Incorporating Quantitative Literacy into General Education Courses

1. Incorporating Quantitative Literacy into General Education Courses John Holcomb October 9, 2007

2. Overview • New General Education Criteria • Why should we care about quantitative literacy? • Criteria • Objectives • Examples of ways to incorporate QL into courses • Thinking about your own course • Applying for the QL skill area

3. General Education • Breadth of Knowledge • Arts and Humanities • Social Sciences • Natural Sciences • Social Diversity • African-American • Human Diversity

4. Skill Areas • Writing • Oral Communication • Quantitative Literacy • Group Work • Critical Thinking • Information Literacy

5. Why care about QL? • Necessary for Democracy (Taken from Mathematics and Democracy: The Case for Quantitative Literacy) • Historian Lawrence Cremin sees literacy as “liberating” in which individuals command both the enabling skills needed to search out information and the power of mind necessary to critique it, reflect upon it, and apply it in making decisions. • John Dewey calls this “popular enlightenment,” that can inform and animate a vital democracy.

6. Ideal Quantitatively literate citizens need to know more than formulas and equations. They need a predisposition to look through the world though mathematical eyes, to see the benefits (and risks) of thinking quantitatively about commonplace issues, and to approach complex problems with confidence in the value of careful reasoning. Quantitative literacy empowers people by giving them tools to think for themselves, to ask intelligent questions of experts, and to confront authority confidently. These are skills required to thrive in a modern world.

7. Criteria • Involve quantitative work distributed over the course of the semester. • Provide explicit instruction in quantitative methods and quantitative reasoning. • Designate that at least 15% of the student’s grade is based on an evaluation of quantitative literacy. • Address at least the first three objectives.

8. Objectives • Interpret mathematical models such as formulae, graphs, tables, and schematics and draw inferences from them. • Represent and interpret mathematical information that is presented symbolically, visually, numerically, or verbally. • Use arithmetic, algebraic, geometric, statistical models and technology, or appropriate combinations of these to solve problems.

9. Objectives (con’t) • Estimate and check answers to mathematical problems in order to determine their reasonableness, identify alternatives, and select optimal results. • Recognize the limits of mathematical and statistical models and be able to explain those limitations in context.

10. Examples of Subjects requiring QL • Much of this information taken from the Mathematics Across the Curriculum Project at Dartmouth College • Electronic Bookshelf for College Courses • http://www.math.dartmouth.edu/~matc/eBookshelf/index.html

11. The Golden Ratio φ= w/l = 1.618

12. The Golden Rectangle Construction: Subdivide a square of side 1 into two equal rectangles. Then lay out a distance equal to the diagonal of one of these half-squares, plus half the side of the original square. The ratio of this new distance to the original side, 1, is the golden ratio.

13. Other Manifestations The Great Pyramid of Cheops

14. Environmental Science

15. Squaring the Circle: Geometry in Art and Architecture • Paul Calter • Book to be published by Key Curriculum Press in late 2007 • http://math.dartmouth.edu/~matc/math5.geometry/

16. Other Biology Areas • BIOMATH: Problem Solving for Biology Students • Addison-Wesley • This problem-solving supplement teaches biology students the mathematical concepts they need to succeed in their introductory biology courses. Instructors can either incorporate the biological math problems into their courses or ask students to use the booklet as a self-study tool.

17. Biology (con’t) • Better Nutrition by Analyzing Food Labels • In this module students learn how to interpret food labels and analyze the nutritional composition of foods. • The math includes calculating percents; writing formulas; reading, interpreting, and graphing data. • http://www.math.dartmouth.edu/~mqed/UNR/Nutrition/Nutrition.phtml

18. Biology (con’t) • Likelihood of Cancer • In this module students will determine the likelihood of developing cancer by examining various data. They will be presented with two pie charts, one showing the leading cause of death in the United States for people ages 10-24 and one for people ages 25 and older (pie chart data for 33 individual states are also available on line). • The mathematics involved is reading and interpreting pie charts; calculating and understanding percentages and proportions. • http://www.math.dartmouth.edu/~mqed/UNR/Cancer/Cancer.phtml

19. Biology (con’t) • VACCINES:An Introduction to Risk • Three case studies of diseases and their vaccines are described in this monograph. Smallpox, swine flu, and whooping cough have presented different sorts of problems for people trying to decide whether to be vaccinated or take their chances with the disease. • The mathematics is all elementary probability. There are nine problems, six of which are mathematical in nature. • http://www.math.dartmouth.edu/~mqed/NLA/Vaccines/Vaccines.phtml

20. Physical Science Possibilities • GASOLINE:From Unwanted By-product to Essential Fuel for the Twentieth Century • Gasoline is divided into three parts: historical studies, technological discussions, and questions for students. • In addition to historical background, this volume includes a description of chemical process calculations based on mass and energy balances. The mathematics involves solving two linear equations in two unknowns. • http://www.math.dartmouth.edu/~mqed/NLA/Gasoline/Gasoline.phtml

21. Physical Science (con’t) • THE ELECTRIFICATION OF LOS ANGELES:Engineering, Science, and History • This module identifies selected scientific principles associated with major technological advances in electrical power production. • The mathematics is an application of basic algebra to calculate physical quantities. Five multi-part problems are provided. • http://www.math.dartmouth.edu/~mqed/NLA/Electrification/Electrification.phtml

22. Music • COMPUTER MUSIC:Science and Technology of a New Art • Topics covered in this monograph (all written in easy-to-understand fashion) include the MIDI System, waves, synthesizers, coding, and computer music applications. • In addition to algebra applications, this volume provides an application of the trigonometric functions to analyzing sound waves, including a novice's introduction to Fourier series. • http://www.math.dartmouth.edu/~mqed/NLA/CompuMusic/CompuMusic.phtml

23. Music (con’t) • Music and Computers: A Theoretical and Historical Approach • Key Curriculum Press • Focuses on the history and theory of computer music composition. The text seamlessly integrates the fields of mathematics, computer science and music. This online course is supplemented with a student Course Guide. • http://www.keycollege.com/catalog/titles/music_and_computers.html

24. Literature • Chaos Theory, Fractals, etc. in Tom Stoppard's Arcadia • Robert Devaney Boston University • Lecture viewed on Real Player • http://www.math.dartmouth.edu/~matc/video/video.html

25. Writing • Essay Writing for ESL Students • This module consists of writing assignments (one essay assignment with lead-in exercises pertaining to statistics) that could be used in a high school English class, an advanced ESL class, or an introductory college writing course. • The mathematics needed for this module are an ability to compute basic operations on numbers, decimals, and percents and a basic understanding of descriptive Statistics. • http://www.math.dartmouth.edu/~matc/eBookshelf/literature/EAP.phtml

26. Communication • The Visual Display of Quantitative Information • Edward Tufte • http://www.edwardtufte.com/tufte/

27. Duck Hunting Assignment • Find a graphic in the mainstream media that is misleading to the viewer. Provide the complete source. Clearly explain the components of the graphic that are misleading or confusing. Conjecture as to whether you believe the graphic was constructed to be misleading or was the confusion accidental.

28. Good Graphic • Find a graphic in the mainstream media that successfully communicates sophisticated quantitative information. Provide the complete source. Explain the components of the graphic that are successful.

29. QL in a course from your Dept. • Breadth of Knowledge • Arts and Humanities • Social Sciences • Natural Sciences • Social Diversity • African-American • Human Diversity Think about QL as one of the key skill areas.

30. Questions for Skill Area Certification • How (e.g. based on what assignments) will quantitative literacy constitute at least 15% of a student’s grade? • How will at least the first three objectives outlined above be addressed? • How will the instructor be involved in teaching quantitative literacy skills? • How will quantitative literacy assignments be distributed over the course of the semester?