use, misuse, and missed use of quantitative reasoning in student writing nathan d. grawe carleton...

Use, Misuse, and Missed Use Use, Misuse, and Missed Use of Quantitative Reasoning in of Quantitative Reasoning in

Student Writing Student Writing

Nathan D. GraweNathan D. GraweCarleton CollegeCarleton College

With support from the US Department of Education’s Fund for the Improvement of Post-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.Secondary Education, the National Science Foundation, and the WM Keck Foundation.

What is QR?What is QR?


The habit of mind to consider the The habit of mind to consider the power and limitations of quantitative power and limitations of quantitative evidence in the evaluation, evidence in the evaluation, construction, and communication of construction, and communication of arguments in public, professional, arguments in public, professional, and personal life.and personal life.


Four facets of QR:Four facets of QR:

1) 1) QR requires a QR requires a basic skill setbasic skill set



1) QR requires a 1) QR requires a basic skill setbasic skill set

2) 2) QR demandsQR demands application in context application in context

"The test of numeracy, as of any literacy, is "The test of numeracy, as of any literacy, is whether a person naturally uses appropriate whether a person naturally uses appropriate

skills in many different contexts" skills in many different contexts"

-National Council on Education and the -National Council on Education and the Disciplines (2001) Disciplines (2001)




2) QR demands2) QR demands application in context application in context

3) 3) QR involves QR involves argumentargument






““Deploying numbers skillfully is as Deploying numbers skillfully is as important to communication as important to communication as deploying verbs.”deploying verbs.”

-Max Frankel, -Max Frankel, The New The New York Times MagazineYork Times Magazine






““Numbers [are] the principal language Numbers [are] the principal language of public argument.” of public argument.”

-BBC Program -BBC Program More or More or LessLess





3) QR involves 3) QR involves argumentargument

4) 4) QR is a QR is a habit of mindhabit of mind

““[QR] is not a discipline but a way of [QR] is not a discipline but a way of thinking….” thinking….” -Lynn -Lynn SteenSteen

Achieving Quantitative LiteracyAchieving Quantitative Literacy


“…“…sophisticated reasoning with sophisticated reasoning with elementary mathematics more than elementary mathematics more than elementary reasoning with elementary reasoning with sophisticated mathematics.”sophisticated mathematics.”

-Lynn Steen-Lynn Steen

Achieving Quantitative LiteracyAchieving Quantitative Literacy

What to the numbers show?What to the numbers show?

““Consumption of green products that Consumption of green products that claim to be more environmentally claim to be more environmentally benign has steadily increased in benign has steadily increased in recent years.”recent years.”

What do the numbers show?What do the numbers show?

How representative is that? How representative is that?

Compared to what?Compared to what?

How was the variable How was the variable operationalized?operationalized?

Is the outcome statistically Is the outcome statistically significant?significant?

What’s the effect size?What’s the effect size?

Are the results those of a Are the results those of a single study or of a single study or of a

literature?literature?

What’s the research design What’s the research design (correllational or (correllational or experimental)?experimental)?

Fact: Those who work with Fact: Those who work with computers earn 15-20% more than computers earn 15-20% more than others.others.

““Thus, computer training may, at Thus, computer training may, at least in the short run, be a profitable least in the short run, be a profitable investment for public and private job investment for public and private job training programs.”training programs.”

What’s the research design What’s the research design (correllational or (correllational or experimental)?experimental)?

Other interesting returns:Other interesting returns:

Calculator = 12.8%Calculator = 12.8%

Telephone = 11.4%Telephone = 11.4%

Pencil/Pen = 11.2%Pencil/Pen = 11.2%

Work while sitting = 10.1%Work while sitting = 10.1%

Controlling for what?Controlling for what?

Carleton’s QuIRK InitiativeCarleton’s QuIRK Initiative

• Situate QR in the context of Situate QR in the context of argumentargument

• Look for evidence of QR proficiency Look for evidence of QR proficiency in student papersin student papers

Our Population: The College Our Population: The College Writing PortfolioWriting Portfolio

Sophomore Writing PortfolioSophomore Writing Portfolio

3-5 papers plus reflective essay written 3-5 papers plus reflective essay written in 2 of the 4 college divisions in 2 of the 4 college divisions

-observation-observation

-analysis-analysis

-interpretation-interpretation

-documented sources -documented sources

-thesis-driven argument -thesis-driven argument

Two Types of QR Use in Two Types of QR Use in Student PapersStudent Papers

Central Use:Central Use:

Use of numbers to address a central Use of numbers to address a central question, issue, or themequestion, issue, or theme

Peripheral Use:Peripheral Use:

Use of numbers to provide useful Use of numbers to provide useful detail, enrich descriptions, present detail, enrich descriptions, present background, or establish frames of background, or establish frames of referencereference

Two Types of QR Use in Two Types of QR Use in Student PapersStudent Papers

The importance of the periphery:The importance of the periphery:““Even for works that are not inherently Even for works that are not inherently quantitative, one or two numeric facts quantitative, one or two numeric facts can help convey the importance or can help convey the importance or context of your topic.”context of your topic.”

-Jane -Jane Miller Miller

The Chicago Guide to The Chicago Guide to Writing About NumbersWriting About Numbers

Evidence from Student WritingEvidence from Student WritingExcerpt #: 1Excerpt #: 1

Title: “Modeling the Implicit Learning of Title: “Modeling the Implicit Learning of Language Acquisition”Language Acquisition”

Thesis: Even if people aren’t aware of the Thesis: Even if people aren’t aware of the systems undergirding our language, they systems undergirding our language, they implicitly learn the system through implicitly learn the system through experience.experience.


Discussion includes:Discussion includes:• Critical analysis of effect sizeCritical analysis of effect size• Information on central tendency Information on central tendency

(mean (mean andand mode) mode)• Information on extreme scoresInformation on extreme scores


Title: Denmark: A Modern Social Title: Denmark: A Modern Social Democracy”Democracy”

Thesis: Denmark is a model of social Thesis: Denmark is a model of social democracy for the rest of the democracy for the rest of the European Community.European Community.


““world-class standard of living,” “high world-class standard of living,” “high labor costs,” “high taxation,” “drastic labor costs,” “high taxation,” “drastic changes” by right wingers in changes” by right wingers in 1980s,“inflation brought under control,” 1980s,“inflation brought under control,” “economy…fundamentally strong,” “economy…fundamentally strong,” “since 1992…export performance slipped “since 1992…export performance slipped considerably”considerably”


Luxembourg $79,851 Ireland $48,524

Norway $63,918 Denmark $47,769

Iceland $53,290 United States

$41,890

Qatar $52,240 Sweden $39,637

Switzerland $49,351 Netherlands $38,248

Top 10 GDP per capita in $US, 2005

And Denmark reports the least income inequality of all countries measured by the UN.


Title: “Daycare and Development”Title: “Daycare and Development”

Topic: Review of literature on the Topic: Review of literature on the effects of day care on child effects of day care on child development.development.

Examples from Student WorkExamples from Student Work

““With rising inflation…, many With rising inflation…, many families are forced” to make tough families are forced” to make tough child care choices.child care choices.

““Nonparental child-care is on the rise Nonparental child-care is on the rise as more and more mothers choose to as more and more mothers choose to work….”work….”

Examples from Student WorkExamples from Student Work

Alternative:Alternative:

““Understanding the effects of day care on Understanding the effects of day care on child development is increasingly important child development is increasingly important as labor force participation among married as labor force participation among married women with children, ages 25-34, increased women with children, ages 25-34, increased from 28% in 1960 to 68% in 2005. In fact, from 28% in 1960 to 68% in 2005. In fact, the number of working women with children the number of working women with children nearly tripled during those 45 years from 8.1 nearly tripled during those 45 years from 8.1 million to 26.2 million.”million to 26.2 million.”


Title: “Democracy in India”Title: “Democracy in India”

Thesis: India represents a challenge to Thesis: India represents a challenge to dominant political models of the dominant political models of the determinants of democracy that can determinants of democracy that can help refine that theory.help refine that theory.


Uses of data:Uses of data:• CountsCounts• RatiosRatios• PercentagesPercentages

The Need for Integrative The Need for Integrative LearningLearning

• 30% of gen ed papers are centrally 30% of gen ed papers are centrally QR relevantQR relevant• Of these, nearly 50% are outside natural Of these, nearly 50% are outside natural

sciencessciences• Another 25% are peripherally soAnother 25% are peripherally so

• Of these, 90%+ are Of these, 90%+ are outsideoutside natural natural sciences and 50%+ are in Arts, Lit, & sciences and 50%+ are in Arts, Lit, & HumanitiesHumanities


Rhetorical slant on QR engages Rhetorical slant on QR engages faculty across curriculumfaculty across curriculum

QuIRK 18-month participation rateQuIRK 18-month participation rate

Overall: Overall: 65%65%

Natural & Social Sciences:Natural & Social Sciences: 75%75%

Arts, Lit, & Humanities:Arts, Lit, & Humanities:55%55%


• Religion and American Public LifeReligion and American Public Life

“…“…discussions across a variety of discussions across a variety of disciplines about the existing and disciplines about the existing and proper place of religion in American proper place of religion in American public life (legal studies, journalism, public life (legal studies, journalism, sociology, history, public theology, sociology, history, public theology, and ethics)”and ethics)”


• Classics 100Classics 100

“…“…a close reading of an extended a close reading of an extended passage of Pausanias' passage of Pausanias' Description of Description of GreeceGreece. In it he records in great . In it he records in great detail an inventory of all the statues detail an inventory of all the statues of athletes (nearly 200) that he of athletes (nearly 200) that he observed in the Sanctuary of Zeus at observed in the Sanctuary of Zeus at Olympia….”Olympia….”


• Modern Indian Fiction 2Modern Indian Fiction 2“…“…Salman Rushdie asserts the supremacy of Indian Salman Rushdie asserts the supremacy of Indian literature in English over all other language literature in English over all other language traditions…. [I will] anchor these discussions in a traditions…. [I will] anchor these discussions in a study of the actual numbers involved in publishing, study of the actual numbers involved in publishing, readership, and language education. Students would readership, and language education. Students would be able to use the data both to contextualize claims be able to use the data both to contextualize claims such as Rushdie’s (just how many Indians read such as Rushdie’s (just how many Indians read English? what fraction of Indian publishing is actually English? what fraction of Indian publishing is actually in English? how do writers in English fare in literary in English? how do writers in English fare in literary prizes awarded within India?) and to better prizes awarded within India?) and to better illuminate an understanding of how complex the illuminate an understanding of how complex the Indian literary landscape is.”Indian literary landscape is.”

ReferencesReferences

ABC News. February 21, 2007. “Do Libras Live Longer?” ABC News. February 21, 2007. “Do Libras Live Longer?” (http://abcnews.go.com/Technology/story?id=2890150&page=1)(http://abcnews.go.com/Technology/story?id=2890150&page=1)

Bialik, Carl. November 2006. “The Numbers Guy: Grading the Pollsters.” Bialik, Carl. November 2006. “The Numbers Guy: Grading the Pollsters.” Wall Street Wall Street Journal Journal (http://www.mason-dixon.com/public/index.cfm?(http://www.mason-dixon.com/public/index.cfm?FuseAction=PressOffice.Article&ContentRecord_id=f1e66ca1-1372-fa49-99bd-FuseAction=PressOffice.Article&ContentRecord_id=f1e66ca1-1372-fa49-99bd-58f6c5a4e505).58f6c5a4e505).

Brakke, David F. 2003. "Addressing Societal and Workforce Needs," in Brakke, David F. 2003. "Addressing Societal and Workforce Needs," in Quantitative Quantitative Literacy: Why Numeracy Matters for Schools and CollegesLiteracy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn , Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

De Lange, Jan. 2001. "Mathematics for Literacy" in De Lange, Jan. 2001. "Mathematics for Literacy" in Mathematics and Democracy: The Mathematics and Democracy: The Case for Quantitative LiteracyCase for Quantitative Literacy, Lynn Arthur Steen, ed. Princeton, NJ: National Council on , Lynn Arthur Steen, ed. Princeton, NJ: National Council on Education and the Disciplines. Education and the Disciplines.

Fishman, Charles. 2006. Fishman, Charles. 2006. The Wal-Mart EffectThe Wal-Mart Effect. New York: The Penguin Press.. New York: The Penguin Press. Frankel, Max. 1995. “Word and Image; Innumercy,” Frankel, Max. 1995. “Word and Image; Innumercy,” New York Times, New York Times, March 5.March 5. Hughes Hallett, Deborah J. 2001. "The Role of Mathematics Courses in the Development Hughes Hallett, Deborah J. 2001. "The Role of Mathematics Courses in the Development

of Quantitative Literacy" in of Quantitative Literacy" in Mathematics and Democracy: The Case for Quantitative Mathematics and Democracy: The Case for Quantitative LiteracyLiteracy, Lynn Arthur Steen, ed. Princeton, NJ: National Council on Education and the , Lynn Arthur Steen, ed. Princeton, NJ: National Council on Education and the Disciplines.Disciplines.

Miller, Jane E. 2004Miller, Jane E. 2004. The Chicago Guide to Writing about Numbers. . The Chicago Guide to Writing about Numbers. Chicago: University Chicago: University of Chicago Press. of Chicago Press.

More or LessMore or Less, British Broadcasting Corporation radio program. Retrieved April 27, 2007, , British Broadcasting Corporation radio program. Retrieved April 27, 2007, from http://news.bbc.co.uk/2/hi/programmes/more_or_less/1628489.stm.from http://news.bbc.co.uk/2/hi/programmes/more_or_less/1628489.stm.

References (Cont.)References (Cont.)

National Council on Education and the Disciplines. 2001. National Council on Education and the Disciplines. 2001. Mathematics and Democracy: The Mathematics and Democracy: The Case for Quantitative LiteracyCase for Quantitative Literacy. Washington DC: Mathematical Association of America.. Washington DC: Mathematical Association of America.

NewsweekNewsweek. November 21, 2005. “How to Beat the Big Energy Chill.” . November 21, 2005. “How to Beat the Big Energy Chill.” (http://www.newsweek.com/id/51208) (http://www.newsweek.com/id/51208)

Newsweek.Newsweek. August 6, 2007. “When Medical Studies Collide: Contradictory Reports? Meta- August 6, 2007. “When Medical Studies Collide: Contradictory Reports? Meta-Analysis May Make Things More Confusing.” Analysis May Make Things More Confusing.”

Nurnberg, H. George; Paula L. Hensley; Julia R. Heiman; Harry A. Croft; Charles Debattista; 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 and Susan Paine. 2008. “Sildenafil Treatment of Women with Antidepressant-Associated Sexual Dysfunction.” Sexual Dysfunction.” Journal of the American Medical AssociationJournal of the American Medical Association, 300(4): 395-404., 300(4): 395-404.

(http://www.businessweek.com/magazine/content/07_32/b4045052.htm)(http://www.businessweek.com/magazine/content/07_32/b4045052.htm) ReutersReuters. November 26, 2007. “New Poll Shows Clinton Trails Top 2008 Republicans.” . November 26, 2007. “New Poll Shows Clinton Trails Top 2008 Republicans.”

(http://www.reuters.com/article/politicsNews/idUSN2645320920071126)(http://www.reuters.com/article/politicsNews/idUSN2645320920071126) Shafer, Jack. 2005. “Weasel Words Rip My Flesh! Spotting a Bogus Trend Story on Page One Shafer, Jack. 2005. “Weasel Words Rip My Flesh! Spotting a Bogus Trend Story on Page One

of Today’s of Today’s New York Times,New York Times,” ” SlateSlate, September 20., September 20. Steen, Lynn Arthur. 2004. Steen, Lynn Arthur. 2004. Achieving Quantitative Literacy: An Urgent Challenge for Higher Achieving Quantitative Literacy: An Urgent Challenge for Higher

EducationEducation. Washington, DC: Mathematical Association of America.. Washington, DC: Mathematical Association of America. Story, Louise. September 20, 2005. “Many Women at Elite Colleges Set Career Path the Story, Louise. September 20, 2005. “Many Women at Elite Colleges Set Career Path the

Motherhood.”Motherhood.” New York Times New York Times. . Wallis, Claudia. 2007. “Is the Autism Epidemic a Myth,” Wallis, Claudia. 2007. “Is the Autism Epidemic a Myth,” Time,Time, January 12. January 12. WCCO. 2007. “Report: Indians Denied Home Loans More Often,” December 30.WCCO. 2007. “Report: Indians Denied Home Loans More Often,” December 30. Wiggins, Grant. 2001. "'Get Real!': Assessing for Quantitative Literacy" in Wiggins, Grant. 2001. "'Get Real!': Assessing for Quantitative Literacy" in Mathematics and Mathematics and

Democracy: The Case for Quantitative LiteracyDemocracy: The Case for Quantitative Literacy, Lynn Arthur Steen, ed. Princeton, NJ: National , Lynn Arthur Steen, ed. Princeton, NJ: National Council on Education and the Disciplines.Council on Education and the Disciplines.

use, misuse, and missed use of quantitative reasoning in student writing nathan d. grawe carleton...

Documents

facets of qr

argument slide

habit of mind qr

evidence of qr proficiency

quantitative literacy

context of argument

basic skill

new york times magazine