Use, Misuse, and Missed Use of
Quantitative Reasoning in
Student Writing
Nathan D. Grawe
Carleton College
With support from the US Department of Education’s Fund for the Improvement of Post-Secondary
Education, the National Science Foundation, and the WM Keck Foundation.
What is QR?
What is QR?
The habit of mind to consider the power
and limitations of quantitative evidence in
the evaluation, construction, and
communication of arguments in public,
professional, and personal life.
What is QR?
Four facets of QR:
1) QR requires a basic skill set
What is QR?
Four facets of QR:
1) QR requires a basic skill set
2) QR demands application in context
"The test of numeracy, as of any literacy, is
whether a person naturally uses appropriate
skills in many different contexts"
-National Council on Education and the
Disciplines (2001)
What is QR?
Four facets of QR:
1) QR requires a basic skill set
2) QR demands application in context
3) QR involves argument
What is QR?
Four facets of QR:
1) QR requires a basic skill set
2) QR demands application in context
3) QR involves argument
“Deploying numbers skillfully is as important
to communication as deploying verbs.”
-Max Frankel, The New
York Times Magazine
What is QR?
Four facets of QR:
1) QR requires a basic skill set
2) QR demands application in context
3) QR involves argument
“Numbers [are] the principal language of
public argument.”
-BBC Program More or Less
What is QR?
Four facets of QR:
1) QR requires a basic skill set
2) QR demands application in context
3) QR involves argument
4) QR is a habit of mind
“[QR] is not a discipline but a way of
thinking….”
-Lynn Steen
Achieving Quantitative Literacy
What is QR?
“…sophisticated reasoning with
elementary mathematics more than
elementary reasoning with sophisticated
mathematics.”
-Lynn Steen
Achieving Quantitative Literacy
What to the numbers show?
“Consumption of green products that
claim to be more environmentally benign
has steadily increased in recent years.”
What do the numbers show?
How representative is that?
Compared to what?
How was the variable
operationalized?
Is the outcome statistically
significant?
What’s the effect size?
What’s the effect size?
What’s the effect size?
Are the results those of a single
study or of a literature?
Are the results those of a single
study or of a literature?
What’s the research design
(correllational or experimental)?
Fact: Those who work with computers
earn 15-20% more than others.
“Thus, computer training may, at least in
the short run, be a profitable investment
for public and private job training
programs.”
What’s the research design
(correllational or experimental)?
Other interesting returns:
Calculator = 12.8%
Telephone = 11.4%
Pencil/Pen = 11.2%
Work while sitting = 10.1%
Controlling for what?
Carleton’s QuIRK Initiative
•
•
Situate QR in the context of argument
Look for evidence of QR proficiency in
student papers
Our Population: The College
Writing Portfolio
Sophomore Writing Portfolio
3-5 papers plus reflective essay written in
2 of the 4 college divisions
-observation
-analysis
-interpretation
-documented sources
-thesis-driven argument
Two Types of QR Use in
Student Papers
Central Use:
Use of numbers to address a central
question, issue, or theme
Peripheral Use:
Use of numbers to provide useful detail,
enrich descriptions, present background,
or establish frames of reference
Two Types of QR Use in
Student Papers
The importance of the periphery:
“Even for works that are not inherently
quantitative, one or two numeric facts can
help convey the importance or context of
your topic.”
-Jane Miller
The Chicago Guide to
Writing About Numbers
Evidence from Student Writing
Excerpt #: 1
Title: “Modeling the Implicit Learning of
Language Acquisition”
Thesis: Even if people aren’t aware of the
systems undergirding our language, they
implicitly learn the system through
experience.
Evidence from Student Writing
Excerpt #: 1
•
•
•
Discussion includes:
Critical analysis of effect size
Information on central tendency (mean
and mode)
Information on extreme scores
Evidence from Student Writing
Excerpt #: 2
Title: Denmark: A Modern Social
Democracy”
Thesis: Denmark is a model of social
democracy for the rest of the European
Community.
Evidence from Student Writing
Excerpt #: 2
“world-class standard of living,” “high
labor costs,” “high taxation,” “drastic
changes” by right wingers in
1980s,“inflation brought under control,”
“economy…fundamentally strong,” “since
1992…export performance slipped
considerably”
Evidence from Student Writing
Excerpt #: 2
Top 10 GDP per capita in $US, 2005
Luxembourg
Norway
$79,851
$63,918
Ireland
Denmark
$48,524
$47,769
Iceland
Qatar
Switzerland
$53,290
$52,240
$49,351
United States $41,890
Sweden
$39,637
Netherlands $38,248
And Denmark reports the least income inequality of
all countries measured by the UN.
Evidence from Student Writing
Excerpt #: 3
Title: “Daycare and Development”
Topic: Review of literature on the effects
of day care on child development.
Examples from Student Work
“With rising inflation…, many families are
forced” to make tough child care choices.
“Nonparental child-care is on the rise as
more and more mothers choose to
work….”
Examples from Student Work
Alternative:
“Understanding the effects of day care on child
development is increasingly important as labor
force participation among married women with
children, ages 25-34, increased from 28% in
1960 to 68% in 2005. In fact, the number of
working women with children nearly tripled
during those 45 years from 8.1 million to 26.2
million.”
Evidence from Student Writing
Excerpt #: 4
Title: “Democracy in India”
Thesis: India represents a challenge to
dominant political models of the
determinants of democracy that can help
refine that theory.
Evidence from Student Writing
Excerpt #: 4
•
•
•
Uses of data:
Counts
Ratios
Percentages
The Need for Integrative Learning
• 30% of gen ed papers are centrally QR
relevant
• Of these, nearly 50% are outside natural
sciences
• Another 25% are peripherally so
• Of these, 90%+ are outside natural sciences
and 50%+ are in Arts, Lit, & Humanities
The Need for Integrative Learning
Rhetorical slant on QR engages faculty
across curriculum
QuIRK 18-month participation rate
Overall:
65%
Natural & Social Sciences:
75%
Arts, Lit, & Humanities:
55%
The Need for Integrative Learning
• Religion and American Public Life
“…discussions across a variety of
disciplines about the existing and proper
place of religion in American public life
(legal studies, journalism, sociology,
history, public theology, and ethics)”
The Need for Integrative Learning
• Classics 100
“…a close reading of an extended passage
of Pausanias' Description of Greece. In it
he records in great detail an inventory of
all the statues of athletes (nearly 200)
that he observed in the Sanctuary of Zeus
at Olympia….”
The Need for Integrative Learning
• Modern Indian Fiction 2
“…Salman Rushdie asserts the supremacy of Indian
literature in English over all other language
traditions…. [I will] anchor these discussions in a
study of the actual numbers involved in publishing,
readership, and language education. Students would
be able to use the data both to contextualize claims
such as Rushdie’s (just how many Indians read
English? what fraction of Indian publishing is actually
in English? how do writers in English fare in literary
prizes awarded within India?) and to better illuminate
an understanding of how complex the Indian literary
landscape is.”
References
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ABC News. February 21, 2007. “Do Libras Live Longer?”
(http://abcnews.go.com/Technology/story?id=2890150&page=1)
Bialik, Carl. November 2006. “The Numbers Guy: Grading the Pollsters.” Wall Street
Journal (http://www.masondixon.com/public/index.cfm?FuseAction=PressOffice.Article&ContentRecord_id=f1e66ca11372-fa49-99bd-58f6c5a4e505).
Brakke, David F. 2003. "Addressing Societal and Workforce Needs," in Quantitative
Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn
Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.
De Lange, Jan. 2001. "Mathematics for Literacy" in Mathematics and Democracy: The Case
for Quantitative Literacy, Lynn Arthur Steen, ed. Princeton, NJ: National Council on
Education and the Disciplines.
Fishman, Charles. 2006. The Wal-Mart Effect. New York: The Penguin Press.
Frankel, Max. 1995. “Word and Image; Innumercy,” New York Times, March 5.
Hughes Hallett, Deborah J. 2001. "The Role of Mathematics Courses in the Development of
Quantitative Literacy" in Mathematics and Democracy: The Case for Quantitative Literacy,
Lynn Arthur Steen, ed. Princeton, NJ: National Council on Education and the Disciplines.
Miller, Jane E. 2004. The Chicago Guide to Writing about Numbers. Chicago: University of
Chicago Press.
More or Less, British Broadcasting Corporation radio program. Retrieved April 27, 2007,
from http://news.bbc.co.uk/2/hi/programmes/more_or_less/1628489.stm.
References (Cont.)
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National Council on Education and the Disciplines. 2001. Mathematics and Democracy: The Case
for Quantitative Literacy. Washington DC: Mathematical Association of America.
Newsweek. November 21, 2005. “How to Beat the Big Energy Chill.”
(http://www.newsweek.com/id/51208)
Newsweek. August 6, 2007. “When Medical Studies Collide: Contradictory Reports? MetaAnalysis May Make Things More Confusing.”
Nurnberg, H. George; Paula L. Hensley; Julia R. Heiman; Harry A. Croft; Charles Debattista; and
Susan Paine. 2008. “Sildenafil Treatment of Women with Antidepressant-Associated Sexual
Dysfunction.” Journal of the American Medical Association, 300(4): 395-404.
(http://www.businessweek.com/magazine/content/07_32/b4045052.htm)
Reuters. November 26, 2007. “New Poll Shows Clinton Trails Top 2008 Republicans.”
(http://www.reuters.com/article/politicsNews/idUSN2645320920071126)
Shafer, Jack. 2005. “Weasel Words Rip My Flesh! Spotting a Bogus Trend Story on Page One of
Today’s New York Times,” Slate, September 20.
Steen, Lynn Arthur. 2004. Achieving Quantitative Literacy: An Urgent Challenge for Higher
Education. Washington, DC: Mathematical Association of America.
Story, Louise. September 20, 2005. “Many Women at Elite Colleges Set Career Path the
Motherhood.” New York Times.
Wallis, Claudia. 2007. “Is the Autism Epidemic a Myth,” Time, January 12.
WCCO. 2007. “Report: Indians Denied Home Loans More Often,” December 30.
Wiggins, Grant. 2001. "'Get Real!': Assessing for Quantitative Literacy" in Mathematics and
Democracy: The Case for Quantitative Literacy, Lynn Arthur Steen, ed. Princeton, NJ: National
Council on Education and the Disciplines.