# Bite-Size Modeling

Written by

Cheryl Gann, NCSSM Durham Chair of Mathematics

May 2021

Welcome to the NCSSM Math Department’s blog! We’ll be posting here monthly to share our thoughts and ideas, and hopefully create opportunities to learn from others too.

If you have come to our annual conference or seen any of us present elsewhere, you’ll know we are huge proponents of mathematical modeling. But what is mathematical modeling?

At NCSSM, we consider a mathematical experience in which students make choices about how to use mathematics to create representations of a real-world process to be a form of mathematical modeling. Modeling is the process of creating representations (models) that help us understand a phenomenon while using mathematical concepts and the principles and language of mathematical symbolism. There are many different illustrations of the modeling process. I like this one from the SIAM Modeling Getting Started and Getting Solutions Handbook:

"By taking just a little bit of extra time and having students generate the questions, I gave them a chance to think about the scenario more, consider what other information they might want, and primed them for future modeling experiences."

I have often heard teachers wonder about how to introduce modeling to students. Incorporating smaller problems that require students to think and struggle is beneficial in its own right. This also helps prime the students for more extensive modeling in the future. One way this can be done is by giving students problems to work on before showing them a new technique. Another approach can be to take away some details of a problem so that they must make decisions about what information they need. Let’s take a look at an example of some bite-size modeling.

The graph shows data from a 2015 leak of methane at Aliso Canyon facility. What do you notice? What do you wonder? What questions do you have about the data and the leak?

Students could offer a variety of responses. What are some questions that occur to you? What do you think your students might say or ask about?

When I shared this graph with my students, I wanted to develop different numerical methods for integration in calculus and have them calculate the total amount of methane that leaked. After this discussion, we began working on a project that provided them with more information and questions to explore.

But by taking just a little bit of extra time and having students generate the questions, I gave them a chance to think about the scenario more, consider what other information they might want, and primed them for future modeling experiences.

How could you introduce some bite-size modeling experiences in your classes?