Engaging Students in Mathematical Modeling through Service-Learning

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  • This article was downloaded by: [Portland State University]On: 20 October 2014, At: 00:46Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK

    PRIMUS: Problems, Resources,and Issues in MathematicsUndergraduate StudiesPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/upri20

    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): 354360, 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 hearWhat units are you guys using for energy consumption? or I found a placethat recycles solar panels. or Whats 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 Hadlocks 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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    mailto:ocarducci@esu.edu

  • 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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    http://structuredsettlementcashguide.com/http://structuredsettlementcashguide.com/

  • 356 Carducci

    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 dontgive 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-we