Mathematical modeling is an open-ended research subject where no definite answers exist for any problem. Math modeling enables thinking outside the box to connect different fields of studies together including statistics, algebra, calculus, matrices, programming and scientific writing. As an integral part of our society, it is the foundation for many economical, medical and engineering research fields. Without mathematical modeling, we would live in a world without traffic engineering, stock market analytics and tremor predictions.
Columbia University mathematician Henry O. Pollak has noted: “Problem solving may not refer to the outside world at all. Even when it does, problem solving usually begins with the idealized real-world situation in mathematical terms, and ends with a mathematical result. Mathematical modeling, on the other hand, begins in the ‘unedited’ real world, requires problem formulating before problem solving, and once the problem is solved, moves back into the real world where the results are considered in their original context."
So why aren’t more high schoolers being introduced to a topic this important?
In the U.S., the typical high school math curriculum covers only four topics: algebra, geometry, statistics and calculus. Society pushes high schoolers to see math as a binary subject with only true or false answers solved through one standardized method. On the flipside, subjects like art and computer science are presented in a much more creative light, often involving open interpretation and numerous creative outcomes. However, in daily life, math typically connects with applicable research in the form of mathematical modeling, and the purpose of math is to explain the phenomena of our physical and digital world with creative problem-solving. The accessibility of math modeling allows anyone to produce meaningful results and make an impact on the world.
Due to the poor illustration of math in most American schools, there is a great need to emphasize the practical applications of mathematics and create opportunities for motivated students to expand on their own education. As a result, the nonprofit Association of Computational and Mathematical Modeling (AoCMM) aims to inform, excite and educate high school students about mathematical modeling. Initially founded by students of Cupertino High School and later expanded to several chapters across the U.S., China and India, AoCMM strives to remove the stigma attached to high school mathematics and instead open the eyes of promising students to the importance of math.
AoCMM also hosts an annual modeling competition for those envisioning broader challenges. Traditionally, prestigious science competitions around the world have been dominated by students from wealthier backgrounds who can work in laboratories of private institutions at their own convenience. However, their experiences do not tell the story of the world's high school students as a whole. Most students have access to few or no resources and end up discouraged from doing research for reasons entirely out of their control.
We as an organization want to address this issue and try to bridge the gap by introducing people to mathematical modeling. It overcomes the two main issues an average high schooler faces regarding research: lack of laboratory exposure and costly resources. Mathematical modeling can be done by anyone and everyone, and promoting this subject will in turn reduce the general negative stigma towards mathematics. With more confidence in their mathematical abilities, students will be able to produce meaningful research and carry their passion towards STEM throughout life as opposed to having their interests stripped away due to the high barrier of entry to the research world.
For AoCMM’s team competition, the problems are designed by cooperation between our organization and world-class professors from universities such as Northwestern, Brown and Harvard. After the competition, each submitted paper is analyzed by judges and critiqued via annotations. The prize for winning our research-oriented competition is scholarship money and education products to enable the best team to pursue bigger and better prospects. Last year, our competitions garnered $6,000 in sponsorship from Art of Problem Solving, the American Statistical Association, Elite Educational Institute, Maplesoft and other great organizations. More than 100 teams from 13 different countries participated in its annual mathematical modeling competition.
One unique difference between AoCMM and other math modeling competitions is the amount of time allotted. For example, the High School Mathematical Competition in Modeling from the Consortium for Mathematics and Its Applications has a time span of 36 hours. This restriction leaves students barely enough time to gather necessary data and construct an elementary model, let alone presenting it in the form of a research paper. These types of competitions significantly discourage novice students from entering the field of research. Regardless of knowledge, every student suffers from the same issue: competitions are becoming tests of stamina rather than tests of capability. AoCMM’s 2015 Grand Prize Winner Charlin Duff pointed out that balancing the time spent working and sleeping across the three days of the competition was key to her success. Consequently, AoCMM has increased its time limit from three days to 15, ensuring that all competitors can thoroughly elaborate on every idea they have in their paper while facing a level of pressure similar to that in professional STEM fields. As a result, teams will have the time to build their models upon their mistakes, closely resonating with the trial and error seen in a modern research environment.
Although existing websites do explain math modeling, many of them assume readers come from the undergraduate and graduate level. Without college-level knowledge, high schoolers will not only struggle to learn new material, but also quickly lose interest in the subject. Take modeling the Ebola epidemic as an example. The prerequisite of understanding the existing solutions is differential equations, a subject typically taught in junior year of undergraduate studies. However, there is a much simpler way that high schoolers can easily understand: by using a method known as the Monte Carlo Simulation, the epidemic can be more simply described with two line if-else statements in programming code instead of walls of text involving complicated differentiation. This simplification of a traditionally difficult subject is exactly why AoCMM exists. We want to lower the barrier of entry for research by giving all students guidance and resources to perform meaningful analysis of real-world scenarios.
Addressing the issue of overly complex introductory resources, AoCMM offers free courses for mathematical modeling that are easily understood with just an algebra background. Students will be able to follow many of our comprehensive, yet simple resources, which include tutorials on mathematical algorithms, MATLAB, statistics and many more research-related subjects.
This year, AoCMM also plans to offer free, high-quality courses online for K-12 students and partnering with schools in the three countries where it currently operates. Its website, AoCMM.org, already features a series of tutorials ranging from basic math algorithms to detailed feedback on math modeling papers from previous years.
Tony Lin is the chief finance officer at the Association of Computational and Mathematical Modeling. Sasan Erfan is the chief marketing officer.