hollins university’s program in quantitative reasoning across the curriculum

28
4 2 5 1 0011 0010 1010 1101 0001 0100 1011 Hollins University’s Program in Quantitative Reasoning Across the Curriculum Phyllis Mellinger [email protected] Christina Salowey [email protected] Joe Leedom [email protected]

Upload: osias

Post on 05-Feb-2016

46 views

Category:

Documents


0 download

DESCRIPTION

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 Presentation

TRANSCRIPT

Page 1: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

Hollins University’s Program in Quantitative Reasoning

Across the CurriculumPhyllis Mellinger

[email protected]

Christina [email protected]

Joe [email protected]

Page 2: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 3: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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.

Page 4: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 5: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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)

Page 6: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 7: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

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

Page 8: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 9: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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.

Page 10: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 11: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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?

Page 12: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 13: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 14: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 15: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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)

Page 16: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 17: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 18: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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.

Page 19: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

42510011 0010 1010 1101 0001 0100 1011

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.

Page 20: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

Doric Order and Plan

Page 21: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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)

Page 22: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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.

Page 23: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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.

Page 24: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 25: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 26: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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.

Page 27: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011

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

Page 28: Hollins University’s Program in  Quantitative Reasoning  Across the Curriculum

4251

0011 0010 1010 1101 0001 0100 1011Questions