1. Unpacking “ESTEEM” Excel: ubiquitous, easy, flexible, non-intimidating Exploratory: apply to real-world data; extend & improve Experiential: students engage directly with the math

2. The ESTEEEM Project Homepage 55 modules: Broad range of topics and data sets Go to Island Biogeography http://bioquest.org/esteem

3. Module Main Page Screenshots & brief description Mathematical expression Research articles & primary data User manual & curriculum materials (in progress) Downloadable Excel sheet

4. Population genetics Population growthBioinformatics Operon function

5. PhylogeneticsEpidemiology Protein structure Enzyme kinetics

6. Three Boxes Black box: Hide the model ? y = ax b Glass box: Study the model y = ax b No box: Build the model! How do students interact with the mathematical model underlying the biology?

7. Copyleft download use modify share Users may freely the software, w/proper attribution More info available at Free Software Foundation website

8. Continuous Growth Models Biological Goals: Explore the growth of microbial populations Discriminate among alternate hypotheses Quantitative Goals: Distinguish between absolute & relative, limited & unlimited growth Gain hands-on experience with selecting & fitting models

9. Continuous Growth Models 1. Wet lab portion Inoculate bread Take digital pictures at 1-day intervals Calculate mold area using ImageJ (Mac) or Scion Image (PC) — or have students estimate area! Prediction: What pattern of growth will you see?

10. Continuous Growth Models 2. Computational portion Open "Continuous Growth Models" workbook Go to "Data" tab Enter observed data Go to "Plots—Size" tab to view three diff. models of mold population growth

11. Linear growth: Constant absolute growth rate (e.g., 20 mm 2 / day) Exponential growth: Constant relative growth rate (e.g., 20% / day) Logistic growth: Relative growth rate  as pop. size  (e.g., 0% / day at 700 mm 2 ) Which model, & what parameter values, can best explain the observed data?

12. Go to “Plots—Growth” tab These graph the same models & data as before: How do they differ from the previous graphs?

13. Epidemiological Model Goal: Introduce students to the process of modeling a biological system Hook: Predict the outbreak and course of a specific epidemic; model the efficacy of different intervention strategies

14. Epidemiological Model 1.Building formulas in Excel 2.Setting parameters and variables 3.Translating biology into math 4.Implementing a mathematical model in Excel 5.Visualizing & interpreting results Five-step process:

15. Epidemiological Model Open “SIR Model” Simple model: 3 variables, 2 parameters From this information, how would you calculate the initial # Susceptible, Infected, Recovered? Go to View menu, choose “Formula Bar” In Cells B2-D2, enter formulas to carry out those calculations

16. Biological Knowledge  Mathematical Equations SIR How do individuals move from one category to another? Write “word equations”; for example: The # of Susceptibles at Time 1 = The # of Susceptibles at Time 0 ± The # of newly infected Susceptibles ?? Write formulas for: # newly infected Susceptibles # newly recovered Infecteds –

17. Future Directions More thorough documentation on biology, math, Excel Pre-built curricular resources: “I need something NOW!” More modules & improvements to current ones: share resources among community of ESTEEM users