Strengthening the Quantitative Reasoning of First-Year Students:

A Seminar on “Measured Thinking”

Strengthening the Quantitative Reasoning of First-Year Students:

A Seminar on “Measured Thinking”

Neil Lutsky, Carleton College nlutsky@carleton.edu

Neil Lutsky, Carleton College nlutsky@carleton.edu

Appalachian College Association Summit, 2011, Asheville, North CarolinaAppalachian College Association Summit, 2011, Asheville, North Carolina

BackgroundBackground

• Carleton’s QuIRK Initiative: Quantitative Inquiry, Reasoning, and Knowledge

(2004-).

•Arguments and Inquiry First-Year Seminar Program (2010).

• Measured Thinking: Reasoning with Numbers about World Events, Health, Science,

and Social Issues (2003).

• Carleton’s QuIRK Initiative: Quantitative Inquiry, Reasoning, and Knowledge

(2004-).

•Arguments and Inquiry First-Year Seminar Program (2010).

• Measured Thinking: Reasoning with Numbers about World Events, Health, Science,

and Social Issues (2003).

Aspirations:Aspirations:

• Promoting Critical Thinking about quantitative and non-quantitative

claims.

•Broadening an Appreciation for QR, for the illuminating power of

quantitative analysis.

• Strengthening Communication Skills when discussing quantitative

information.

• Promoting Critical Thinking about quantitative and non-quantitative

claims.

•Broadening an Appreciation for QR, for the illuminating power of

quantitative analysis.

• Strengthening Communication Skills when discussing quantitative

information.

“The deepest pitfall with numbers owes nothing to

numbers themselves and much to the slack way they are

treated, with carelessness all the way to contempt.”

-Blastland & Dilnot

“The deepest pitfall with numbers owes nothing to

numbers themselves and much to the slack way they are

treated, with carelessness all the way to contempt.”

-Blastland & Dilnot

A true critic ought to dwell rather upon excellencies than imperfections, to discover the concealed beauties of a writer and communicate to the world such things as are worth their observation. -Joseph Addison

A true critic ought to dwell rather upon excellencies than imperfections, to discover the concealed beauties of a writer and communicate to the world such things as are worth their observation. -Joseph Addison

How can we help students develop an

appreciation for quantitative reasoning?

How can we help students develop an

appreciation for quantitative reasoning?1. Readings and examples that represent the contributions of

quantitative reasoning.

2.Applications that do so as well.

1. Readings and examples that represent the contributions of

quantitative reasoning.

2.Applications that do so as well.

Casualties of War, pp. 51-69.Casualties of War, pp. 51-69.

The Score, pp. 169-200.The Score, pp. 169-200.

Compelling Examples:Compelling Examples:

Numbers Have Value

Numbers Have Value

David Hemenway, Private Guns Public

Health

David Hemenway, Private Guns Public

Health

• Richard Doll & Bradford Hill.

• Richard Doll & Bradford Hill.

T. Weller (1985), Culture Made Stupid T. Weller (1985), Culture Made Stupid

“Statistics, however fraudulent or irrelevant, lend an air of authority to any argument. When embodied in a graph of chart, they become even less comprehensible, and

therefore more convincing.”

“Statistics, however fraudulent or irrelevant, lend an air of authority to any argument. When embodied in a graph of chart, they become even less comprehensible, and

therefore more convincing.”

Edward Tufte, Visual Explanations

(Visual and Statistical Thinking)

Edward Tufte, Visual Explanations

(Visual and Statistical Thinking)

John Snow’s Cholera Map (1854)

John Snow’s Cholera Map (1854)

Challenger Launch Decision (1986)

Challenger Launch Decision (1986)

Bar ChartBar Chart

64 kcal/day64 kcal/day

From The EconomistFrom The Economist

“What is it, Lassie--is Timmy in trouble?”

“What is it, Lassie--is Timmy in trouble?”

“Progress means simplifying not complicating.”

Bruno Munari, Designer

“Progress means simplifying not complicating.”

Bruno Munari, Designer

“A simple line allows us to appreciate at a glance a succession of numbers which the most subtle mind would

find it difficult to retain and compare.”

-Adolphe Quetelet

“A simple line allows us to appreciate at a glance a succession of numbers which the most subtle mind would

find it difficult to retain and compare.”

-Adolphe Quetelet

Valued Applications:Valued Applications:

Girl Scouts Council.

Jesse James Bike Tour.

Girl Scouts Council.

Jesse James Bike Tour.

Current collaboration with the Northfield Middle School.

Current collaboration with the Northfield Middle School.

Chris JordanChris Jordan

-The number of aluminum cans used in the United States every 30 seconds:

106,000!

-The number of aluminum cans used in the United States every 30 seconds:

106,000!

“It sort of makes you stop and think,

doesn’t it?”

“It sort of makes you stop and think,

doesn’t it?”

How many?How many?

“For instance is no proof.”-Yiddish Saying

“For instance is no proof.”-Yiddish Saying

10 QR Questions at the Ready

10 QR Questions at the Ready

•What do the numbers show?

•How representative is that?

•Compared to what?

•Is the outcome statistically significant?

•What’s the effect size?

•Are the results those of a single study or of a literature?

•What’s the research design?

•How was the variable operationalized?

•Who’s in the sample?

•Controlling for what?

•What do the numbers show?

•How representative is that?

•Compared to what?

•Is the outcome statistically significant?

•What’s the effect size?

•Are the results those of a single study or of a literature?

•What’s the research design?

•How was the variable operationalized?

•Who’s in the sample?

•Controlling for what?

10 QR Questionsat

the Ready:

10 QR Questionsat

the Ready:

Exercise Responsible Cautionand Amiable Skepticism

Exercise Responsible Cautionand Amiable Skepticism

Argue ResponsiblyArgue Responsibly

Support claims with evidence.

Address the reasonable questions of a careful reader.

Recognize limitations and complexities.

Support claims with evidence.

Address the reasonable questions of a careful reader.

Recognize limitations and complexities.

Promote writing with numbers.Promote writing with numbers.

• Students are going to be reading writing with numbers.

• Students are going to be writing with numbers themselves.

• Students are going to be reading writing with numbers.

• Students are going to be writing with numbers themselves.

• Writing with numbers has the potential to strengthen fundamental intellectual skills and values.

• Writing with numbers has the potential to strengthen fundamental intellectual skills and values.

Numbers We Should Know Assignment:

Numbers We Should Know Assignment:

Numbers We Should Know Assignment:

Numbers We Should Know Assignment:

• Find a number we should know.

• Make it meaningful.

• Assess its reliability & complexities.

• e.g., Unemployment rate, Election participation, Obesity rate, CO2 emissions, Fresh water consumption.

• Find a number we should know.

• Make it meaningful.

• Assess its reliability & complexities.

• e.g., Unemployment rate, Election participation, Obesity rate, CO2 emissions, Fresh water consumption.

Miller’s (2004) Seven Basic Principles

• Establish the context.

• Choose effective examples and analogies.

• Use an appropriate vocabulary.

• Decide where to present numbers.

• Report and interpret numbers in text.

• Specify the size and direction of associations.

• Summarize overall patterns:

GEE.

-Jane Miller, The Chicago Guide to

Writing about Numbers

-Jane Miller, The Chicago Guide to

Writing about Numbers

Get this book(59% of

your peers own it!)

Get this book(59% of

your peers own it!)

Writing about the mean (Blastland & Dilnot):Writing about the mean (Blastland & Dilnot):

“The average income in the United States is...”“The average income in the United States is...”

“The average of incomes in the United States is...”“The average of incomes in the United States is...”

Opening of a paper on Chronic and Psychogenic Pain:

“At one time or another, some of us have gone to see a physician for pain treatment only to be told, ‘It’s all in your head.’ Many people experience acute or chronic pain whose severity, duration, or degree of resulting disability cannot be explained by a possible, underlying physical disorder alone. Others suffer psychogenic pain...”

Opening of a paper on Chronic and Psychogenic Pain:

“At one time or another, some of us have gone to see a physician for pain treatment only to be told, ‘It’s all in your head.’ Many people experience acute or chronic pain whose severity, duration, or degree of resulting disability cannot be explained by a possible, underlying physical disorder alone. Others suffer psychogenic pain...”

Opening of a paper on Chronic and Psychogenic Pain:

“At one time or another, some of us have gone to see a physician for pain treatment only to be told, ‘It’s all in your head.’ Many people experience acute or chronic pain whose severity, duration, or degree of resulting disability cannot be explained by a possible, underlying physical disorder alone. Others suffer psychogenic pain...”

Opening of a paper on Chronic and Psychogenic Pain:

“At one time or another, some of us have gone to see a physician for pain treatment only to be told, ‘It’s all in your head.’ Many people experience acute or chronic pain whose severity, duration, or degree of resulting disability cannot be explained by a possible, underlying physical disorder alone. Others suffer psychogenic pain...”

Weasel wordsWeasel words

Measuring Measured Reasoning:Measuring Measured Reasoning:

• Evaluation data.

• Quirk writing assessments.

• Evaluation data.

• Quirk writing assessments.