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Quantitative Reasoning at Yale

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Quantitative Reasoning at Yale. Yale University. 11 Graduate and Professional Schools. Yale College. 5300 Undergraduates from all 50 states and >70 countries Middle 50% SAT scores 690-790 40% of students receiving need-based financial aid.

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Yale University

11 Graduate and Professional Schools

Yale College

5300 Undergraduates from all 50 states

and >70 countries

Middle 50% SAT scores 690-790

40% of students receiving need-based

financial aid


Yale College Distribution Requirements

(late 1970s through class of 2008)

Three courses in each of four distributional groups

Group I – languages and literature

Group II – other humanities

Group III – social sciences

Group IV – math, science, engineering

(at least two courses must

be in natural sciences)


Committee on Yale College Education

Richard Brodhead, Chair

formed in Fall, 2001

report published April, 2003

42 faculty, students and recent alumni

Recommendations included enhancement of education in sciences and institution of new

distribution requirements, including

a quantitative reasoning requirement.


New Distribution Requirements

Class of 2009 and beyond

Skills Requirement

2 courses in writing

2 courses in quantitative reasoning

1-3 courses in foreign language

Area Requirement

2 courses in humanities

2 courses in social sciences

2 courses in natural sciences


Faculty QR Council

Paul Hudak, Computer Science, Chair

Joseph Chang, Statistics

Michael Frame, Mathematics

Donald Green, Political Science

Roger Howe, Mathematics

Roman Kuc, Electrical Engineering

Benjamin Polak, Economics

William Segraves, Yale College

R. Shankar, Physics

Steven Stearns, Ecology and Evolutionary Biology

Teresa Treat, Psychology

Kurt Zilm, Chemistry

Steven Zucker, Computer Science


Key Questions

What is QR?

What courses should count as QR courses?

Core vs. Applied QR


Key Questions

What is QR?

What courses should count as QR courses?

Math (and applications)

Stats (and applications)

Comp Sci?



A course may be used to satisfy the quantitative reasoning

requirement if it meets the following criteria:  

•A primary aim of the course is to develop quantitative reasoning

or its application. Quantitative reasoning includes mathematics,

statistics, algorithms, and formal symbolic logic. Calculation,

quantification, and measurement can supplement but cannot

replace quantitative reasoning and problem solving.     

•A substantial proportion (generally a majority) of course

exercises, such as problem sets, should be designed to develop and

strengthen quantitative reasoning skills through regular practice.

Examinations or assigned projects should similarly be primarily

quantitative in nature and should require students to demonstrate

their quantitative reasoning skills.


QR Courses without Prerequisites (32)

Various courses for majors and non-majors in calculus, statistics, comp sci, engineering and physical sciences, and others including:

Applied Math – The Pleasures of Counting

Architecture – Introduction to Structures

Comp Sci - Visualization: Data, Pixels and Ideas

Great Ideas in Computer Science

Economics - Introductory Microeconomics (3 versions)

Environmental Studies/G&G – Atmosphere, Ocean and

Environmental Change

Math - Fractal Geometry (plus freshman seminar)

Music – Math, Music and Mind

Operations Research – Introduction to Management Science:

Probabilistic Models

Philosophy – First Order Logic

Psychology – Statistics


Council Review - Implications


Departmental Interests

Individual Faculty Concerns


Review of new and existing courses

Tracking of distributional designations


Variations on QR Requirements

  • Place-out permitted
  • Students place out on the basis of test scores or
  • take test to place out of requirement
  • What to provide for students who don’t place out
  • All students required to take QR courses
  • How to meet needs of diverse student population
  • How to place students

Assessment of QR Preparation

Placement Questionnaire

Length - needs to be short

Breadth- test full range of QR areas

Is it more valuable than SAT?

Iatrogenic effects


Placement and Advising

Individual Advising

Web-based tools


Outcomes Assessment

  • Enrollment in QR Courses
  • Evaluation of Individual Courses
  • Skills assessment
  • What skills should we expect to see change?
  • Omnibus QR exit assessment?
  • Attitudes assessment

Tutoring Support

STARS Program

Residential College Tutors (grad students, walk-in)

Science and QR Tutors (assigned, mostly undergrad)

Course-Based Peer Tutors


Support for Teaching

Training for Teaching Fellows and Faculty

Assistance with Course Development

and Implementation of New Teaching Methods


Challenges in QR Education


Negative Experiences

Stereotype Threat


*Schmader, T., & Johns, M. (2003). Converging evidence that stereotype

threat reduces working memory capacity. Journal of Personality and Social

Psychology, 85, 440-452..


Communicate the message that you think everyone has the potential to succeed in quantitative courses

  • Communicate that all individuals are welcomed, supported, and valued whatever their background and experiences
  • Remind students of malleability of quantitative skill
  • Facilitate specific, external, unstable attributions for quantitative difficulties
  • Minimize activation of stereotypes and presence of stereotypic expectations

Faculty Buy-In

Support for career

Logistical support

Pedagogical support

Valuing teaching