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Engaging Students inMathematical Modeling throughService-LearningOlivia M. CarducciAccepted author version posted online: 24 Jan2014.Published online: 28 Mar 2014.

To cite this article: Olivia M. Carducci (2014) Engaging Students inMathematical Modeling through Service-Learning, PRIMUS: Problems, Resources,and Issues in Mathematics Undergraduate Studies, 24:4, 354-360, DOI:10.1080/10511970.2014.880862

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PRIMUS, 24(4): 354–360, 2014Copyright © Taylor & Francis Group, LLCISSN: 1051-1970 print / 1935-4053 onlineDOI: 10.1080/10511970.2014.880862

Engaging Students in Mathematical Modelingthrough Service-Learning

Olivia M. Carducci

Abstract: I have included a service-learning project in my mathematical modelingcourse for the last 6 years. This article describes my experience with service-learningin this course. The article includes a description of the course and the service-learningprojects. There is a discussion of how to connect with community partners and identifyservice-learning projects.

Keywords: Service-learning, community engagement, math modeling.

If you walk into my Introduction to Mathematical modeling class during thelast third of the semester, you may have trouble determining who the professoris. No one is standing at the front of the room and if anything is written on theboard it is an announcement about the next Math Club meeting. The studentsand I are gathered in groups around the computer screens and everyone is talk-ing over everyone else. If you do not listen to the conversations, it could bemy son and his friends at the local internet cafe competing against each otherin their favorite online game. There might even be a little good-natured trashtalking going on. However, if you listen to the conversations, you may hear“What units are you guys using for energy consumption?’ or “I found a placethat recycles solar panels.” or “What’s the difference between kilowatts andkilowatt hours?” The class is engaged in our service-learning project.

Incorporating service-learning into the mathematical modeling courseseems natural now, but it was scary and hard to conceive of 6 years ago. I hadregularly used realistic projects based on current events or on presentationsby local businesspeople in the course, but never attempted a service-learningproject. I read Charles Hadlock’s book [4] about service-learning. (A morerecent option for someone starting out with service-learning is the special issue

Address correspondence to Olivia M. Carducci, Department of Mathematics, EastStroudsburg University, 300 Prospect St, East Stroudsburg, PA 18301-2999, USA.E-mail: ocarducci@esu.edu

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Mathematical Modeling and Service-Learning 355

of PRIMUS on service learning [5].) Still, I worried. What if the students can-not, or will not, complete the project? What if the community partner hasunrealistic expectations? Although I would not say incorporating a service-learning project is easy, all my fears turned out to be unfounded. As a wholethe students have worked hard. Every class has included those students whostepped up and took responsibility for the projects. Many students go beyondall reasonable expectations to make sure the project succeeds. Believe in thestudents; then let them do it.

Who are these super students? The students are taking Math 425:Introduction to Mathematical Modeling. The prerequisites for the course areCalculus III and Linear Algebra, but in practice the students have had a lotmore math courses than that. There are two basic groups of math majors:seniors majoring in one of our applied math concentrations and juniors in thesecondary education concentration. Most sections include a couple computerscience or physics majors. Class size ranges between 18 and 25. They attenda typical state institution with modest admission standards, but they have self-selected into the math major, meaning they are survivors and are not looking forthe easy way to a degree. Generally speaking they are bright, reliable, practical,and hard-working.

Before starting the service-learning project, the students work on threewarm-up projects. I divide them into groups of three (my preference) or four(the course enrollment is not always a multiple of three). They have 2 weeksto develop a model to answer a realistic question. I like to have two groupsworking on the same question, hoping to see two different approaches tothe problem. One of the questions I assigned on the first class day this pastspring was:

Project 0: Structured SettlementsDue February 12

Teams 1 & 2

Lately, ads for companies looking to purchase structured settlements haveappeared on cable TV. A structured settlement is an agreement to pay a largesum in smaller installments. For example, a person injured in an auto acci-dent may receive a structured settlement from the driver who injured them.The driver will make monthly payments to the injured party. These companiesare offering to make a single lump sum payment for the structured settlement.The injured party gets the money up front, but the company gets the monthlypayments.

Please develop a mathematical model to determine a fair value for a structuredsettlement.

You can find further information on structured settlements at http://structuredsettlementcashguide.com/

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For the first model, the students in each group are to agree on a model andproduce a written report on the model. Each group also gives a presenta-tion on their model. While the students are working on the model, I presentinformation from the text on different aspects of mathematical models. Theinformation presented in class (often leading to the logistic model of popu-lation growth) has nothing to do with the projects the students are workingon. I expect them to bring their knowledge from other courses to bear on thisproject. For subsequent models, half the groups write the group reports andgive a group presentation while the other half write individual reports and don’tgive a presentation. When the students write individual reports, the group stillagrees on a single model. The only project that corresponds to a lecture topicis the simulation project. For that project I tell the students to use a computersimulation to answer the question and I offer instruction on what a simulationis and examples of how to write one.

Once the students have completed the three warm-up projects, they areready to tackle the service-learning project. The whole class works on theproject together. Over the years, the projects I have used include:

● proposing population modeling methods to the Lehigh Valley PlanningCommission (LVPC);

● estimating emissions generated by students, faculty, and staff commuting toand from campus for the East Stroudsburg University (ESU) SustainabilityCommission;

● modeling the complete life-cycle costs of gas fracking for the PoconoEnvironmental Education Center (PEEC);

● modeling the complete life-cycle costs of commercial electricity generationusing solar or wind power for PEEC.

Typically, we start these projects during week 8 or 9 of our 14-week semester.A representative from the organization presents the projects. I also ask a librar-ian to make a presentation about using library resources to gather informationabout the specific topic we’re working on. When we have done a project forESU, someone from Academic and Institutional Research presented the datafor the project and described how the data set was organized. In the midst ofthese presentations, I help the class elect their leadership and get organized intogroups. After that the students are left to their own devices. I still attend class,but I let them run the show. I observe how the students are working; after all,I have to give them a grade on the project and not everyone deserves the samegrade. If the students ask me a question, I am willing to help, but I avoid gettingtoo involved. In lieu of a final exam, the students make a presentation duringour final exam time to representatives of the organization that proposed theproblem and deliver a written report as well as the model. I invite members ofthe campus community (the math faculty, the members of the service-learning

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initiative committee, the librarian who made the research methods presenta-tion, the members of the sustainability committee, the dean of my college,provost, university president, and anyone else who contributed to the project)to attend the final presentation. The math department has been gracious enoughto fund simple food (bagels, coffee, donuts, fruit, water and coffee for an8 AM final or subs, chips, fruit, water, and soda for an 11 AM final) for afterthe presentation to allow the students and guests to mingle informally. I alsorequire the students to write a reflection paper about their experience with theproject that counts for 30% of their project grade. Reflecting on the project andthe process of developing the final product is an important part of codifyingthe learning from the project. Students are sometimes surprised by what theylearned and so am I. The service-learning project counts for 30% of their coursegrade.

At this point I hope you are thinking, “Sounds great.” I realize you mayalso be thinking, “Where am I going to find a project?” I understand becausethis was my biggest stumbling block, but this is the wrong question. You are notgoing to “find” a project. It is not something out there waiting to be discovered.You need to sell your class’ services and you need a little luck. My first projectcame from a flyer that our Career Services department sent around. The LVPCwas advertising a summer job gathering traffic data. Career Services sent thead to the math faculty asking us to distribute it to our students. I looked at it anddecided anyone who was collecting that type of data was doing something I wasinterested in. I sent an email to the contact person on the flyer describing theclass and what I was looking for. Luckily, that person forwarded my email toheads of technical work groups and the population-modeling group was inter-ested. I met with them at their office over the summer and began planninga course that included their project for the Spring semester. (Introduction toMathematical Modeling is offered every Spring.) At the meeting, I advised theLVPC representatives of my timeline and told them the best project is a ques-tion they would like to work on but do not have time to work on. We agreed ona project at that meeting. The next two projects were for the ESU Commissionon Sustainability. The University sent several emails that they had establisheda Commission on Sustainability. I figured there was a project in there some-where and contacted the chair of the Commission. Again the chair forwardedmy email to the chairs of the various committees that make up the commissionand the carbon footprint committee needed our services. Meetings followed(I found myself appointed to the committee) and we defined a project. I gotinvolved with PEEC through a science and technology career day sponsored byCareer Services. I went up to every table, spoke to the person there, and gavethem a letter, with my card attached, describing myself, the class, and what Iwas looking for. Apparently the representative from PEEC passed my infor-mation on to the Executive Director who had some projects they couldn’t fund.A few short meetings later, we had agreed on a project. I also managed to find aproject through the University’s Vice President for Economic Development and

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Research Support. She runs a business accelerator with several small start-upcompanies. Part of the business accelerator’s mission is to connect the busi-nesses with the educational mission of the University. Ironically, I had spokento representatives from some of these companies at the Science and TechnologyCareer Day, but even though they expressed interest in my FREE services,nothing came of it. Even the Vice President had trouble convincing these busypeople that this was worthwhile, but now that we have completed a project,they’re approaching me about future projects. What’s the theme here? All thecontact came through University organizations I have easy access to, but hadnot really been involved with. When I pitched my case, I gave them some-thing they could easily pass on; either an email they could forward or a letter.I explicitly ask them to pass my information on. Even though I only need oneproject per year, I speak to dozens of people. Most don’t follow through, but Ionly need one who does. As in any sales operation, it gets easier as you makecontacts.

If it seems like this involves a lot of extra preparation and stress, it does. Itis hard for me to approach these organizations about a project. The benefits tomy students and me far outweigh the extra effort. What are these big benefits?Many fine studies demonstrate the value of service-learning [1,3]. The follow-ing excerpts from my students’ reflection papers further illustrate the value ofservice-learning:

● This was the first project I did for a math class that didn’t feel like I was justfollowing steps and plugging in numbers.

● Because of the fact that we had to start from scratch, when the project wasover, I felt a great sense of pride from our work. It’s something that we canclaim to be truly ours.

● While I had my doubts about this project early in the semester, I becamevery involved with it once we began working and really enjoyed it. . . . Thiswas by far one of the most interesting, engaging, and enjoyable project [sic] Ihave done through my academic career and I was grateful for this experience.

● I thought I understood math before, but now I see just how efficient it can bein describing complicated and controversial situations.

● This experience has been informative, inspiring, and, for lack of a betterword, “real.”

Hopefully you can see that the students are personally invested in the projects.Their view of how mathematics interacts with the world expands. This projectgives them a taste of what it might be like to work as an applied mathematician.Hopefully they are better prepared to be self-starters on their first job, whateverit may be.

What are the benefits to me? I take great pleasure in seeing what thestudents accomplish. When I think about how satisfying this is compared to

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looking over the results of a calculus final, it is astonishing. I am known aroundcampus for doing this type of project and the service-learning committee reg-ularly asks me to be a part of their panel discussions and workshops. I havegrown as a teacher and human being as I let the students work it out for them-selves. I grow close to many of these students and hear from them after theyhave left the University. It is simply a very rewarding opportunity.

At first I was disappointed that the students used mostly, but notexclusively, lower-level mathematics (primarily elementary statistics and pre-calculus), but now I realize that they are doing an incredible amount of criticalthinking. My students seem to be at a stage of development that allows them tounderstand high-level mathematics or to apply very advanced critical thinkingskills to a problem, but not both. Since the critical thinking skills are crucial, Iaccept the lower level of mathematical sophistication. (Others have expressedsimilar low levels of mathematical sophistication [2].)

I highly recommend incorporating service-learning into math classes ina meaningful way. Most universities have a service-learning committee oroffice. Get involved with them. Even if it feels like they cannot help youidentify projects (mine could not), the support you receive will be invaluable.Attend workshops on service-learning, especially those directed at the sci-ences. Choose the right course for your first service-learning activity. Frankly,it is easier to incorporate service-learning into a broad-based course like mathmodeling than to incorporate it into a techniques-based course. In a techniques-based course, you would need a project that can be addressed using thetechniques of the course. I have found this to be a much harder proposition.Take the leap—it is a wild ride, but you and your students will be betterfor it.

REFERENCES

1. Astin, A. W., L. J. Vogelgesang, E. K. Ikeda, and Jr. A. Yee. 2000.How Service-Learning Affects Students. http://heri.ucla.edu/pdfs/rhowas.pdf. Accessed 27 June 2013.

2. Donnay, V. J. 2013. Using sustainability to incorporate service-learning intoa mathematics course: A case study. PRIMUS: Problems, Resources, andIssues in Mathematics Undergraduate Studies. 23(6): 519–537.

3. Eyler, J. S., D. E. Giles, Jr., C. M. Stenson, and C. J. Gray. 2001. At aGlance: What We Know About the Effects of Service-Learning on CollegeStudents, Faculty, Institutions, and Communities 1993–2000. http://www.compact.org/wp-content/uploads/resources/downloads/aag.pdf. Accessed27 June 2013.

4. Hadlock, C. (ed.). 2005. Mathematics in Service to the Community:Concepts and Models for Service-Learning in the Mathematical Sciences.Washington, DC: The Mathematical Association of America.

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5. PRIMUS. 2013. PRIMUS: Problems, Resources, and Issues in MathematicsUndergraduate Studies. 23(6): Special Issue on Service-Learning inMathematics.

BIOGRAPHICAL SKETCH

Olivia M. Carducci received her Ph.D. from Carnegie Mellon University in1989. Her first college teaching positions were at private liberal arts colleges.After a 5-year stint as a stay at home mom, she returned to the classroomwith a new interest in connecting mathematical ideas to the world outside theclassroom. She also enjoys sharing her mathematical insights with her fourchildren.

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