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Students’ Ambiguity Tolerance as a Success Factor in Learning to Reason Statistically. Robert H. Carver Stonehill College/Brandeis University June 12, 2007. Quick Outline. Genesis of this Research Classroom experience Literature review JSM 2006 presentation Current project - PowerPoint PPT Presentation
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Students’ Ambiguity Tolerance as a Success Factor in Learning to Reason Statistically
Robert H. CarverStonehill College/Brandeis UniversityJune 12, 2007
Quick Outline
Genesis of this Research Classroom experience Literature review JSM 2006 presentation
Current projectInvitation to participateQ&A
Genesis of the ResearchSome observations from the classroom…
Learning statistics is difficult in many ways Intro Stats can activate profound emotional
responses “but usually I like/I dislike math classes…”
Stat Ed literature Focus on variation as a central theme Studies on activities, techniques, topics Relatively little work on variation among
learners
Learners Vary!
Variation among learners Prior coursework Level of effort—motivation, capacity, etc. Aptitude Attitudinal orientation (Schau, et al.) Myers-Briggs (BTI) Other personality/emotional characteristics
Ambiguity Tolerance
Frenkel-Brunswik, Else (1948) Ambiguity Tolerance Construct:
Some are stimulated by ambiguity, some are threatened
Personality trait vs. preferred process Stable personality attribute vs. context-
dependent Relationship to rigidity, uncertainty tolerance,
openness
The inner conflict
Per Frenkel-Brunswick:
Low ambiguity tolerance
conflict & anxiety in ambiguous situations
rigid adherence to preconceived ideas
failure to process contrary evidence
Statistical Thinking
Statistical thinking requires simultaneous consideration of variation within one sample and among possible samples.
Statistical methods provide a means of making decisions in inherently ambiguous situations, relying on incomplete information.
Inference requires a leap of faith—a ready embrace of ambiguity
Contrast with ’Ambiguity’ in Decision Theory
Ambiguity as a property of the situation or state of knowledge
Ambiguity as property or proclivity of the thinker
Ambiguity Tolerance
Measurement Scales Budner,1962 Rydell; Rydell & Rosen 1966 MacDonald, 1970 Norton, 1975 McLain, 1993
Questions
Do students with high AT have an advantage in learning to think statistically?
Do students with low AT tend to “shut down” when presented with instruction in inferential reasoning and techniques?
OR Do students with low AT welcome statistical
thinking as a way to cope with ambiguity?
Methods
Sample: 85 undergraduates enrolled in 4 sections over 2
semesters Differences among sections
Technology: Minitab vs. SAS Normal, Learning Community, Honors
Informed consent Credit & incentives Course-embedded data collection
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
Purpose of CAOS test
The CAOS test was designed to provide an instrument that would assess students’ statistical reasoning after any first course in statistics. Rather than focus on computation and procedures, the CAOS test focuses on statistical literacy and conceptual understanding, with a focus on reasoning about variability.
ARTIST project, University of Minnesota
CAOS post-test
Illustrative question:
Researchers surveyed 1,000 randomly selected adults in the US. A statistically significant, strong positive correlation was found between income level and the number of containers of recycling they typically collect in a week. Please select the best interpretation of this result.
A. We cannot conclude whether earning more money causes more recycling among US adults because this type of design does not allow us to infer causation.
B. This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the US
C. This result indicates that earning more money influences people to recycle more than people who earn less money.
CAOS post-test
A. We cannot conclude whether earning more money causes more recycling among US adults because this type of design does not allow us to infer causation.
B. This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the US
C. This result indicates that earning more money influences people to recycle more than people who earn less money.
CAOS post-test
A study examined the length of a certain species of fish from one lake. The plan was to take a random sample of 100 fish and examine the results. Numerical summaries on lengths of the fish measured in this study are given.
Mean 26.8mm
Median 29.4 mm
Std. Dev. 5.0 mm
Minimum 12.0 mm
Maximum 33.4 mm
CAOS post-test
Mean 26.8mm
Median 29.4 mm
Std. Dev. 5.0 mm
Minimum 12.0 mm
Maximum 33.4 mm
CAOS post-test
Mean 26.8mm
Median 29.4 mm
Std. Dev. 5.0 mm
Minimum 12.0 mm
Maximum 33.4 mm
CAOS post-test
CAOS post-test
807060504030
90
80
70
60
50
40
30
CAOSPre
CA
OSPost
MaleFemale
Gender
Post vs. Pre-test Scores
CAOS post-test
807060504030
90
80
70
60
50
40
30
CAOSPre
CA
OSPost
MaleFemale
Gender
Post vs. Pre-test Scores
Improvem
ent
Measuring AT
Independent Measures & variables: Abiguity Tolerance:
McLain’s 22 question instrument 7-point Likert Scales
Max score for extreme tolerance = 74Min score for extreme intolerance = - 58
Reliability: Cronbach’s alpha = 0.897
Selected items:I don’t tolerate ambiguous situations
well. I’m drawn to situations which can be
interpreted in more than one way.I enjoy tackling problems which are
complex enough to be ambiguous.I find it hard to make a choice when
the outcome is uncertain.
Measuring AT
Covariates
Other explanatory factors and controls tested: Score on CAOS Pre-test Section controls Cohort (55% 2006; 45% 2007) Gender dummy (49% female; 51% male) First-year student dummy (61% 1st year) Math SAT Prior Stat Education (37% had some) Course cumulative average Attendance
Findings: CAOS Pre-test Variable Coeff Signif
Constant 9.07 0.438
Female dummy -1.13 0.638
AT scale 0.048 0.537
First year dummy -5.581 0.028
Prior course dummy 5.256 0.032
Math SAT score 0.063 0.001
F 4.89 0.001
Adj R2 21.3%
A.T. did not have a significant main effect on Pre-test scores
Findings:CAOS Post-Test Variable Coeff Signif
Constant 33.374 0.000
CAOS Pre-test score 0.559 0.000
AT scale 0.110 0.079
First Year dummy -3.726 0.072
Prior course dummy -3.406 0.099
F 12.29 0.000
Adj R2 37.0%
AT score has a significant (p < 0.10) effect on Post-Test reasoning score
Findings:CAOS 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 (p < 0.05) effect on Post-Test reasoning score
AT non-significant in predicting pre-test scores Suggests that the pre-test does not measure
ambiguity tolerance Significant findings re: prior coursework,
academic preparation (though not much explanatory power), Math SAT
Summary of Key Findings
AT is significant in predicting Post-Test scores
Also significant Pre-Test score Prior statistics coursework (but negative) First year dummy Course results
Not significant Gender, cohort, section, MathSAT
Summary of Key Findings
Discussion
Main Findings: Ambiguity Tolerance may have a positive main effect Low A.T. likely to be surmountable
Caveats: CAOS scales measure several aspects of statistical
thinking Small sample Substantial unexplained variance Measurement issues: effort, engagement
Discussion
Implications: An individual’s orientation toward ambiguity can
affect his/her success with statistical reasoning. Tolerance of ambiguity construct may provide a
motivation for success Course pedagogy may address A.T. directly
Note: Course averages not explained by AT
Discussion/Invitation
Research directions: Can these results be replicated, especially in larger
samples? Would the results hold up with different measures of
statistical reasoning? Do other personality or personal style variables shape
success in statistical reasoning? How can we structure pedagogy to address personality
variation among learners? Does A.T. affect application of statistical reasoning in
practice?
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Personality, 11, 625-632.Budner, S. (1962). Intolerance of ambiguity as a personality variable. Journal of Personality, 30(1), 29-50.DeRoma, V. M., Martin, K. M., & Kessler, M. L. (2003). The relationship between tolerance for ambiguity and need for course structure. Journal of
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Education, 46(4), 11-18.Fibert, Z., & Ressler, W. H. (1998). Intolerance of ambiguity and political orientation among israeli university students. The Journal of Social
Psychology, 138(1), 33-40.Frenkel-Brunswik, E. (1948). Tolerance of ambiguity as an emotional and perceptual personality variable. Journal of Personality, 18, 108-143.Friedland, N., & Keinen, G. (1991). The effects of stress, ambiguity tolerance, and trait anxiety on the formation of causal relationships. Journal of
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Leadership and Organizational Studies, 10(3), 69-81.MacDonald, A. P. (1970). Revised scale for ambiguity tolerance: Reliability and validity. Psychological Reports, 26, 791-798.McLain, D. L. (1993). The mstat-i: A new measure of an individual's tolerance for ambiguity. Educational and Psychological Measurement, 53, 183-
189.Norton, R. W. (1975). Measurement of ambiguity tolerance. Journal of Personality Assessment, 39(6), 607-619.Wittenburg, K. J., & Norcross, J. C. (2001). Practitioner perfectionism: Relationship to ambiguity tolerance and work satisfaction. Journal of Clinical
Psychology, 57(12), 1543-1550.