The document discusses an experimental statistics course taught to 11 high-performing engineering students using an alternative textbook that focused on statistical thinking and systems thinking. It describes how the course used case studies, discussions, and activities instead of lectures to help students develop better mental models. Student feedback indicated they found this approach more engaging and better helped them understand how statistics is applied in real-world settings compared to their regular course. The author recommends expanding this approach in introductory statistics courses, including more faculty training, collaborative teaching, and active learning activities to improve student understanding and retention.

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
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3. The Setting
• Introductory course in probability and statistics for
engineers
• Text: Hogg and Ledolter
• Class: 85 engineers, mainly electrical engineers
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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
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5. The Alternate Textbook Used
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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)
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7. Topics
• Systems thinking
• Mental Models
• Statistical Thinking & Application
• Discussion of topics covered in the regular course
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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
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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
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10. Incorrect Mental Models
The Trade-off
Concepts &
Thinking
Methods
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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
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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
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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.”
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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
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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
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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
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17. The Shock
• When they step out into the real world:
– problems are ill-defined
– rules are unclear
– no standard solutions
– insufficient / incomplete / incorrect sometimes useless
data
– so many roads, which one to take ?
• A bunch of tools but no theory to back up their use
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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
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19. Conventional View of Classroom
“Teacher is lecturing to the class”
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20. “Teacher is lecturing to the class”
10 commandments
10 commandments
Mountain
Students
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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
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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)
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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
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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”
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25. Systems View
S
S S
S S
S
S
Team Learning
Work S T
S
S
S
S S
S S
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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
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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
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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.”
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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.”
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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”
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31. Recommendations
• TA & faculty training
• Faculty Collaboration
• Empathy, Creativity, Shared responsibility
• Exams & Laboratories for learning and testing
• Less lecture, more class activities
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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
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33. Reference Books
• The Fifth Discipline-Peter M. Senge(1990)
• The 7 habits of highly effective people-Stephen
R.Covey (1989)
• Enlightened Leadership-Ed Oakley and Doug
Krug (1991)
• Cognition-Margaret W. Matlin
• 15 Proven ways to get your message across-Ernest
W. Brewer (1997)
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