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

2. 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 20 November 20072

3. Frenkel-Brunswik (1948) stimulated threatened  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 20 November 20073

4. 4 “Never, ever, think outside the box” High AT? Low A.T.?

5. AMBIGUITY TOLERANCE When AT is low, people tend to cling to preconceived notions, reluctant to process contrary information STATISTICAL THINKING Drawing actionable conclusions based on incomplete information Methods for incorporating new information with pre- existing assumptions 20 November 20075

6. 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) 20 November 20076

7. 7 Ignore Fail to detect? Overlook? FLEE!? Allow for Anticipate Design safeguards Control Change system to reduce or manage Adapted from Wild & Pfannkuch, 1999

8. 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? 20 November 20078

9. Sample: 85 undergraduates enrolled over 2 semesters Differences among sections  Technology: Minitab vs. SAS (Learning Ed.)  Ordinary, Learning Community, Honors 20 November 20079

10. 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… 20 November 200710

11. 20 November 200711

12. 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 20 November 200712

13. 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% 1 st year) Math SAT Selected interactions with AT 20 November 200713

14. 20 November 200714 VariableCoeffSignif Constant-2.5290.751 CAOS Pre-test score0.4370.000 AT scale0.1170.039 Course Cumulative Avg0.4730.000 Prior course dummy-3.9460.035 F19.460.000 Adj R 2 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

15. 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? 20 November 200715

16. “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? 20 November 200716

17. Contact me…  rcarver@stonehill.edu rcarver@stonehill.edu  rcarver@brandeis.edu rcarver@brandeis.edu  http://faculty.stonehill.edu/rcarver/ http://faculty.stonehill.edu/rcarver/ 20 November 200717