weather forecasting and traffic patterning to election forecasts and advertising. As the prevalence of these concepts grows in education and professional life, elementary education would benefit from introducing these principles earlier, Aguirre said.

“Very little has been done to find the best approaches for introducing mathematical modeling at the elementary school level,” said Aguirre. “What we’re trying to do is lay a basic foundation for developing an elementary curriculum around mathematical modeling and providing resources to educators.”

Aguirre and her colleagues believe children are naturally curious and observant. Their experiences and knowledge from their homes and communities can help them make sense of complex issues and situations they encounter. The researchers want to work with teachers to modify traditional textbook story problems — which have one specific answer — into mathematical tasks that reflect community situations and may have multiple answers depending on assumptions students identify.

Here is a traditional mathematics problem that elementary students might typically encounter: 24 students are going on a week-long camping trip. Each student receives three healthy meals each day. How many healthy meals are needed for the camping trip?

“An approach based on mathematical modeling first introduces the situation to students: ‘How much food do we need to bring on this trip?'” said Aguirre.

That lack of structure allows students to come up with their own process to address this situation.

“They can define assumptions and take action, starting by asking themselves key questions and coming up with answers,” said Aguirre. “‘How many of us are going on this trip? How long will the trip last? What exactly constitutes a healthy meal? How far are we traveling, and do we need to factor in travel time?'”

What was once a “plug-and-chug” multiplication problem becomes a mathematics process that uses both student-generated creativity and critical thinking skills. Ideally, students would see the connection between this scenario and the problem-solving processes that occur in their lives outside of school, such as planning family trips or community events.

Aguirre and her collaborators will explore teaching concepts, methods and community-based resources to introduce mathematical modeling at the third-, fourth- and fifth-grade levels. Their team will recruit elementary school teachers in the Pacific Northwest and Southwest to meet regularly and discuss which existing teaching methods could be adapted to introduce mathematical modeling to students. They will also develop new methods as needed, and eventually test the effectiveness of these methods in classroom settings. Lesson planning tools, resources and modeling tasks will be archived in a digital library for educator to use.

“We are very excited to work with teachers to make mathematics more rich, rigorous and relevant for students,” Aguirre said.

Her partners in this endeavor are Amy Roth McDuffie at Washington State University Tri Cities, Erin Turner at the University of Arizona and Mary Foote at Queens College, City University of New York.


For more information, contact Aguirre at 253-692-4820 or jaguirre@uw.edu.