THE USE OF MATHEMATICAL MODELING AS A SUMMATIVE ASSESSMENT IN SCIENCE COURSES

A climate science course taught in an NSF funded undergraduate program begins with atmospheric chemistry and physics and until the Fall of 2014, ended with a final exam. The final exam has been replaced with a model which describes the atmospheric system being studied using mathematical concepts and language. The primary objective for this adaptation was to increase the rigor of the concluding summative assessment. The chemistry, physics and Micro-Electro-Mechanical System (MEMS) section-based on NOx detection research done at MIT-are assessed individually. The fourth and last course component begins with Gaussian Plume Equations (GPE) and ends with the development of the model. Gaussian plume models, applicable for continuous point source releases with uniform turbulent flow, are used for air quality impact analysis and assessment of pollutants. This course can be algebra or calculus based so the sophistication of the model varies. In one instance, utilizing sample data/atmospheric conditions, students must predict the direction of the plume and the concentrations of contaminants at different distances within it. In another, students are given sample data to construct a model to make predictions of future values and trends. The design rubric for the model was formerly used for the exam design. The final grade for the model is 70% (development, accuracy and design) and 30% narrative (model-based questions and design justification). A comparison between the final exam and the final model revealed, as an aggregate, similar percentages by letter grade. 86 students took a final exam and 82 students completed a final model instead. There was an 11% difference in the grade distribution across all levels (A-F) between these two groups. The grades trended downward among the middle grades (B-D) in the classes that took the model as the final assessment. In a sample of 10 students who took both assessments after completing the summer course, the grades [Final/Model] were: [92%/86%]; [90%/82%]; [86%/80%]; [84%/77%]; [80%/77%]; [78%/73%]; [77%/72%]; [76%/70%]; [72%/74%]; [68%/62%]. Overall, the scores on the model are consistently lower than those on the final exam. The students who took both did not know which final score would count towards their grade. The difference between the final assessment types indicates the model challenges students. It will remain a course component due to the comprehensive evaluation it provides; however, students will receive additional help to complete it.