What is math modeling?

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Young people are frequently exposed to ambitious dreams of changing the world, and a practical way of expressing said interest is through research in science fairs; however, do science fairs provide everyone an equal opportunity to produce meaningful research? One study by the University of Toronto¹ suggests that students who have laboratory exposure typically dominate high school science fairs, such as Intel, Google, and Siemens. For the majority of high school students around the world, this is not the case. Most do not have access to a high-level laboratory such as the ones used for the winning contestants, creating a high visible barrier of entry to research for the average high school student. However, one field that has been historically underrepresented in our education system can alleviate the needs of aspiring high schoolers who are not fortunate enough to have laboratory access: mathematical modeling. Mathematical modeling is essentially a logical approach to research, relying on statistics and mathematical algorithms to perform an analysis. The accessibility of the topic allows ANYONE to produce meaningful results and impact the world.

Outside of the education perspective, mathematical modeling is an integral part of our society, as it is the foundation for many economic, medical, and engineering research fields. Without mathematical modeling, we would live in a world without traffic engineering, stock market analytics, and tremor predictions.

The importance of mathematical modeling and its low barrier of entry to research poses the question: why aren’t high schoolers being introduced to a topic this important?

In the United States, the high school math curriculum typically only covers four themes: 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. However, in real life applications, math typically connects with research that is expressed through mathematical modeling; and the purpose of math is to explain the phenomena of our physical and digital world with creative problem solving.

Although there are existing websites that explain math modeling, many of them are founded on undergraduate and graduate level subjects. Without college level knowledge, high schoolers will not only find themselves struggling with learning the material but can also quickly lose interest in producing possible changes in the world through research. Take Ebola modeling, for example, the prerequisite to understand the existing algorithm 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 Monte Carlo Simulation, the epidemic can be simply described as two line ifelse statements in Matlab instead of walls of text involving partial differentiation. This simplification of a traditionally difficult subject is the reason why AoCMM exists. We want to LOWER the barrier of entry for research by giving any student guidance and resources to perform meaningful analysis of real world scenarios.

Addressing the issue of overly complicated introductory resources, AoCMM offers free courses for mathematical modeling that students can easily understand with 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.

If students need help, we offer online tutoring at an affordable cost that will assist their research. Additionally, we plan to partner with local high schools to motivate ambitious students to conduct research independently. We will further expand our volunteer program where all students and staff interested can work in each of our eight subchapters to stimulate the research among the students.

aocmm To supplement educational interests, AoCMM also hosts an annual modeling competition for those envisioning broader challenges. One unique aspect about AoCMM’s variant of the typical modeling competition is the time length. To compare, take a look at the High School Mathematical Competition in Modeling’s (HiMCM) time span: 36 hours. This restriction leaves students barely enough time to gather necessary data and construct a simple 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: a test of stamina rather than a test 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 rather crucial to her success. By now increasing the time limit from three days to fifteen, AoCMM ensures 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. Thus, failed initial attempts will not simply end the competition, but rather teach the teams how to build upon their models, which closely resonates with the trial and error seen in a modern research environment.

For this team competition, the problems are designed by cooperation between AoCMM and its affiliated world class professors: they hail from the likes of 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 none other than a research-oriented reward: scholarship money and education products to enable the best team to pursue bigger and better prospects. Last year, our competitions success garnered $6,000 of sponsorship from the Art of Problem Solving, the American Statistical Association, Elite Academy, the American Mathematical Society and other great organizations. This year’s competition will be held from 10/4 to 10/18. For more information, please visit http://aocmm.org.

This year’s competition will be held from 10/4 to 10/18. For more information please visit http://aocmm.org.

Citation:
Bencze, John Lawrence, and Gervase Michael Bowen. “A National Science Fair: Exhibiting Support for the Knowledge Economy.” Taylor & Francis Online. N.p., 2009. Web. 18 July 2016. http://www.tandfonline.com/doi/abs/10.1080/09500690802398127?tab=permissions

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