PIC Math Experience: Teaching at a Liberal Arts College

My PIC Math Experience Teaching The PIC Math Class At A Small, Private Liberal Arts College Ron Buckmire Occidental College ron@oxy.edu

Outline My PIC Math Experience Before: Preparing For the Class During: Teaching the Class After: Evaluating the Class Lessons Learned Things NOT To Do Things To Do Things I d Like To Happen Questions 2

My PIC Math Experience: Before Details of the class Math 396 : Mathematical Modeling (Industrial Mathematics) o 2-units (Tuesdays 1:30-2:55pm for 14 weeks) o Limited class size (No more than 12) o Pre-requisites: (multivariable calculus AND linear algebra) OR permission of instructor 300-level math class (suitable for math majors or minors) Advertised during Differential Equations class in Fall 2014 ( clinical capstone experience & hands-on seminar ) 3

My PIC Math Experience: Before Details of the class: grading Group and individual evaluations: 15% Participation: 15% Progress Reports: 20% Final Written Presentation: 25% Final Oral Presentation: 25% 4

My PIC Math Experience: Before Details of the class: course goals provide students with the experience of using mathematics to solve an actual real world problem of their choice by o developing, testing and implementing a mathematical model of their own devising o performing calculations and evaluating their results for accuracy and appropriateness assist in the preparation of students for a potential career in industrial or applied mathematics by o exposure to non-academic stakeholders in business, industry or government; o developing collaboration skills by working in small teams towards a common goal o improving communication skills (especially of mathematical/technical content) 5

My PIC Math Experience: During Actual class 10 students o 7 male, 3 female o Majors: 7 Math, 1 Cognitive Science, 2 physics, 1 Biochemistry, 1 French(!) 2 double majors (math/physics and math/french) o 7 seniors, 2 juniors, 1 advanced sophomore o 2 Latino, 1 Asian, 1 International, 2 first-generation 6

My PIC Math Experience: Before Finding Industrial Math Problems Five B.I.G. Industrial Math problems from PIC-Math Contacted (by phone and by e-mail with attached PDF letters) six companies (found from list of recent internships) Initiated conversations with four (Kaiser Permanente, Southern California Edison, Occidental College Facilities Department and Payden & Riegel) Resulted in one local problem (another fell in my lap!) 7

My PIC Math Experience: Before Local Problem 1 Industrial Liaison: Michelle Hill, Assistant Director of Energy Services, Facilities Management, Occidental College The original question What is the total amount of carbon sequestered by all the trees on the campus of Occidental College, what is its monetary value as a carbon offset and how do these quantities change with time? 8

My PIC Math Experience: Before Local Problem 1 Expected Deliverable: Occidental College would like to know the annual amount of carbon sequestered by the trees located on its campus. Additionally, calculating the monetary value of this carbon for offset purposes and how it compares to the value of the trees themselves and how these quantities vary relative to each other with time. 9

My PIC Math Experience: Before Local Problem 2 Industrial Liaison: Jason Heidecker, Founder, BeastScore.com The original question Can one create a scoring system that can be used to predict how people will perform in an athletic competition given a large data set of individual performance metrics for various athletic events? 10

My PIC Math Experience: Before Local Problem 2 Expected deliverable The client would like a 100x100 table of BeastScores where B(i,j) represents the location in the ith row and jth column of the table of the probability that a competitor with BeastScore i will be ranked higher in the national athletic competition (NAC) than a competitor with BeastScore j with the condition that B(i,j)+B(j,i)=1. 11

My PIC Math Experience: During Organizational questions Select teams first or problems first? Who decides? o Team selected first Each student had 2 minutes to present to the class a spiel (classes taken, special skills, work habits, useful experience) o Who should pick teams? Students or professor? Polled students with indecision as main result Professor decided on groups (3-3-4) 12

My PIC Math Experience: During Organizational questions Who gets which problem? Bijection or not? o One-to-one correspondence between teams and problems . (Yes, bijection from problems to teams.) Process for determining selection order of problems? o None / Quasi-random Process for selection of problem by team? o None / Quasi-random 13

My PIC Math Experience: During Organizational questions What does the professor do during class time? o (Early in semester) Discuss the modeling process in general and characteristics and processes all teams should follow (i.e. parameter estimation, sensitivity analysis, English->Math->English, literature search) o (Middle of semester) Get frequent updates on solution progress from groups in written and oral form, work 1- on-1 with groups to understand and help 14

My PIC Math Experience: During Organizational questions What does the professor do during class time? o (Late in semester) Encourage students to produce documents that start summarizing the work that has been done to date and characterizing the solutions in a way that connects to the problem statement; provide feedback on these documents; o (End of semester) Provide rubric(s) on how written and oral presentations will be evaluated 15

My PIC Math Experience: During Organizational questions How to judge final product of students? o Assemble panel of external judges (Industrial Liaison of Selected Problem, Potential Industrial Liaison, Associate Dean) to judge team s oralpresentation How to integrate PIC-Math competition (i.e. $1000 $2000 in travel funds) with class? o I made selection of the PIC-Math team a prize to be earned by the best-performing team according to judges 16

My PIC Math Experience: After Lessons Learned: What NOT To Do Next Time No group size larger than three o Group with four had widest variation in assessment of individual participation o Groups with three people seemed more well-balanced Discuss video presentation and written paper earlier in semester o The logistics of taping student presentations can be daunting (especially if you have not done this before) 17

My PIC Math Experience: After Lessons Learned: What NOT To Do Next Time Have fewer one-on-one oral progress reports o There were written progress reports due at the beginning of class every other week but these became repetitive towards the end of the semester: (suggestion) each member of the group should have specific responsibility for (atleast) one written and one oral progress report 18

My PIC Math Experience: After Lessons Learned: What NOT To Do Next Time Have fewer classes end with no explicit progress goals for next time o At the end of every class, each group should have to put in writing what they want have accomplished by the next class, with each student member committing to what they want to get done (this can be maintained in the cloud) 19

My PIC Math Experience: After Lessons Learned: What To Do Next Time Be more explicit and intentional about assessing individual student contributions Require draft of final paper before end of semester Provide an example/model of well-done solution Have teams pick name and set up online file drive immediately Have firm date by which problem selection is final Have some kind of individual student journal/log 20

My PIC Math Experience: After Things I Would Like To Happen Next Time Students from different teams interact with each other more collaboratively o (Suggestion) This might be facilitated by more all-class discussion/dissection of team progress reports Students learn more about mathematicians and the use of mathematics in industry and careers More structured use of class time on days when progress reports are not due 21

Thanks! To Michael Dorff, Suzy Weeks, Linda Braddy and the PIC-Math organizing team for the invitation to speak today To the National Science Foundation and Mathematical Association of America for support To all of YOU! 22

Questions? Ron Buckmire Occidental College ron@oxy.edu http://sites.oxy.edu/ron/math/396/15 OR http://bit.ly/oxypicmath 23