How to use math modeling to engage students

Posted January 27, 2020 by Joshua neubert

At a Glance:

The U.S. has stagnated in how many students are proficient in mathematics on international assessments. The cause for this may be in how we structure our mathematics instruction by focusing on contrived teach-to-the-test methodologies.

Math modeling is one strategy for teachers to re-focus their efforts on real-world, problem-solving mentalities to better engage students in mathematics.

Mathworks Math Modeling (M3) Challenge is an opportunity that high school math educators can use to better engage their students in the math curriculum. Registration for M3 Challenge is open through February 21st, 2020.

 This featured article was written with Mathworks Math Modeling (M3) Challenge. M3 Challenge, sponsored by MathWorks and organized by Society for Industrial and Applied Mathematics, is an exciting opportunity to connect 11th and 12th grade students with real-world problem-solving challenges. Registration is open through February 21st, 2020.


Since the beginning of the modern formal education system, the mathematics classroom has been a kingdom of its own, separated from the world around it. This land of numbers, symbols and signs has its own language. For some students, this is an exciting wonderland where crisp, clean calculations lead to discoveries that capture even the wildest of imaginations. However, for many this kingdom of numbers remains a strange, foreign and often scary land  – one where they do not understand the meaning of the symbols and, perhaps most importantly, one where they do not recognize the importance of even speaking the language.

The 2017 National Assessment of Educational Progress (NAEP) showed that student proficiency in math in the U.S. has stagnated at 33%. On the 2015 Program for International Student Assessment (PISA), the U.S. ranked 38th out of 71 countries. These numbers have been commonly cited as demonstrations that our schools are failing us. However, the problem is not with our students, or with our teachers, but rather with the way our formal education system separates math into its own walled gardens and demands that students focus on answering simplified, standardized test questions with little connection to the real world. This focus on teaching to the test has ripped a wide gap in mathematics education between the real-world excitement of mathematics and what our students get in their classrooms.

Even though much of the educational system is still based on teach-to-the-test methodologies, there is hope for change. More and more schools have been adopting innovative educational programs that help connect their students with real-world applications of mathematics. In particular, math modeling has become an important subset of these programs demonstrating a great power to help students focus on the problem-solving value and usefulness of mathematics.


Math modeling is a process that uses mathematics to represent, analyze, make predictions or otherwise provide insight into real-world phenomena.


In 2015, the Consortium for Mathematics and its Applications (COMAP) and Society for Industrial and Applied Mathematics (SIAM) released a report, Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME). The report explains how math modeling can be a solution to the challenges many schools face with engaging their students in learning math.

Math modeling is a process that uses mathematics to represent, analyze, make predictions or otherwise provide insight into real-world phenomena. Used in a variety of scientific disciplines, models are abstractions of reality that respect reality, and can lead to scientific advances, be the foundation for new discoveries, and help leaders make informed decisions.

Math modeling is different from simply creating word-problems to help students conceptualize a mathematics process. The example using two trains moving in opposite directions and asking the students to calculate the distance between them is the classic example of a word-problem. These types of problems do little to connect students to the real-world problem-solving power of mathematics.

The GAIMME report illustrates the evolution from a “regular” math problem to a modeling problem through the figure noted above. Further explanation in the distinctions between these problem types were provided from Ben Galluzzo (Clarkson University) in a 2019 NCSM talk on math modeling. Going left to right from a math problem to word problem, to application problem to modeling problem we can see the changes in how students are engaged with the mathematics.

While converting problems into a math-modeling structure will not solve all of our mathematics classroom woes, it does help with many. To help educators do this, SIAM has created a series of resources that can be used to incorporate math modeling problems into the classroom curriculum; find these handbooks, guidelines, videos, sample problems and more under the “Resources” tab on the M3 Challenge website.

Mathworks Math Modeling (M3) Challenge is an opportunity to use custom designed challenges with your students that use this problem-solving structure to engage students. You can learn more about this contest on the M3 Challenge website and find many sample problems from past years that you can use with your students. Additionally, M3 Challenge provides up to $100,000 in scholarship awards to students each year!

Registration for this Challenge is open through February 21st, 2020, and is completely free. We encourage any high school math educator to explore the resources provided through M3 Challenge. The experience is likely to help you increase your students’ engagement and performance on mathematical assessments, as well as truly increasing their interest in mathematics by including a real-world, problem-solving structure in your classroom.