Robert H. CarverStonehill College/Brandeis University

Session ST-18DSI2007 Phoenix AZ

• What is Ambiguity Tolerance (AT)?

• Is it related to the development of statistical reasoning skills?

• Some empirical findings Methods Results• Implications for more effective

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• Frenkel-Brunswik (1948) Some are stimulatedstimulated by

ambiguity, some are threatenedthreatened Personality trait vs. preferred

process Relationship to rigidity,

uncertainty tolerance, openness Enduring personality attribute vs.

context-dependent

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“Never, ever, think outside the box”

High AT?

Low A.T.?

AMBIGUITY TOLERANCE

When AT is low, people tend to cling to preconceived notions, reluctant to process contrary information

STATISTICAL THINKINGD

rawing actionable conclusions based on incomplete information

Methods for incorporating new information with pre-existing assumptions

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• Wild & Pfannkuch (1999) 4 dimensions of Statistical Thinking Investigative (PPDAC) Types of thinking (critical,

imaginative, transnumerative…) Interrogative (critical assessment of

observations) Dispositions (personal styles,

qualities)

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Adapted from Wild & Pfannkuch, 1999

•Is ambiguity tolerance (AT) a predictor of success in a student’s development of statistical thinking skills?

•Does AT interact with other success factors?

•If AT is a predictor of success, can we modify our teaching approaches to anticipate it?

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Sample: • 85 undergraduates enrolled over 2

semesters• Differences among sections Technology: Minitab vs. SAS (Learning Ed.) Ordinary, Learning Community, Honors

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Dependent variable: • Score on Comprehensive Assessment of

Outcomes for a first course in Statistics (CAOS) post-test

Developed by Web ARTIST Project (U.Minnesota and Cal Poly) team

Pre- and Post-test (40 items each)• Note: some questions are, themselves

ambiugous…

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100806040200

100

80

60

40

20

0

CAOSPre

CA

OSPost

Post vs. Pre-test Scores

Independent Measures & variables:

• McLain’s AT scale: 22 question instrument 7-point Likert Scales

Max score for extreme tolerance = 74 Min score for extreme intolerance = - 58

Reliability: Cronbach’s alpha = 0.897 In this sample = 0.872

Did not predict performance on the pre-test

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• Score on CAOS Pre-test• Prior Stat Education (37% had some) • Section dummy variables (Honors, L.C., etc.)• Course Performance variables • Attendance• Gender dummy (49% female; 51% male)• First-year student dummy (61% 1st year)• Math SAT• Selected interactions with AT

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Variable Coeff Signif

Constant -2.529 0.751

CAOS Pre-test score 0.437 0.000

AT scale 0.117 0.039

Course Cumulative Avg 0.473 0.000

Prior course dummy -3.946 0.035

F 19.46 0.000

Adj R2 48.9%

AT score has a significant effect on Post-Test reasoning scoreAlso: evidence of interaction between AT & PreTest scoreSlightly Better fit with log-linear model

• Need to replicate Carolyn Dobler, Gustavus Adolphus Jennifer Kaplan, Michigan State Stonehill, Spring 2008 (75 students)

• Recognize and Confront this variation among students

Differentiate from low effort/low aptitude/poor attitude

• Re-frame the value of statistical thinking for low-AT context

• Search for other personality variables with similar effects?

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“It seems… that misconceptions are part of a way of thinking about events that is deeply rooted in most people, either as learned parts of our culture or (in the extreme) even as brain functions arising from natural selection in a simpler time.”

Garfield & Ahlgren, 1988

How shall we respond to this variation in our students? Allow for? Control? Ignore?

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• Contact me… rcarver@stonehill.edu rcarver@brandeis.edu

http://faculty.stonehill.edu/rcarver/

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