Statistical Thinking, Systems Thought and Mental Models

1. Statistical Thinking, Systems Thought and Mental Models Vinay P. Kulkarni M.S.Candidate, Industrial Engineering Systems and Industrial Engineering University of Arizona Tucson, Arizona 85721 E-mail: vinay@email.arizona.edu Ph: 520-624-7593(Home), 520-6617593(Mobile)

2. Presentation Topics • Teaching Statistical Thinking-an Experience • Mental Models • Student Thinking and Teacher Thinking • The Shock of the Real World • Class Reactions • Recommendations for Future Courses Vinay P. Kulkarni, University of Arizona

3. The Setting • Introductory course in probability and statistics for engineers • Text: Hogg and Ledolter • Class: 85 engineers, mainly electrical engineers Vinay P. Kulkarni, University of Arizona

4. What We Did • Selected 11 best students at the end of the semester • All of them were awarded “A’s” at this point • 3 sessions, more than 1 hour each • Alternate text: Hoerl and Snee Vinay P. Kulkarni, University of Arizona

5. The Alternate Textbook Used Vinay P. Kulkarni, University of Arizona

6. Statistical Thinking A philosophy of learning and action : • All work occurs in a system of interconnected processes • Variation exists in all processes • Understanding and reducing variation are the keys to success Glossary of Statistical Terms, Quality Press (1996) Vinay P. Kulkarni, University of Arizona

7. Topics • Systems thinking • Mental Models • Statistical Thinking & Application • Discussion of topics covered in the regular course Vinay P. Kulkarni, University of Arizona

8. What We Did • Background on Statistics and Probability • Students were given articles on “team work”, asked to respond by e-mail • Case studies from Hoerl & Snee and others • E.g: The soccer team performance case study • Importance of group learning explained • Communication channels opened Vinay P. Kulkarni, University of Arizona

9. Mental Models • Conventional Wisdom, typically not based on fact and frequently wrong • Adversely influences: • How teachers teach • Students learn • How they interact with each other Vinay P. Kulkarni, University of Arizona

10. Thinking Concepts & Methods Incorrect Mental ModelsThe Trade-off Vinay P. Kulkarni, University of Arizona

11. An Analogy • Mathematical Statistics-Hardware • Statistical Thinking-Software What use is hardware without software? The converse is also true, but, the hardware is “dead” without the software Vinay P. Kulkarni, University of Arizona

12. Statistical Thinking Vs. Mathematical Detail “…Good statistics is not equated with mathematical rigor or purity, but is more closely associated with careful thinking” - Robert V.Hogg Vinay P. Kulkarni, University of Arizona

13. Incorrect Mental Models:an Example “Faculty in a national study ‘overwhelmingly’ said developing effective thinking was their primary educational purpose, but most of the 4,000 course goals they submitted related to teaching concepts in their disciplines, rather than developing the intellectual skills they said were so important.” Vinay P. Kulkarni, University of Arizona

14. Dealing With Mental Models (MMs) • Instructors should: • explore their own • list and test the assumptions on which their MMs are built • assist students to discover and change their MMs • replace the wrong MMs with correct ones Vinay P. Kulkarni, University of Arizona

15. Student Thinking • In typical statistics courses problems are • completely defined, clearly stated • data already collected, neatly tabulated • causes known, solutions available • Its only a matter of figuring out the right formula/equation to be used • They expect the same when they get out of school Vinay P. Kulkarni, University of Arizona

16. Student Thinking • Theory • its easy • do not waste time with it • to be memorized • just fill some pages, will get at least half the points • reserve these questions for the last on an exam • does not require intelligence • only counts for 10 -15 points on the exam anyway Vinay P. Kulkarni, University of Arizona

17. The Shock • When they step out into the real world: • problems are ill-defined • rules are unclear • nostandard solutions • insufficient / incomplete / incorrect sometimesuseless data • so many roads, which one to take ? • A bunch of tools but no theory to back up their use Vinay P. Kulkarni, University of Arizona

18. Teachers’ Role • Teachers foster this thought Process : • Spend less time on introduction • fewer conceptual questions on exams • no detailed explanation & discussion of concepts in class • assume students know the theory and concentrate on the math • ask students to read theory by themselves Vinay P. Kulkarni, University of Arizona

19. Conventional View of Classroom “Teacher is lecturing to the class” Vinay P. Kulkarni, University of Arizona

20. 10 commandments “Teacher is lecturing to the class” 10 commandments Mountain Students Vinay P. Kulkarni, University of Arizona

21. When a Student Does Not Understand What Is Being Said • Silence • Self-doubt • Pretends understanding • Turns frustration outward-disturbs class-violence • Cheats in exams • Drops the course • Teacher does not get feedback Vinay P. Kulkarni, University of Arizona

22. What Students Do During Lectures “If students are not thinking during lectures, what are they doing? Their attention drifts after only 10 to 20 minutes. They are listening, asking or responding to questions, or taking notes only half of the time. Up to 15 percent of their time is spent fantasizing”-Lion F.Gardiner (1998) Vinay P. Kulkarni, University of Arizona

23. Teacher Thinking • Students are: • dumb • have an attitude problem • not working hard • not interested in what I am teaching • I do not care about them anymore Vinay P. Kulkarni, University of Arizona

24. Systems View “Teacher and students are engaged in the process of creating knowledge and understanding. They influence each other and learn from each other. They have a shared vision of their mission in the class-They are a team” Vinay P. Kulkarni, University of Arizona

25. Systems View S S S S S S S S Team Work Learning T S S S S S S S Vinay P. Kulkarni, University of Arizona

26. Learning by Doing • That is how nature intended us to learn • Driving Lecture Vs. Driving Lessons • The Tulving Memory Model • Semantic, Episodic and Procedural Memories • People with good semantic memories can give an impression of understanding • Often, contents of Procedural Memory cannot be easily put into words Vinay P. Kulkarni, University of Arizona

27. Student Buy-in • Buy-in before application of concept • Will you be willing to buy a car without first test driving it? • Create the capacity for change Vinay P. Kulkarni, University of Arizona

28. Student Reaction to the Regular Course “…a statistics course should include more topics on the usefulness of the analytical methods… amount of "raw math" taught be decreased and explanations for why we use hypothesis testing, distribution curves, etc. be added to the course curriculum.” Vinay P. Kulkarni, University of Arizona

29. Statistical Thinking Course-Response “….was easier for me to relate to the soccer field than to relate to a job environment…the questions asked stimulated participation, aided in the learning process, made us think more deeply about what was being said.” Vinay P. Kulkarni, University of Arizona

30. An Insightful Student Response   “….most classes dull your brain and kill any creative process..…the more time that you spend in classes, the more bored you become with a subject and the less likely you are to learn and succeed. But, I remember more from those two Statistical Thinking lectures than I can recall from any other two lectures in any class--even when I just get out of that class” Vinay P. Kulkarni, University of Arizona

31. Recommendations • TA & faculty training • Faculty Collaboration • Empathy, Creativity, Shared responsibility • Exams & Laboratories for learning and testing • Less lecture, more class activities Vinay P. Kulkarni, University of Arizona

32. Recommendations • Understanding & Retention vs. Width of exposure • Encourage ‘Christopherian’ confrontations • Increase the efficiency of the learning process • Communicate instructions in writing • Students • Teaching Assistants Vinay P. Kulkarni, University of Arizona