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.*

**Related Posts:**

Emphasis on Math Stops Some from Full Participation in Education, Economy

Reducing Math Obstacles to Higher Education

Remedying NEBHE’s Journal Piece on Developmental Math: A Letter to the Editor

Math Task Force’s Bad Calculation

Successful Developmental Math: “Review-Pretest-Retest” Model Helps Students Move Forward

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## A Model for Math Modeling

by Tony Lin and Sasan Erfan

August 30, 2016

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

anyoneto 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

lowerthe 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 Linis the chief finance officer at the Association of Computational and Mathematical Modeling.Sasan Erfanis the chief marketing officer.Related Posts:Emphasis on Math Stops Some from Full Participation in Education, Economy

Reducing Math Obstacles to Higher Education

Remedying NEBHE’s Journal Piece on Developmental Math: A Letter to the Editor

Math Task Force’s Bad Calculation

Successful Developmental Math: “Review-Pretest-Retest” Model Helps Students Move Forward

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Tags: math modeling, Columbia University, Association of Computational and Mathematical Modeling (AoCMM)

## One Response to “A Model for Math Modeling”

Yes I whole heartedly agree with this article that it is past time that math modeling incorporated into the K-16 curricula. The need is urgent.

I hope that AoCMM will join in collaboration with those educators who have toiled in this area for many decades. They have developed and promoted, innovative, free or low cost ways to train teachers and educate K-16 students. Example, The Creative Learning Exchange, CLE (http://www.clexchange.org/ ), located in Acton MA, has an extensive, rich, online repository of math models (system thinking/dynamics) for K-12 educators in all subject areas including English and the social sciences. The CLE website has teacher training materials and lesson plans too. The BioQUEST Curriculum Consortium (http://bioquest.org/ ), also contains a wealth of resources for faculty teaching undergraduate life science courses. BioQUEST has for 30 years promoted student-driven science inquiry and runs annual week-long workshops for college faculty. Check out the ESTEEM collection of modeling assignments to download and run with MS EXCEL (http://bioquest.org/esteem/esteem_result.php ). More recently NSF has funded the 5 year QUBES Project, Quantitative Undergraduate Biology Education and Synthesis, (https://qubeshub.org/ ) “to improve learning opportunities for all students enrolled in undergraduate biology courses by reflecting the centrality of quantitative approaches in modern biology.” One innovation is (free) access to what can be expensive modeling software that runs online for students and their instructors. This bypasses the need to install modeling software on classroom computers.

Why is all this important? As presented in the article, we need to prepare students for the current and future career realities where math and modeling are critical to business, finance, engineering, and life sciences. For example, researchers are succeeding in unraveling biological mysteries once considered too complex and difficult to even attempt. NIMBios, National Institute for Mathematical and Biological Synthesis,( http://www.nimbios.org/ ) a NSF sponsored Center, supports “cutting-edge, cross-disciplinary research at the interface of mathematics and biology.”

I have mentioned only a few of the organizations laboring to bring math and modeling into K-16 classrooms. There are others out there with lengthy track records. I am pleased that AoCMM is adding their expertise and resources.

Linda M. Grisham, Ph.D., Board chair, BioQUEST Curriculum Consortium