Khoon Yu Tan Math Teacher John H Reagan High School Houston Independent School District

1. Stochastic Healthcare Facility Configuration Problem: Expected Excess Demand & Expected Excess Capacity Study Dr. Wilbert WilhelmBarnes Professor Industrial and Systems Engineering Department Texas A&M University Khoon Yu Tan Math TeacherJohn H Reagan High School Houston Independent School District

2. Content • Research overview • Element of research for classroom project • College Board AP Calculus learning objectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

3. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

4. Research Overview • A particular difficulty in decidingcapacityconfigurationswhilemaximizing total revenueexcessisuncertainty in patientdemand • Toallowthemodeltodealwithpatientuncertainty, expectedexcesscapacity and expectedexcessdemandfunctions are introduced and analyzed • Theexpectedexcessdemand, E[u] and expectedexcesscapacity, E[o] functions are as followrespectively: whereKrepresentscapacity, M mean of patientdemand, standarddeviation of patientdemand, and cummulative (probability) densityfunction of patientdemand. Credit: Xue (Lulu) Han

5. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

6. Element of Research for Classroom Project • Thekeyelement are theexpectedexcessdemand and expectedexcesscapacityfunctions: • Students use analytical and graphicaltools of Calculus and Pre-Calculustostudythefunctions • Thestudy of thefunctionshelpsimprovethemodelthatsolvesthehealthcarefacilityconfigurationproblem, which in turnhelpstoimprovecapacity-settingdecisions, increasingcosteffectiveness Credit: Xue (Lulu) Han

7. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

8. College Board AP CalculusLearningObjectives • Functions, Graphs, and Limits a) Analysis of graphs b) Asymptotic and unboundedbehavior: understandingasymptotes in terms of graphicalbehavior II. Derivatives a) Concept of thederivative: derivativepresentedgraphically, numerically, and analytically b) Derivative at a point: i) slope of a curve at a point ii) tangent line to a curve at a point and local linear approximation c) Derivative as a function: relationshipbetweentheincreasing and decreasingbehavior of f and thesign of f’ d) Secondderivatives: relationshipbetweentheconcavity of f and thesign of f’’ e) Applications of derivatives: analysis of curves, includingthenotions of monotonicity and concavity Asymptotes credit: Wolfram MathWorld Derivatives credit: http://clas.sa.ucsb.edu/staff/lee

9. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

10. Day One of Project ENGAGE • E3 experience: industrial engineering, healthcare data, mathematical model • Students inquire pre-day one about their or their parents’ healthcare spending: insurance, out-of-pocket cost • Poster, pictures, video, • authentic data from students EXPLORE • Engineering fields and what engineers do in each • Matching-cards game using pictures of engineering work from students’ everyday life & names of engineering fields • Think-pair-share and class sharing • Shortest flight time: discuss variables e.g. distance, route, • time, speed, airport location Engage credit: http://www.dreamstime.com Explore credit: http://selinasvintage.blogspot.com

11. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

12. Days Two & Three of Project EXPLAIN • Students are to investigate the convexity of the expected excess demand & capacity functions • Students are to linearly approximate the functions within a certain percentage error • Students follow the engineering design process Design Process credit: Project Lead The Way Explain credit: http://rikowski.wordpress.com/

13. Days Two & Three of Project ELABORATE • Students are grouped in threes • Groups are differentiated by tasks: investigate convexity with respect to different variables • Each group builds approximation models after selecting its approach • The models differ in terms of approximation error, complexity (piecewise), computational cost (time) • Each group selects its “best” model and presents its findings to the class Design Process credit: Project Lead The Way Elaborate credit: http://activedabawenya.blogspot.com/

14. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

15. Days Four of Project EVALUATE • When a group presents, other groups and teacher evaluate based on a rubric • Within each group, members anonymously evaluate each other’s contribution • Rubric clarifies assignment of points for different steps of the design process, reasoning, conclusion, and presentation • Post-test Evaluate credit: http://www.strategicinteractions.com/

16. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

17. Sample Pre-Test & Post-Test QUALITATIVE QUANTITATIVE • Why is excess demand an important factor in deciding where to open a healthcare facility, or to expand, contract or close an existing facility? • Excess demand is costly • Excess demand influences the decision to open a new facility or expand an existing one • Excess demand causes loss of business (patients) • Some patients may be unhappy • I and II only b) II and III only • c) I, II, and III only d) all of them Differentiate the function with respect to capacity level assuming other variables are held constant? *Four multiple-choice responses but correct response is

18. Content • Research overview • Element of research for classroomproject • College Board AP Calculuslearningobjectives • Day one of project • Days two and three of project • Day four of project • Sample pre-test and post-test • Acknowledgements

19. Acknowledgements • Texas A&M University E3 Program • Dwight Look College of Engineering • National Science Foundation • Nuclear Power Institute • Chevron • Dr. Wilbert Wilhelm, faculty adviser • Xue (Lulu) Han, Ph.D. candidate • Amy Brown, RET participant • David Carmona & Brittany Tarin, REU participants