By Rachel Levy, Kara Maki, and Kathleen Fowler
SIAM has a vital role to play in supporting the integration of mathematical modeling into K-16 education. Current efforts led by SIAM members demonstrate that students can experience mathematical modeling and industrial mathematics in many contexts: school coursework and projects; summer, weekend, and after-school camps; and, at the undergraduate level, internships and capstone experiences. The SIAM Committee on Education, which plans to pilot new ideas in coordination with the new SIAM Activity Group on Applied Mathematics Education, would like to hear from readers about related efforts.
One important way in which applied mathematicians can help is to support teachers as they implement the Common Core State Standards for Mathematics (CCSSM) practice called “model with mathematics.” To begin, we can help teachers understand what mathematicians mean by the word “model,” which teachers use in many ways. Teachers refer to both demonstrating a mathematical technique and using manipulatives to illustrate mathematical ideas as “modeling the mathematics.” And teachers may think of traditional story problems as mathematical modeling, when they represent only a small element of what we might do as mathematical modelers.
Mathematical modeling and industrial mathematics can be a natural way to introduce more open-ended and realistic problems to school curricula. As applied and industrial mathematicians know, modeling inspires/requires creativity, teamwork, communication, and perseverance through iteration, as well as testing and evaluation of results. Students trained in these metacognitive skills will be able to master information and solve problems more easily.
The CCSSM raise the question of how mathematical modeling can be introduced as early as elementary school. A three-year NSF-funded project, IMMERSION (Integrating Mathematical Modeling, Experiential Learning and Research through a Sustainable Infrastructure and an Online Network), was initiated in an NSF–SIAM–ASA Modeling Across the Curriculum workshop. This program will be implemented at three institutions (George Mason University, Montana State University, and Harvey Mudd College), in collaboration with three school districts (Fairfax, Virginia; Bozeman, Montana; and Pomona, California); it will provide professional development in mathematical modeling for in-service elementary school teachers, follow-up lesson study in which teachers observe each other implementing lessons, and regional conferences. Outcomes of the project will include freely available online mathematical modeling resources disseminated via a new SIAM-sponsored repository of curricular resources for mathematical modeling.
Exposing students to mathematical modeling may be especially valuable in developing a diverse STEM-workforce pipeline, but we need to do more longitudinal work in this regard . Many researchers are looking into the influence of informal science experiences on students’ study and career choices. With the issue of gender imbalance, for example, mathematical ability has been shown to be a key barrier to girls’ pursuit of STEM degrees, and strongly dictates the male-female difference in choice of scientific versus non-scientific majors . The mathematics barrier persists even among female students who have had informal STEM experiences . McCreedy and co-workers found that young women participants in any of six different informal STEM programs still perceived math as a barrier to science participation. Their recommendation to informal STEM educators is to integrate math more strategically into STEM programs: “There is an opportunity for informal STEM programs to make math more engaging and meaningful by embedding it into the rich authentic activities that are so common in such programs.”
Mathematical modeling naturally embeds mathematics into studies of the world around us, including culturally and geographically relevant problems . An example of one such effort is the FOCUS program (Females of Color Underrepresented in STEM) at George Mason University, run through the STEM Accelerator program (which recently won the “2015 Program that Works” in the state of Virginia). The initially small four-day FOCUS camp has received an award from the Northern Virginia’s Business Women’s Giving Circle to expand and include 100 girls. Each day focuses on a different letter from STEM through mathematical modeling activities.
Eighth-grade girls participated in Rochester Institute of Technology’s SMASH program, gaining first-hand lab experience. After reviewing a lesson on ratios, the students created serial dilutions for an enzyme-linked immunosorbent assay. The next step was fitting the ELISA data to a line to help with a crime scene investigation. Photo courtesy of SMASH.
Teachers will need support as they begin to implement mathematical modeling tasks in the classroom. A great resource for communicating the many elements of the iterative modeling process has been developed in conjunction with the Moody’s Mega Math Challenge, a modeling competition for high school students; having gradually expanded since its introduction in 2006, the competition will soon become nationwide and then international. The materials, freely available online, include a handbook, reference cards, and a mapping between modeling practices and the CCSSM. The site also shows problems and solutions from previous years, which provide a great view of the multiple ways in which students have approached the problems. Another set of resources and problems can be found at the Hi-MCM3 and MCM/ICM sites, and at COMAP’s Modeling Forum. These COMAP programs attract teams at high school and undergraduate levels internationally to modeling competitions each year.
Two summer experiences provide examples of ways to draw young people into mathematical modeling. The SMASH Experience for Girls, held at Rochester Institute of Technology, was developed to explore how mathematical modeling can be used to help break mathematics barriers that may keep girls from entering STEM fields. This week-long experience is aimed at girls entering 8th grade. Underlying SMASH is the hypothesis that informal math and science learning experiences, guided by the principles of mathematical modeling and coupled with self-affirmation activities, will increase participants’ intrinsic motivation for learning mathematics as well as their confidence in their ability to do mathematics. The week’s curriculum, after introducing participants to the steps involved in constructing mathematical models, positions them to pose their own questions about the world and to begin thinking about how they could use mathematics to answer those questions.
An instructor at Clarkson University’s summer rollercoaster camp prepared two participants to test their design on the Max Flight VR2002 Virtual Reality Programmable Roller Coaster. Photo courtesy of Christopher Lenney, © Clarkson University.
A summer rollercoaster camp at Clarkson University is part of the university’s state-funded Science and Technology Entry Program, IMPETUS (Integrated Mathematics and Physics for Entry To Undergraduate STEM) for Career Success. The camp, now in its ninth year, gives students programming and modeling experience that they can use to design their own virtual roller coasters. The students test their projects and ride their roller coasters on a Max Flight VR2002 Virtual Reality Programmable Roller Coaster.
A resource for readers interested in incorporating mathematical modeling into their undergraduate curricula is PIC Math (Preparation for Industrial Careers in Mathematical Sciences). SIAM is a sponsor of the program, which provides training for faculty through a summer course, content for a semester-long, credit-bearing course focused on industrial problems, and a contest for students. The course could be used as a senior capstone, major requirement, or an elective.
To communicate many of these ideas about mathematical modeling to a wide audience, SIAM and COMAP are organizing an international writing collaboration to create a report titled Guidelines for Assessment and Instruction in Math Modeling Education (GAIMME). This report is modeled on the very successful GAISE reports, which helped bring more statistics into the K-16 curriculum. SIAM also participates in outreach to the public about applied and industrial mathematics through two national events: the USA Science and Engineering Festival and the new Math Midway, created by the Museum of Mathematics (MoMath) in New York. Many parents who attend these events have questions about careers in mathematics and about mathematics enrichment programs. The events have been a great way for SIAM student chapters to participate in outreach.
“It is exciting to see so many really great initiatives under way,” says Peter Turner, chair of the new SIAG on Applied Mathematics Education. “Some of these had their seeds in, or reflect collaborations that started at, the two SIAM–NSF Modeling across the Curriculum workshops. The future for both the SIAG and the SIAM Committee on Education is bright and includes ever closer ties with sister professional organizations, notably the ASA, MAA and NCTM.”
The SIAM community has many opportunities to inspire the next generation of problem solvers and leaders. We encourage interested readers to join the SIAG on Applied Mathematics Education and volunteer for projects organized by the SIAM Committee on Education. “The SIAM education committee is very excited to form new links between academia and industry and involve SIAM members in education initiatives,” says SIAM VP for education Rachel Levy. “We hope many members will join the new SIAG/ED and participate in the first SIAG/ED conference, which is coming soon.”
 The Cognition & Technology Group at Vanderbilt. (1997). The Jasper Project: Lessons in Curriculum, Instruction, Assessment, and Professional Development. New York, NY: Routledge.
 R.D. Goldman and B.N. Hewitt (1976). The Scholastic Aptitude Test explains why college men major in science more often than college women. J. Counseling Psych., 23(1), 50.
 D. McCreedy and L.D. Dierking. (2013). Cascading influences: Long-term impacts of informal STEM experiences for girls. Tech. Rep.
 B. Greer, L. Verschaffel, and S. Mukhopadhyay, Modelling for life: Mathematics and children’s experience. In Modelling and Applications in Mathematics Education. P.L. Galbraith, H.-W. Henn, and M. Niss, eds., Springer, New York, 2007, 89-98.
Rachel Levy is SIAM VP for Education, as well as an associate professor in the Department of Mathematics and Associate Dean for Faculty Development at Harvey Mudd College. Kara L. Maki is an assistant professor in the School of Mathematical Sciences at the Rochester Institute of Technology. Kathleen Fowler is an associate professor of mathematics at Clarkson University and a member of the SIAM Education Committee.