Model-Eliciting Activities (MEAs) - The UTeach Institute

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Adem Ekmekci & Gladys Krause HANDOUTS UTeach Institute - NMSI Annual Conference Austin, TX / May 24 – 26, 2011 College Level Students’ Reasoning of an Optimization Problem: Historic Hotel MEA (Model-Eliciting Activity) Adem Ekmekci University of Texas at Austin ekmekci@mail.utexas.edu Angeles Domínguez Instituto Tecnologico de Estudios Superiores de Monterrey angeles.dominguez@itesm.mx Model-eliciting activities (MEAs) are based on real-life situations where students, working in small groups, present a mathematical model as a solution to a client’s need (Zawojewski and Carmona, 2001). The problem of Historic Hotels is an MEA in which students are asked to develop a mathematical model to maximize profit that can be calculated with a quadratic equation. In the problem, there is a client who inherited a historic hotel and does not have management skills. He wants to determine the rate per room where he was told by the previous owner that all of 80 rooms are occupied when the daily rate is $60 per room; the rate per room increases by $1 for every vacant room; and each occupied room has a $4 cost for service and maintenance. The problem can be solved by using quadratic formulas, 1 st and 2 nd derivative method, or simply looking at the profit for each value. In this study, college level students are asked to solve this optimization problem to see possible their ways of solution to the problem. Two groups of students were given this non-traditional problem. The first group was a calculus class where the majority of students were engineering major and the second one was an education course required for teaching certification where students were either science or math major. There were 23 groups of 3 in calculus class and 11 groups of 3 in the other. After the problem was solved in groups, students were asked to present their models to their class-mates. Discussions about different solutions were done after each presentation. Authors and their colleagues observed students and took field notes while students were working on the problem and discussing their results afterwards. This particular type of MEA made students’ thinking about optimization as a mathematical concept visible to both their peers and teachers. Formative assessment (Black & William, 1998) cycles that students went through appeared in the problem solving process. Students’ final works are analyzed in terms of the function they used, variables and their definitions, graphical representations, and generalizations. Analysis of solutions of both groups to the problem and observations by authors and their colleagues will be reported in the poster. In addition, math major students’ and pre-service teachers’ ways of thinking will be discussed. Following questions will also be touched upon in the poster: - How much calculus knowledge do college level students associate with solving an optimization problem? - In what ways, did college level students model the maximization of profit in the given context? - What symbols and tool did students use in solving the problem? - Were there any differences in the method used between calculus students and students in teacher certification program? 1
Adem Ekmekci & Gladys Krause HANDOUTS UTeach Institute - NMSI Annual Conference Austin, TX / May 24 – 26, 2011 References Aliprantis, C.D. & Carmona, G. (2003). Introduction to an economic problem: A Models and Modeling Perspective. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 255-264). Mahwah, NJ: Erlbaum. Black, P. & Wiliam, D. (1998). Inside the black box: raising standards through classroom assessment. Phi Delta Kappan, October 1998, 139-148. Dominguez, A. (2007). Single solution, multiple perspectives. Proceedings of thirteenth annual meeting of The International Community of Teachers of Mathematical Modeling and Applications (ICTMA). Bloomington, IN. Lesh, R., Hoover, M., Hole, B., Kelly, E., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Mahaway, NJ: Lawrence Erlbaum. Zawojewski, J., & Carmona, G. (2001). A developmental and social perspective on problem solving strategies. In R. Speiser & C. Walter (Eds.), Proceedings of the twentythird annual meeting of the north American chapter of the international group for the psychology of mathematicseducation. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Citation for this proceeding: Ekmekci, A. and Dominguez, A. (2007, Oct) "College Level Students’ Reasoning of an Optimization Problem: Historic Hotel MEA (Model-Eliciting Activity)" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, University of Nevada, Reno, Reno, Nevada Online Retrieved 2008-09-04 from http://www.allacademic.com/meta/p201387_index.html Publication Type: Poster 2
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