The Power of Interdisciplinary Bridges: Throwing the Net Widely

1. The Power of Interdisciplinary Bridges: Throwing the Net Widely Deborah Hughes Hallett University of Arizona & Harvard Kennedy School

2. Common Core Standards • Focus on mathematical structure and understanding What does this mean for teachers? • Need deeper understanding of the mathematics • Theoretical: How topics fit together • Applied: How and where this is used Teachers need a “view from the balcony” of the mathematics they teach and where it is leading

3. What are Students’ Views? • Some students appreciate mathematical elegance • Some students absorb an idea better when they know how it is used How Do Students’ Views Affect Teachers’ Needs? • Teachers may not know where a topic they teach is leading, or why it is important • Mathematicians can provide professional development that fills in these gaps and enables teachers “to climb to the balcony”

4. What Kind of Professional Development is Needed? • Interaction between teachers, mathematicians, mathematics educators • Providing perspective and inspiration • Answering questions, creating a sense of community • Providing continuity of expectations as students move between school and college We will look at examples that respond to “How is this used?”

5. “Why Do I Need to Know This?”: Contexts for Rates of Change • Slope • Linear and exponential growth • Change and percent change • Rate of change and percent rate of change • The number e • Continuous and annual rate of change • Extrapolation and interpolation

6. Understanding the Debate about Climate Climate change in past: • Temperatures rose 1-2 F during 1906-2005 • CO2 in atmosphere increased from 316 ppm in 1959 to 386 ppm in 2008 • Greenhouse gasses tend to warm the planet From Tom Pfaff and http://www.epa.gov/climatechange/science/stateofknowledge.html and http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html#mlo Climate change predictions: • Temperatures will continue to rise, perhaps accelerating • Greenhouse gasses such as CO2 in atmosphere will increase, perhaps accelerating • Sea levels will rise, leading to flooding • From http://www.esrl.noaa.gov/gmd/ccgg/trends/ and http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt

7. Predicting Future Carbon Dioxide Levels http://cdiac.ornl.gov/new/keel_page.html

8. “Why Do I Need to Know This?”: Contexts for Algebraic Manipulation • Linear functions • Logarithms • The number e • Linearization

9. Linearizationin Economics How fast has CPI (Consumer Price Index) grown over last century?

10. Another View of Same CPI Data

11. Linearizationin Biology • V0 initial velocity of reaction • [S]0 is initial concentration of substrate • Vmax, KM are constants Michaelis-Menten Equation

12. How Do You Know If a Reaction Follows Michaelis-Menten? Linearize:

13. “Why Do I Need to Know This?”: Contexts for Proportion & Probability • Ratio and proportion • Rounding and estimation • Probability • Conditional probability (what is in the denominator?) • Bayes’ Theorem

14. Is There Racial Profiling in LA?From Lily Khadjavi, Loyola Marymount

15. Numbers in Thousands • About 5% of white drivers were searched when stopped • About 20% of African-American drivers were searched when stopped Mathematics: Estimation and Percentage

16. Another Example:“Drug Testing Set For Student Athletes In Illinois”Reporting Dorothy Tucker CHICAGO (CBS) Jan 15, 2008 6:23 pm US/Central As CBS 2's Dorothy Tucker explains, now some high school athletes in Illinois will have to take another [test]…, a drug test. This year's state finals will be the last games students play without being tested for steroids. Next year, whether it's basketball, football, or any other sport, whether it's girls or boys, every athlete competing in sectionals, regionals or championship games will be subject to random testing of banned drugs. Questions: How likely is it that a student is falsely accused? How likely is it that a cheating student is missed?

17. “Why Do I Need to Know This?”: Contexts for Graph Reading & Calculus • Graphical differentiation • Differential equations • Slope fields / Phase diagrams • Separation of variables • Integration techniques: partial fractions • Logistic function • Estimating parameters • Fitting lines to data

18. Predicting Peak Oil Production What is peak oil production? When will/did US oil production peak? When will/did world oil production peak? Why is this important? What are the economic implications? (Analyze using 2008 data at www.eia.doe.gov. Calculus, Hughes Hallett at al)

19. US Oil Production (1900 to 2005)

20. Total US Oil Pumped since the Beginning of Time

21. http://en.wikipedia.org/wiki/Predicting_the_timing_of_peak_oilhttp://en.wikipedia.org/wiki/Predicting_the_timing_of_peak_oil US oil production (crude oil only) and Hubbert high estimate, peak ≈ 1970 Norway, peak ≈ 2001

22. Preventing the Spread of SARSThere is an outbreak of SARS in a nearby city. As you are working in the mayor’s office, you are asked which is the most effective policy for preventing the spread to the disease to your city: • Close off the city from contact with the infected region. Shut down roads, airports, trains, busses, and other forms of direct contact. • Install a quarantine policy. Isolate anyone who has been in contact with a SARS patient or anyone who shows symptoms of SARS. (Analyze using 2003 World Health Organization data from Hong Kong. Calculus, Hughes Hallett at al)

23. Progress of the Disease: Without Quarantine

24. Progress of the Disease: With Quarantine

25. Now is The Time • Common Core Standards have led to calls for more and better professional development for teachers • What are our own departments/states doing? • What could we be doing? • Interaction between teachers and mathematicians is valuable : We can contribute a “view from the balcony”