COMAP Exploring Math Modeling in and Outside of the Classroom Webinar Series #1
The Introduction to Math Modeling Webinar Series is a series of 6 - 7 free webinars organized by COMAP held from October 2020 through May 2021. The goal of the webinar series is to promote student and teacher engagement in mathematical modeling in the classroom and through participation in math modeling contests such as HiMCM and MCM/ICM. The webinars are led by classroom teachers, professors and mathematicians. These experts hope to demonstrate how math modeling can be used to foster mathematical curiosity and engage students in real world problem solving. This engagement can serve to promote student agency and help students see themselves as learners and doers of mathematics.
Webinar #1
Introduction to Math Modeling in Middle School and High School: The Midge Problem
We can invite all students into the mathematical conversation by offering them opportunities to engage in real-world math modeling tasks. These tasks can help students move away from prescriptive solution methods to more creative and thoughtful engagement in problem-solving.
In this session, we will explore the midge problem: In 1981, two new varieties of a tiny biting insect called a midge were discovered by biologists W.L. Grogan and W.W. Wirth in the jungle of Brazil. They dubbed one kind of midge an Apf midge and the other an Af Midge. The APf midge is a carrier of a debilitating disease while the Af midge is harmless.
We will build mathematical models and try to answer the question: How can biologists distinguish between the Apf and the Af midges? Join us to see how middle and high school students can use a variety of mathematical ideas to engage in this problem and experience for yourself the iterative nature of math modeling.
Panelist:
Maria Hernandez, Retired Math Teacher @ The NC School of Science and Mathematics
In 1989, the Mathematical Contest in Modeling offered a wonderful problem about distinguishing a "good" midge from a "bad" midge. It is a fine example of a problem that can be used to excellent effect with students at many different levels. We have been giving a version of this problem to our Precalculus students for the past few years.
Typically, the problem is presented after we have spent time studying techniques of data analysis and linear curve fitting. A unique aspect to this problem, as you'll see, is rather than fit a line to a set of data, the students are asked to use what they've learned to fit a line to the absence of data! What follows is the statement of the problem and five different approaches that student groups have used in solving it.
The shared hope and vision of the Consortium for Mathematics and its Applications (COMAP) and the Society for Industrial and Applied Mathematics (SIAM) is that this report motivates the educational community to make a place for mathematical modeling in curriculum, from pre-K through undergraduate levels. Further, that the value and importance of the skills required to execute math modeling effectively - logical thinking, problem solving, sensitivity analysis, and communication to name a few - are recognized and nurtured.
