What do you remember about learning mathematics? Timed tests might come to mind – racing to recall facts; or maybe absurd problems asking when two trains traveling in opposite directions will meet, but never telling why the trains are on the same track. Perhaps mathematics was assuring – that something can be right and true, regardless of others’ opinions. Maybe you recall the pride of earning an A or the sense of defeat when a class made you feel as if you were not a “math person.”
Faculty at Montana State University and the University of Montana are collaborating with Montana 4-H in a project called Montana Models. Montana Models helps youth see that mathematics is more than memorizing facts, solving obscure problems, and making the grade. Participants use mathematics to answer questions that are significant to them and their communities. They learn their perspectives matter, and mathematics involves being playful, curious, and persistent – qualities many already possess and use in their daily lives. Most importantly, Montana Models helps participants see that a “math person” can be anyone who recognizes, develops, or uses mathematical tools to make the world a better place.
Montana Models focuses on mathematical modeling, a process that uses mathematics to represent, analyze, make predictions, or otherwise provide insight into real-world phenomena. Modeling has longstanding importance in the mathematical sciences and is receiving increased attention in schools. It is interdisciplinary and prepares youth to use mathematics in every aspect of their personal, civic, and professional lives. Modeling tasks are different from problems in most textbooks. Even word problems, designed to help students understand applications of mathematics, are written with a question posed and methods prescribed. Modeling tasks start with problematic situations and broad aims, but without clear questions or solution paths. Modelers, rather than textbook writers or teachers, pose questions and decide what mathematical tools are most appropriate.
In the first year of the Montana Models project, youth from six Montana communities investigated diverse community-based problems including highway safety, recycling, and rural economic health. They engaged in research, networked with professionals and community members, and considered the ways math and statistics help communities understand and resolve local issues.
For example, one team identified deer-human interactions as a significant community issue, and narrowed the problem to focus on deer strikes on a particular stretch of highway. Another team wanted to make a pedestrian crossing safer. They used statistics to investigate full-time resident, part-time resident, and visitor awareness of the crosswalk, garnering the attention of news outlets and the Montana Department of Transportation.
Supporting youth engagement in modeling does not always involve big problems and complex mathematics. Modeling follows the pattern of what happens in creative human activities: Step 1: See something that is worth doing. Step 2: Do it. Step 3: Check to see if you have actually done it. Parents and teachers can nurture young people’s inclination to use math through everyday interactions, even when they are not explicitly about math or statistics. Here are three ways to support youth to use mathematics in everyday life:
• Affirm youth’s problem-solving dispositions within and outside of mathematics. Youth solve problems across their lived experiences. They research strategies for video games, learn challenging music, or simply dive in and try something new. These dispositions, and others, are useful in mathematics. Affirming youth as resourceful, persistent, and willing to take risks builds strong problem-solving identities that can translate to mathematical spaces.
• Nurture curiosity about patterns and variability. Youth usually study mathematics in contrived situations. Textbooks use simplified contexts because complex, real-world situations can obscure specific mathematical ideas. Mathematical modelers do not have this luxury. They decide how to account for the complexities that make problems messy. Ask youth to consider how patterns and variability can both be present in a situation.
For example, if the GPS predicts it will take six hours to reach a destination, ask youth to estimate their arrival time if the car stops for gas or visits a drive-through.
• Encourage civic engagement. Montana Models participants were eager to make a difference in their hometowns. They also recognized the power of mathematics to inform and persuade. Youth who are not motivated to learn mathematics for its own sake may be willing to use mathematical tools to address significant community-based problems. Ask youth why they care about local, state, or national issues. Encourage them to consider who else might care and how multiple perspectives influence how one defines and addresses problems.
Acknowledgement: This work is supported by the National Science Foundation under Grant No. 1810992.