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Quantitative Literacy on the Global Stage

Quantitative Literacy on the Global Stage. A Talk in Three Acts by. Kurt Kreith (UC Davis) and John Thoo (Yuba College). with a little help from our friends Don Chakerian, Kim Holsberry, and Al Mendle. Act I. Quantitative Literacy.

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Quantitative Literacy on the Global Stage

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  1. Quantitative Literacy onthe Global Stage A Talk in Three Acts by Kurt Kreith (UC Davis) and John Thoo (Yuba College) with a little help from our friends Don Chakerian, Kim Holsberry, and Al Mendle Act I

  2. Quantitative Literacy • Many liberal arts colleges have a quantitative literacy (QL) or quantitative reasoning (QR) requirement • Traditionally, many students take college algebra or pre-calculus regardless of major • Not suitable as general education course for majority of students who are non-STEM majors

  3. Some have taken tack to modify college algebra Gordon P. Sheldon, “What’s wrong with college algebra?”PRIMUS XVIII(6), pp. 516–541 (2008) Abstract: Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the actual needs of the students and of the other disciplines that require college algebra of their students—by focusing on conceptual understanding, data, and modeling and problem solving. • Now more colleges offer alternatives to college algebra and pre-calculus

  4. http://www.calstate.edu/AcadSen/Records/Reports/documents/QRTF.FinalReport.KSSF.pdfhttp://www.calstate.edu/AcadSen/Records/Reports/documents/QRTF.FinalReport.KSSF.pdf

  5. For example, CSU Chico offers several

  6. Many colleges have what is typically called “liberal arts mathematics” (LAM) for non-STEM majors. • LAM covers a variety of self-contained topics, including • voting, fair division, apportionment • circuits, networks • geometry, fractals • descriptive statistics • check digits, cryptology • finance

  7. CSU Chico Math 101 is a LAM course

  8. Agnes M. Rash and Sandra Fillebrown, “Courses on the beauty of mathematics: our version of general education mathematics courses,”PRIMUS 26(9), pp. 824–836 (2016) Abstract: This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed “math beauty” courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to master mathematical proofs in the context of the field of study, is described briefly with details given for one. • Some focus on the “beauty of mathematics” • In this example, course draws from number theory to explore beauty in constructing or discovering conjectures, proofs, and counterexamples

  9. Others use the history of mathematics as a vehicle to convey the richness of mathematics and its development over time by different cultures

  10. Continues to be of interest in developing options that interest students or improving current options • MAA and AMATYC • MAA QL webpage • http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/quantitative-literacy • SIGMAA QL http://sigmaa.maa.org/ql/ • Reception and business meeting at MathFest 2017 on Thursday, July 27, 6:30–7:30 p.m. (http://www.maa.org/meetings/mathfest/program-details/2017/sigmaa-activities) • AMATYC ANets Mathematics for Liberal Arts

  11. Sample from PRIMUS (http://www.tandfonline.com/toc/upri20/current) • Using Popular Culture to Teach Quantitative Reasoning (2007) • Group Projects and Civic Engagement in a Quantitative Literacy Course (2011) • A Real-Life Data Project for an Interdisciplinary Math and Politics Course (2012) • Social Choice in a Liberal Arts Mathematics Course (2013) • Taking Math Outside of the Classroom:Math in the City (2013) • Tailoring Modified Moore Method Techniques to Liberal Arts Mathematics Courses (2014) • Learner-Centered Pedagogy in a Liberal Arts Mathematics Course (2016) • An Inquiry-Based Quantitative Reasoning Course for Business Students (2017)

  12. CSU Chico Sustainability Path through GE

  13. Sustainability courses marked by oak leaf

  14. How can mathematics be brought to bear?

  15. Quantitative Literacy on the Global Stage Act II Synopsis ... we will describe four big ideas that address important global issues, the mathematics behind them, and how they can be made accessible at a pre-calculus level. Setting First Year Seminar at UC Davis

  16. Four big ideas underlying a curriculum on Global Numeracy, Global Change (GNGC): • The earth is finite. • Ecology and economics have common roots. • Social and biological change involve delay. • People move from where it is worse to where it is better. Fleshing out these ideas can make use of basic mathematics and quantitative reasoning in a meaningful context.

  17. This curriculum has two Incarnations: • First Year Seminar at UC Davis • Sequenced PowerPoint files in .pps format linked to spreadsheet templates and other assignments. Both involve a "crash course" in Excel. Global Numeracy, Global Change is not being put forward as the "alternative course" per se. But might GNGC serve as a resource in such efforts?

  18. 1. The Earth Is Finite Epistemologist struggle with "What does it mean to know something?" Empiricists believe knowledge is derived from experience (including observation). Rationalists believe knowledge is established by reason and deduction. Educators tend to settle for some combination of the two. Eratosthenes used empiricism (measuring the inclination of the sun's rays) and rationalism (Euclidean geometry) to find the size of the earth in "one of the ten most beautiful experiments of all times." pp. 240-241 of Algebra In Context.

  19. 1. Eratosthenes' Famous Experiment (slightly idealized) 7.5° . Alexandria . Proposition 29 Book One of Euclid "Corresponding angles are equal" 500 Syene Equator Time's a'wasting In Alexandria, 500 miles north of Syene, the sun's rays made an angle of 7.5° with a gnomon (vertical post). The central angle of 7.5° is 1/48th of 360°. Circumference of earth is 48 x 500 ≈ 24,000 miles C = 2πR R ≈ 4,000 miles

  20. Replicating Eratosthenes' experiment is difficult. There are, however, other experiments that enable one to estimate the size of the earth: • A ship whose mast extends 52.8 feet above the water sails from port at 3mph. After 3 hours its flag disappears from view ... • Driving due north 200 miles, the inclination of the north star above the horizon increases by 3° ... • At noon the the sun's rays make angles of 12.5° and 5° with gnomons at points A and B ... All use basic geometry to arrive at R ≈ 4000 miles. They are also absent from most geometry curricula!

  21. Life on earth depends on the biosphere! The surface area of a ball is the same as the area of a rectangular piece of paper that envelops the ball. A = 4πR2 2R R 2πR When unrolled, the paper has base 2πR and height 2R. Wow, look how big Africa really is. S ≈ 4 x π x 40002 S ≈ 200 million square miles

  22. In isolation, big numbers have little meaning. Finding the ratio between a pair of large numbers can give serve to give meaning to both of them. Surface area Population Milestones 200 million mi2 Since 1960 (3 billion) population has increased by 1 billion people about every 13 years: Land area 56 million mi2 1973, 36 billion acres 1986, 1999, 2011, ... Arable land 2017 7.5 billion people 3.7 billion acres

  23. 7.5 billion people 3.7 billion acres The division problem 3.7 ÷ 7.5 is not done in polite company. But Americans use about 2 acres. One can grow a lot of food on ½ acre. Isn't this Malthusian thinking? I wonder what global equity looks like. We have been led to a topic of historical interest ... and to the mathematics of exponential growth!

  24. 2. Ecology and Economics Have Common Roots. These include the mathematics of exponential growth. In a banking context (interest compounded annually) "ending balance = beginning balance + interest" u(n) = u(n-1) + Ru(n-1) u(n) = (1 + R)u(n-1) u(n) = u(0)(1 + R)n These basic ideas are reinforced with some spreadsheet projects.

  25. Ecologists differ from economists by viewing the world with a carrying capacity in mind. Anyone who believes that exponential growth can go on forever in a finite world is either a madman or an economist. - - Kenneth Boulding Carrying capacity may suggest logistic growth: A bank pays a nice interest rate (e.g., R = 0.1 or 10%) but imposes a small annual fee (e.g., E = 0.005 or ½%) that is based on the square of your balance. u(n) = (1+R)u(n-1) – Eu(n-1)2

  26. There also exist less familiar ways of illustrating the role of carrying capacity in shaping one's world view. Choosing a value T (say T = 10 billion) as the number of people the earth can sustainably support, ecologists may focus on the "slack" T – u(n) that a population of size u(n) enjoys. This can be illustrated by data downloaded from the World Bank website.

  27. 3. Social/biological change involves delay. Loyalty Savings Bank offers an attractive interest rate R, but only on funds that have been on deposit more than one year. What rate will Loyalty pay in the long run? u(n) u(n-1) Ru(n-2) Hmm, this looks familiar! = + = + u(n-1) u(n-1) u(n-1) lim n->∞ If x = u(n)/u(n-1) x = 1 + R/x x2 – x – R = 0 Given a longer delay u(n+1) = u(n) + Ru(n - d) with d > 1 the growth rate is reduced more severely.

  28. Theorem. Delay reduces the rate of exponential growth. Corollary. Eliminating delay increases the rate of exponential growth. Without acknowledginging Fibonacci, economists are aware of such phenomena. Eliminating delay is an important tool for stimulating economic growth. Keynesian Multiplier Regulation Debt Unfortunately, we have very little intuitive insight into the effect of delays.

  29. Armageddon Savings Bank After several years of paying an annual fee based on the square of their balance (logistic growth), customers note slow growth and threaten to close their accounts. Armageddon responds with an idea used by Loyalty: After banking here for 9 years, we will now base our fee on your balance of 8 years ago. u(n) = u(n-1) + Ru(n-1) – Eu(n-1)2 for n ≤ 9 u(n) = u(n-1) + Ru(n-1) – Eu(n-9)2 for n ≥ 10 Hmm, my balance was a lot smaller 8 years ago.

  30. 1970 Kvant established in USSR 1990 Quantum established in United States Many of the ideas we have discussed appeared in Quantum during the 11 years of its existence. 1997 25th anniversary of "The Limits To Growth"

  31. While The Limits To Growth relied on systems analysis to develop a complex World3 model, its conclusions correspond to solutions of u(n) = u(n-1) + Ru(n-1) – Eu(n-d)2 The state of global equilibrium could be designed so that the basic needs of each person are satisfied ... The most probable result [of current trends] will be a rather sudden and uncontrollable decline in both population and industrial capacity. If the world's people decide to strive for the first outcome rather than the second, the sooner they begin working to attain it, the greater will be their chance of success.

  32. 4. People Move From Where it is Worse To Where It Is Better The above statement suggests an analogy between migration and heat flow (Newton's Laws of Cooling).

  33. The mathematics of heat flow can be modeled as follows:

  34. Here is a spreadsheet whose wealth sharing corresponds to heat flow an insulated rod. =SUM(C4:H4) =H4 =C4 =C4-.1*(C4-B4)-.1*(C4-D4) Here the total of the assets of the six players remains constant and each approaches the average value 310/6. Try it!

  35. While only a starting point for more realistic models, heat flow provides an abstract approach to human migration. In a world where human fertility varies greatly from country to country, migration appears as a basic human phenomenon (much like the laws of thermodynamics).

  36. Our text is E. O. Wilson's Half Earth.

  37. For further information about "Global Numeracy, Global Change" please contact • Kurt Kreith • Department of Mathematics • UC Davis • Davis, CA 95616 • kkreith@ucdavis.edu

  38. Quantitative Literacy on the Global Stage Act III Where do we go from here?

  39. Where do we go from here? • How do we best address quantitative literacy for non-STEM majors (and STEM majors)? • Can QR be developed in the context of efforts to address global environmental issues? (Which subject areas can and should be addressing this?) • Is there interest in a (one-day) conference on addressing QR?

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