Addressing Ambiguity Tolerance Among Introductory Statistics Students

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Addressing Ambiguity Tolerance Among Introductory
Statistics Students

• Robert H. Carver
• Stonehill College/Brandeis University
• Session ST-18
• DSI2007 Phoenix AZ

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Outline

• What is Ambiguity Tolerance (AT)?
• Is it related to the development of statistical
  reasoning skills?
• Some empirical findings
• Methods
• Results
• Implications for more effective teaching

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What is Ambiguity Tolerance (AT)?

• Frenkel-Brunswik (1948)
• Some are stimulated by ambiguity, some are
  threatened
• Personality trait vs. preferred process
• Relationship to rigidity, uncertainty tolerance,
  openness
• Enduring personality attribute vs.
  context-dependent

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Low A.T.?
High AT?
Never, ever, think outside the box
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What's the connection?

• Ambiguity tolerance

• Statistical thinking

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

• Drawing actionable conclusions based on
  incomplete information
• Methods for incorporating new information with
  pre-existing assumptions

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Statistical Thinking

• 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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Common Responses to Variation
Adapted from Wild Pfannkuch, 1999
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Research Questions

• Is ambiguity tolerance (AT) a predictor of
  success in a students 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

• Sample
• 85 undergraduates enrolled over 2 semesters
• Differences among sections
• Technology Minitab vs. SAS (Learning Ed.)
• Ordinary, Learning Community, Honors

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Methods

• 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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CAOS post-test results
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Methods

• Independent Measures variables
• McLains AT scale
• 22 question instrument 7-point Likert Scales
• Max score for extreme tolerance 74
• Min score for extreme intolerance - 58
• Reliability Cronbachs alpha 0.897
• In this sample a 0.872
• Did not predict performance on the pre-test

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Covariates investigated

• 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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FindingsCAOS Post-Test
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 score Also evidence of interaction
between AT PreTest score Slightly Better fit
with log-linear model
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Discussion If so, then what?

• 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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Final thoughts

• 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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Questions? Replication?

• Contact me
• rcarver_at_stonehill.edu
• rcarver_at_brandeis.edu
• http//faculty.stonehill.edu/rcarver/