Hollins University’s Program in Quantitative Reasoning Across the Curriculum

1. Hollins University’s Program in Quantitative Reasoning Across the Curriculum Phyllis Mellinger pmellinger@hollins.edu Christina Salowey csalowey@hollins.edu Joe Leedom jleedom@hollins.edu

2. Hollins’ New General Education Program:Education through Skills and Perspectives (ESP) ESP Skills Writing Oral Communication Quantitative Reasoning Information Technology ESP Perspectives Aesthetic Analysis Creative Expression Ancient and/or Medieval Worlds Modern and/or Contemporary Worlds Social and Cultural Diversities Scientific Inquiry Global Systems and Languages

3. Hollins’ Definition for Quantitative Reasoning Quantitative reasoning is the application of mathematical concepts and skills to solve real-world problems. In order to perform effectively as professionals and citizens, students must become competent in reading and using quantitative data, in understanding quantitative evidence and in applying basic quantitative skills to the solution of real-life problems.

4. Basic Quantitative Reasoning Requirement (q) Began in Fall 98 QR Assessment q proficiency Enroll in Intro to QR q proficiency upon completion • Pilot QR Tutoring (Fall 99) • Director of QR and “virtual” QR Center (Fall 03) additional tutoring QR Tutor, Theory and Practice Course • Center for Learning Excellence Writing and QR (Fall 04) • Online QR & placement (Fall 2007) Math 100, Math 105, Math 130

5. Applied Quantitative Reasoning Requirement (Q) Hollins Funded Faculty Development Efforts • Workshop to develop preliminary Q modules (98-99) • Faculty Reading Group (99-00) NSF Faculty Development Grant (00-01) New Gen Ed program and two QR requirements started with students entering in Fall 2001 Pilot Site for Bookman/Ganter SGER NSF Grant (03-04) Pilot Site for Madison QRCW NSF Grant (07-08)

6. Hollins Q-Courses from the Mathematical, Natural, and Physical Sciences Chemistry: General Chemistry I and II; Principles of Chemistry; Environmental Analysis; Analytical Chemistry, Experience Chemistry Computer Science: Computer Science I Environmental Studies: Feeding Frenzy; Global warming Mathematics: Precalculus; Intuitive Calculus; Calculus I and II; Linear Algebra Physics: Physical Principles I and II; Oceanography, Analytical Physics I and IIPsychology:Analysis of Behavioral Data; Human Memory Statistics: Introduction to Statistics; Statistical Methods

7. Hollins Q-courses from the Humanities, Social Sciences and Fine Arts Business: Corporate Finance; Investments; International Finance Classics/Art: Ancient ArtCommunications:Research Methods in Communication Dance: Performance Workshop; Sound Design Economics: Economics of Social Issues; Economics of Health Care; Public Finance; Money, Credit and Banking; Macroeconomic Theory and Policy; International Political Economics History: American Social History; The Middle Ages; European Empires; The Renaissance Humanities: France and the French;

8. Hollins Q-courses from the Humanities, Social Sciences and Fine Arts International Studies: Global Systems; French for International Business Music: Music theory III Philosophy: Symbolic Logic Political Science: Research Methods in Political Science; International Political Economy; Globalization and local responses; Seminar in American government Sociology: Sociology of Health, Illness and Medicine; Methods of Social Research Theatre: Lighting Design; Stagecraft Women’s Studies: Globalization and Poverty

9. Course Criteria for Q courses • A quantitative reasoning skills course must involve students in the application of quantitative skills to problems that arise naturally in the discipline, in a way that advances the goals of the course and in a manner that is not merely a rote application of a procedure. • In order to be approved as QR applied, a course must include at least two QR projects and devote class time to the proper use of quantitative skills, building on what is taught in Math 100. The class discussions and the students’ work on these projects must address a significant application of quantitative skills to problem solving within the given discipline. • The end result of each QR project should be a written assignment that includes a statement of the problem, an explanation of the methods used, and a summary of the results. When appropriate, the written assignment should discuss any limitations encountered and possible improvements to the procedure and/or results.

10. Design Plan for Q Projects Project Idea Central topic, natural fit, application of QR Process Use class time to develop necessary background material Handout with specifics -sequence of assigments Group work/activities to foster student discovery and confidence Analysis in language of the discipline Include open-ended questions to encourage multiple approaches Drawing Conclusions Reality check, revisions, limitations, future improvements, reflection

11. Guidelines for Assessing Q Projects Understanding the Problem Problem well defined? Firm grasp on the necessary quantitative methods? Completing the Process Appropriate quantity and quality of data? Implementation and integration of quantitative methods? Appropriate problem solving techniques? Drawing Conclusions Interesting, creative, original? Reasonable? Self-assessment?

12. American Social History Professor Ruth Doan Family in Colonial New England Analysisof family data from Bristol census of 1689 Mean, median and mode • household size, number of children, number of servants Family - extended, blended, nuclear, female-headed

13. Music Theory IIIProfessor Barbara Mackin Study of chromatic musical materials with harmonic analysis of western music through the 19th century Composing variations on a simple melody using chromatic vocabulary and variation techniques Analysis of F. Schubert’s Impromptu in Ab, Opus 90 no.4 • Provide harmonic analysis using Roman numerals and appropriate symbols • Write a paper explaining your findings

14. France and the French: Context in Cultural UnderstandingProfessor Edwina Spodark Multimedia examination of socio-cultural contrasts between France and the U.S. Convert what people think of France and the French into quantitative data from a survey and analyze data to increase awareness of possible biases and stereotypes that are prevalent today Interpret quantitative information represented by statistics and in graph form and to see how they help explain and relate to human events. Collect data on selected topic and input into EXCEL. Create a graph that illustrates your data. Include analysis of results in oral presentation using PowerPoint

15. Symbolic LogicProfessor Michael Gettings Washington Post Editorials - identify categorical syllogisms - determine validity of the syllogisms The Affluent Society by John Kenneth Galbraith - identify conclusion of a given passage - symbolize the argument of given passage using propositional logic - use truth tables to determine validity - construct proof (valid) or show counterexample (invalid)

16. Introduction to Communication Studies Professor Chris Richter Quantitative content analysis of TV News Video recording of one week of ABC, CBS, CNN and NBC national news programs Data collection (hard news, soft news, weather, sports, advertising, teasers and bumpers, opening and closing) Data analysis and conclusions

17. Christina SaloweyAncient Art Quantitative analysis of Doric temple architecture Creation of equations from a Roman architectural text Study of the proportions of actual Doric temples by doing measurements on scale plans Creation of graphs tracking date versus proportions Recreation of a temple from archaeological fragments using the mathematical relationships inherent in the Doric order

18. Columns • Temple of Hera (Basilica) at Paestum. 550 BCE • Parthenon at Athens. 438 BCE • What are the differences in the look of the columns? • We will quantify that today.

19. Premise: There is a mathematical relationship among the elements of a Doric temple. Goals: Introduce the textual and material evidence for the Doric temple. Introduce quantitative skills necessary for deeper understanding of ancient Greek architecture. Show an application of these skills that a working archaeologist would use in the field.

20. Doric Order and Plan

21. Text of Vitruviustext from www.perseus.tufts.edu • The thickness of the columns will be two modules, and their height, including the capitals, fourteen modules….The height of the architrave, including taenia and guttae, is one module, and of the taenia, one seventh of a module. The guttae, extending as wide as the triglyphs and beneath the taenia, should hang down for one sixth of a module, including their regula…Above the architrave, the triglyphs and metopes are to be placed: the triglyphs one and one half modules high, and one module wide in front….The width of the triglyph should be divided into six parts, and five of these marked off in the middle by means of the rule, and two half parts at the right and left….The triglyphs having been thus arranged, let the metopes between the triglyphs be as high as they are wide, while at the outer corners there should be semi-metopes inserted, with the width of half a module. (Vitruvius, de architectura, book IV, chapters iii and iv)

22. Assignments • Determine Vitruvius’ mathematical relationships in a Doric temple: number of modules comprising each architectural element, proportional relationship between elements, equations. • Focus on one relationship: column height to column width. • Measure column height and width using elevation plans for several Doric temples. • Graph column height:column width vs. date. • Evaluate some material and data from real excavations to determine date and size of a temple.

23. Measurements from Elevations • The scale measure at the bottom is in meters. • Figure out a relationship between inches on the scale and meters. • Measure width and height of columns as precisely as possible. • Convert inches into meters.

24. Create a graph • Graph paper, pencil and a little practice. • Create scales that stretch across the x and y axes. • Plot your data.

25. Reconstruction of a Doric Temple • Measure the terracotta triglyph from Cosa and determine the following: • The size in meters of one “module”of this small temple. • The size in meters of a single intercolumniation. • Assuming that the temple is hexastyle prostyle, determine the width and length of the building. Draw a plan of the building. • Assuming that this Roman building would have come close to the ideal Vitruvian proportions, determine the following: • The diameter of a column • The height of a column • The height of the entablature • Calculations • 1 triglyph channel = 1/6 module • 1/6 module = .02 meters • 1 module = .12 m • 1 intercolumniation (IC) = 2 metopes + 2 triglyphs • IC = 2 (1 ½ modules) + 2 (I module) • IC = 5 modules = .60 m • Hexastyle prostyle temple = 5 IC + 2 (1/2 column diameters) • 5 (5 modules) + 2 (1 module) = 27 modules • Width of the temple = 3.24 m • Column diameter = .24 m

26. The Eureka Moment • Discovering that drawing a plan of the temple using the module method is not only easier, but is also probably how ancient architects worked.

27. Challenges • Original reluctance • Prerequisites • Student influences • Support of Director and tutors • Changes in faculty/multiple sections • No set % for QR projects – pass class without Q • New ideas: Patterns in Poetry & Math, Mathematics in fiction

28. Questions