Statistical Thinking, Systems Thought and Mental Models

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  • These are the topics of my presentation today. There are other more extensive topics in this area which have been researched and written about extensively by academicians and professionals from the industry. We here limit ourselves to addressing the issues that appeared to us to be fundamental, as we learnt from our experience.
  • This refers to the regular introductory course taught in the department of Systems and Industrial Engineering at the University of Arizona
  • Convinced that the old ways of teaching are passé and that the new approach to teaching statistical thinking laid out in the text by Hoerl and Snee is promising, we decided to conduct a short “experiencement” to see how students respond to it.
  • The definition of statistical thinking as used by Hoerl and Snee and one which we adopted in teaching this short course
  • We selected a small group of topics which included systems thinking and mental models in addition to statistical thinking. We felt this was important as we believe statistical thinking has emerged from systems thinking and its principles. While systems thought helps us to see the world as it is and to correct our faulty mental models, statistical thinking uses systems thought to weave out a philosophy of learning and action with unlimited applications in all fields of human endeavor and especially to enhance business performance.
  • What is statistics and probability, how it was invented or discovered as the case may be, why it became necessary to create such a discipline, What is its role in our everyday decision making, in personal to professionals settings What is statistical thinking Is it a new discipline or a new way of teaching? How is it different from what we have been doing so far? Why does it stress so much on teamwork?
  • Why is the topic of mental models central to the issue of redesigning the introductory statistics course
  • Statistical thinking does not have a firm mathematical foundation. Counter argument-Statistics is not math. It only uses math for a purpose. Math for math’s sake does not make sense.
  • This is an important and at the same time a controversial issue. We firmly believe that it is not enough to have a great car if you want to reach your destination, you also need a good roadmap to navigate your way through!
  • This is an example to show how the incongruity between conscious noble thought and faulty mental models can prevent teachers from doing what they set out to do.
  • Constantly exploring your own mental models replacing them with realistic and better ones, assisting students to do the same, until both you and your students have developed a shared vision seems to us to be very important to achieve change and improvement
  • This in our opinion is the primary fault with the kind of problem solving taught in classrooms today
  • This is what we discovered from our experience and observations
  • When students step out into the real world, they are greeted by the shock of realization. The realization that what they did in the classroom did not prepare them for the real world. Thus they are now evaluated for something they never learnt in the first place
  • Teachers play a substantial role in the emergence of such a sad situation.
  • This is the typical picture of the instructor in students’ minds. The instructor sitting on his great mountain of authority and preaching to the crowd of silent students
  • Silence-cause they are embarrassed, get into “I’m not ok” kind of situation, or the teacher is bad thought, what to do but pretend to understand, we will deal with the lesson later, never catch up, the error propagates, leads to students dropping the class, cheating in exams and blaming the instructor.
  • An interesting find
  • When the teacher does not get feedback he does not know what is happening, whether the students are understanding what he is teaching, or they are downright stupid-leads to teacher apathy
  • When the classroom is viewed this way by both the teacher and the taught the whole perspective changes and an atmosphere conducive to change and learning is created
  • A brief look at the philosophy of learning by doing. Extensive work has been done in this field by a great number of researchers in various fields and we cannot talk enough about it. Suffice it to say that that is how nature intended us to learn.
  • The two most important steps that can tremendously increase your chances of success with implementing a change is ensuring student buy-in and creating a capacity for change in the students. Neglecting to create this capacity is in our opinion the primary cause of the failure of most improvement programs.
  • This student incidentally was the best student in the class (based on her performance on exams and homework) and had done exceedingly well in the regular introductory statistics course with three straight 100s on three exams and five straight 100s on five homewroks.
  • Here the student is referring to the soccer team performance case study from Hoerl and Snee
  • This is a very insightful response from a student who gave this short course his greatest support and enthusiasm from the word go.
  • Tas and faculty need to be trained in the latest teaching methods and learning theories Faculty teaching various interrelated courses must collaborate and reach a joint understanding on course objectives, teaching methods and evaluation systems Empathy between the students and the instructors, creativity in designing the course and class activities and sharing the responsibility for learning –these things are essential to the success of a course Exams should serve to teach and not merely to evaluate and there aught to be laboratories which can serve as testing grounds for the students to test their theories Less of the class time should be spent on lectures and more time should be devoted to group activities and discussion
  • Tas and faculty need to be trained in the latest teaching methods and learning theories Faculty teaching various interrelated courses must collaborate and reach a joint understanding on course objectives, teaching methods and evaluation systems Empathy between the students and the instructors, creativity in designing the course and class activities and sharing the responsibility for learning –these things are essential to the success of a course Exams should serve to teach and not merely to evaluate and there aught to be laboratories which can serve as testing grounds for the students to test their theories Less of the class time should be spent on lectures and more time should be devoted to group activities and discussion
  • Statistical Thinking, Systems Thought and Mental Models

    1. 1. Statistical Thinking, SystemsThought 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. 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 Courses6/6/2002 Vinay P. Kulkarni, University of Arizona 2
    3. 3. The Setting• Introductory course in probability and statistics for engineers• Text: Hogg and Ledolter• Class: 85 engineers, mainly electrical engineers6/6/2002 Vinay P. Kulkarni, University of Arizona 3
    4. 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 Snee6/6/2002 Vinay P. Kulkarni, University of Arizona 4
    5. 5. The Alternate Textbook Used6/6/2002 Vinay P. Kulkarni, University of Arizona 5
    6. 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 successGlossary of Statistical Terms, Quality Press (1996) 6/6/2002 Vinay P. Kulkarni, University of Arizona 6
    7. 7. Topics• Systems thinking• Mental Models• Statistical Thinking & Application• Discussion of topics covered in the regular course6/6/2002 Vinay P. Kulkarni, University of Arizona 7
    8. 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 opened6/6/2002 Vinay P. Kulkarni, University of Arizona 8
    9. 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 other6/6/2002 Vinay P. Kulkarni, University of Arizona 9
    10. 10. Incorrect Mental Models The Trade-off Concepts & Thinking Methods6/6/2002 Vinay P. Kulkarni, University of Arizona 10
    11. 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 software6/6/2002 Vinay P. Kulkarni, University of Arizona 11
    12. 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.Hogg6/6/2002 Vinay P. Kulkarni, University of Arizona 12
    13. 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.”6/6/2002 Vinay P. Kulkarni, University of Arizona 13
    14. 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 ones6/6/2002 Vinay P. Kulkarni, University of Arizona 14
    15. 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 school6/6/2002 Vinay P. Kulkarni, University of Arizona 15
    16. 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 anyway6/6/2002 Vinay P. Kulkarni, University of Arizona 16
    17. 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 use6/6/2002 Vinay P. Kulkarni, University of Arizona 17
    18. 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 themselves6/6/2002 Vinay P. Kulkarni, University of Arizona 18
    19. 19. Conventional View of Classroom “Teacher is lecturing to the class”6/6/2002 Vinay P. Kulkarni, University of Arizona 19
    20. 20. “Teacher is lecturing to the class” 10 commandments 10 commandments Mountain Students6/6/2002 Vinay P. Kulkarni, University of Arizona 20
    21. 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 feedback6/6/2002 Vinay P. Kulkarni, University of Arizona 21
    22. 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)6/6/2002 Vinay P. Kulkarni, University of Arizona 22
    23. 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 anymore6/6/2002 Vinay P. Kulkarni, University of Arizona 23
    24. 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”6/6/2002 Vinay P. Kulkarni, University of Arizona 24
    25. 25. Systems View S S S S S S S Team Learning Work S T S S S S S S S6/6/2002 Vinay P. Kulkarni, University of Arizona 25
    26. 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 words6/6/2002 Vinay P. Kulkarni, University of Arizona 26
    27. 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 change6/6/2002 Vinay P. Kulkarni, University of Arizona 27
    28. 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.”6/6/2002 Vinay P. Kulkarni, University of Arizona 28
    29. 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.”6/6/2002 Vinay P. Kulkarni, University of Arizona 29
    30. 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”6/6/2002 Vinay P. Kulkarni, University of Arizona 30
    31. 31. Recommendations• TA & faculty training• Faculty Collaboration• Empathy, Creativity, Shared responsibility• Exams & Laboratories for learning and testing• Less lecture, more class activities6/6/2002 Vinay P. Kulkarni, University of Arizona 31
    32. 32. Recommendations• Understanding & Retention vs. Width of exposure• Encourage ‘Christopherian’ confrontations• Increase the efficiency of the learning process• Communicate instructions in writing – Students – Teaching Assistants6/6/2002 Vinay P. Kulkarni, University of Arizona 32
    33. 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)6/6/2002 Vinay P. Kulkarni, University of Arizona 33

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