hollins university’s program in quantitative reasoning across the curriculum
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Hollins University’s Program in Quantitative Reasoning Across the Curriculum. Phyllis Mellinger [email protected] Christina Salowey [email protected] Joe Leedom [email protected]. Hollins’ New General Education Program: Education through Skills and Perspectives (ESP). - PowerPoint PPT PresentationTRANSCRIPT
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Hollins University’s Program in Quantitative Reasoning
Across the CurriculumPhyllis Mellinger
Christina [email protected]
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Hollins’ New General Education Program:Education through Skills and Perspectives (ESP)
ESP SkillsWriting
Oral CommunicationQuantitative ReasoningInformation Technology
ESP PerspectivesAesthetic Analysis
Creative ExpressionAncient and/or Medieval Worlds
Modern and/or Contemporary WorldsSocial and Cultural Diversities
Scientific InquiryGlobal Systems and Languages
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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.
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Basic Quantitative Reasoning Requirement (q)
QR Assessment
q proficiency Enroll in Intro to QR q proficiency upon completiono Pilot QR Tutoring (Fall 99)
o Director of QR and “virtual” QR Center (Fall 03)additional tutoringQR Tutor, Theory and Practice Course
o Center for Learning ExcellenceWriting and QR (Fall 04)
o Online QR & placement (Fall 2007)Math 100, Math 105, Math 130
Began in Fall 98
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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)
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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
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0011 0010 1010 1101 0001 0100 1011Business: Corporate Finance; Investments; International Finance Classics/Art: Ancient Art Communications: 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;
Hollins Q-courses from the Humanities, Social Sciences and Fine Arts
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International Studies: Global Systems; French for International Business Music: Music theory IIIPhilosophy: Symbolic Logic Political Science: Research Methods in Political Science;
International Political Economy; Globalization and local responses; Seminar in American governmentSociology: Sociology of Health, Illness and Medicine; Methods of Social Research Theatre: Lighting Design; Stagecraft Women’s Studies: Globalization and Poverty
Hollins Q-courses from the Humanities, Social Sciences and Fine Arts
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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.
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Design Plan for Q Projects
Project IdeaCentral topic, natural fit, application of QR
ProcessUse class time to develop necessary background material
Handout with specifics -sequence of assigmentsGroup work/activities to foster student discovery and
confidenceAnalysis in language of the discipline
Include open-ended questions to encourage multiple approaches
Drawing ConclusionsReality check, revisions, limitations, future improvements,
reflection
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Guidelines for Assessing Q Projects
Understanding the ProblemProblem 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?
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American Social HistoryProfessor Ruth Doan
Family in Colonial New England
Analysis of 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
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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
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France and the French: Context in Cultural UnderstandingProfessor Edwina SpodarkMultimedia 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
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Symbolic LogicProfessor Michael GettingsWashington Post Editorials- identify categorical syllogisms- determine validity of the syllogismsThe 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)
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Introduction to Communication Studies
Professor Chris RichterQuantitative 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
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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 proportionsRecreation of a temple from archaeological
fragments using the mathematical relationships inherent in the Doric order
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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.
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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.
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Doric Order and Plan
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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)
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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.
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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.
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Create a graph • Graph paper, pencil and a little practice. • Create scales that stretch across the x and y
axes. • Plot your data. Doric Temples
Column Height: Column Diameter600 - 250 BCE
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
200250300350400450500550600Date (BCE)
Heig
ht:D
iamet
er
Ratio Column Height:Width
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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
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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.
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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
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