Rich, Rigorous, Relevant

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Dr. Julia Aguirre is part of a $1.5 million National Science Foundation grant to make mathematical modeling relevant to elementary school students.

UW Tacoma Associate Professor Julia Aguirre is part of a collaborative research project that has been awarded a $1.5 million dollar grant from the National Science Foundation.  Aguirre and colleagues from the University of Arizona, Queens College, City University of New York, and Washington State University Tri-Cities will spend three years investigating how teachers in grades 3-5 learn to teach mathematical modeling.  The project will emphasize connecting mathematical modeling to community and cultural sources of knowledge. 

Mathematical modeling involves a process of using mathematics to analyze, represent, make predictions, and take actions to understand real-world situations or problems.  Mathematical modeling is required material for high school students as dictated by Common Core.  Aguirre and her colleagues want to help students prepare for success which is why they’ve focused their research efforts on upper elementary grades.  

Mathematical modeling is a common tool in STEM related fields says Aguirre.  “You see it a lot in engineering, science, and related fields where the problems are messy and approximations are okay.”

This type of approach has many potential benefits.  “Mathematical modeling allows students to engage in complex problem solving, to think and reason different solutions” said Aguirre.  The one sticking point has been how this method is taught in school. 

This is the second NSF grant for Dr. Aguirre.

The standard for many years has been the use of generic examples in textbooks.  A typical problem might look like this: 24 students are going on their annual seven-day camping trip.  Each student receives four healthy meals per day.  How many healthy meals will need to be made for the camping trip?

The above example is common in that the parameters are already defined.  Students take the information given and work out the answer.  Aguirre and her colleagues want to go in a different direction.  “We want to present a scenario in which kids would think in a more meaningful and relevant way.”

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Instead of a generic math problem, students would use information from their own lives to set parameters and work out a solution.  For example, the camping trip problem would be more open-ended with students tasked with finding out how many healthy meals are needed.  “To do this, students might need to identify how many people are coming, what makes a healthy meal as well as how many meals are needed per day, among other considerations,” said Aguirre. 

The camping trip scenario could just as easily be switched to something like preparing meals at home for family or for a community event.  “We want to work with teachers to find out more about what’s going on in children’s lives, the family activities they do on the weekend, the places they go,” said Aguirre.  “If we’re able to capture the mathematical ideas that are in those community contexts and pair them with a mathematical model situation then we hope students will find this more useful to their education and to their lives.”

One question that arises from a more personalized method is accuracy.  If every student has a different set of parameters, won’t they come up with different answers?  Aguirre stresses what truly matters is how well a student understands the math concepts being used in developing the model.  “This approach provides students with an opportunity to analyze things around them that are complex, that can have different solutions depending on what they decide are the assumptions.”

In other words, finding the correct answer isn’t enough.  Students must also show how they reached their conclusion.  “A big part of mathematical modeling is being able to use your equation in a similar situation,” said Aguirre.  “The idea of generalization is important.”

Over the next three years Aguirre will work with teachers in the Southwest and Pacific Northwest to find out what works and to develop new strategies for engaging elementary students in mathematical modeling.  “One of the outcomes of this project is to have a digital library with tasks and lessons that are customized to the community,” said Aguirre.

The hope is that students will feel more of a connection to math and that, in turn, will provide opportunity.  “How can we support this notion of rich, rigorous, and relevant mathematics?” said Aguirre.  “If we were able to scale that up in a way that every child would be able to experience that kind of mathematics then I think we would see the learning opportunity gaps in schools diminish.”

Dr. Aguirre will be joined in this project by 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.

Written by: 
Eric Wilson-Edge / October 24, 2016
Media contact: 

John Burkhardt, UW Tacoma Communications, 253-692-4536 or