Statistical Thinking By Vinay Kulkarni

Statistical Thinking, Systems Thinking and Mental ModelsThinking and Mental Models

Vi P K lk iVinay P. KulkarniM.S.Candidate, Industrial Engineering

Systems and Industrial Engineeringy g gUniversity Of Arizona

Presented at the “Quality and Productivity ResearchPresented at the Quality and Productivity Research Conference, Arizona State University, Tempe, AZ

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June, 22 2002

Presentation Topics

• Teaching Statistical Thinking-an Experiencep

• Mental Models• Student Thinking and Teacher Thinking• Student Thinking and Teacher Thinking• The Shock of the Real World• Class Reactions• Recommendations for Future Courses

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The Setting

• Introductory Course in Probability and Statistics for engineers

• Text: Hogg and Ledolter• Class: 85 engineers, mainly electrical engineers

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What We Did

• Picked 11 best students near the end of the semester• All of them were awarded “A’s” at this pointp• 3 sessions, more than one hour each• Alternate text: Hoerl and Snee

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The Alternate Textbook UsedThe Alternate Textbook Used

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Statistical Thinking

A philosophy of learning and action based on :– All work occurs in a system of interconnected processesy p– 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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Topics• Systems thinkingSystems thinking• Mental Models • Statistical Thinking & Application• Statistical Thinking & Application • Discussion of topics covered in the regular course

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What We Did

• Background on statistics and probability• Students were given articles on “team work”,g

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 explainedp g p g p• Communication channels opened

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Mental Models

• Conventional Wisdom, typically not based on fact and frequently wrong

• Adversely influences:– How teachers teach– Students learn– How they interact with each othery

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Incorrect Mental ModelsIncorrect Mental ModelsThe Trade-off

Thinkingability

Concepts &Methods

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An Analogy

• Mathematical Statistics-Hardware• Statistical Thinking-Softwareg

What use is hardware without software? The converse is also true, but, the hardware is , ,“dead” without the software


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


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 conceptsi h i di i li h h d l i hin their disciplines, rather than developing the intellectual skills they said were so important.”


Dealing With Mental Models (Mms)

• Instructors should:– explore their own p– 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


Student Thinking

• In typical statistics courses problems are– completely defined, clearly statedp y f y– 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


Student ThinkingStudent Thinking• Theory

– its easy– do not waste time with it

t b i d– to be memorized– just fill some pages, will get at least half the points– reserve these questions for the last on an examreserve these questions for the last on an exam– does not require intelligence – only counts for 10 -15 points on the exam anywayy p y y


The Shock• When they step out into the real world:• When they step out into the real world:

– problems are ill-defined– rules are unclearrules are unclear– no standard solutions– insufficient / incomplete / incorrect sometimes useless

data– so many roads, which one to take ?

h fi d h h b h f l b h• They find they have a bunch of tools but no theory to back up their use and so we have a problem!


Teachers’s Role• Teacher’s foster this thought Process :• Teacher s foster this thought Process :

– less time on introductionfewer conceptual questions on exams– fewer conceptual questions on exams

– no detailed explanation & discussion of concepts in classconcepts in class

– assume students know the theory and concentrate on the mathconcentrate on the math

– ask students to read theory by themselves


Instructor & Student Team

• Typical View: “Teacher is lecturing to the class”


Teacher is lecturing to the classg

10 commandments10 commandments

Mountain

Students


When a Student Does Not UnderstandWhen a Student Does Not Understand What Is Being Said

• Silence• Self-doubt• Pretend understanding• Turn frustration outward-disturb class-violence • Cheat in exams• Wants to finish the course as soon as possibleWants to finish the course as soon as possible• Teacher does not get feedback


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

f th ti Up to 15 percent of their time is spentof the time. Up to 15 percent of their time is spent fantasizing”-Lion F.Gardiner (1998)


Teacher Reaction

• Students are:– dumb– have an attitude problem– not working hardg– not interested in what I am teaching

• I do not care about them anymoreI do not care about them anymore


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 l Th ”class-They are a team”


Systems View

S S SS S

SS

Team Work

LearningTS

SS

S

SS

S S S


Learning by Doing• That Is How Nature Intended Us to LearnThat Is How Nature Intended Us to Learn• Driving Lecture Vs. Driving Lessons• The Tulving Memory Model• The Tulving Memory Model

– Semantic, Episodic and Procedural Memories• People With Good Semantic Memories Can Give• People With Good Semantic Memories Can Give

an Impression of Understanding• Often Contents of Procedural Memory Cannot Be• Often, Contents of Procedural Memory Cannot Be

Easily Put Into Words


Student Buy-in

• Buy-in Before Application of Concept• Will You Be Willing to Buy a Car Without First g y

Test Driving It?• Create the Capacity for Change


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 bemethods… amount of raw math taught be decreased and explanations for why we use hypothesis testing, distribution curves, etc. behypothesis testing, distribution curves, etc. be added to the course curriculum.”


Reaction - Statistical Thinking Course“ was easier for me to relate to the soccer field….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 p p ,learning process, made us think more deeply about what was being said.”


An Insightful Student Response“ most classes dull your brain and kill any….most classes dull your brain and kill anycreative process..…the more time that you spend in classes, the more bored youspend 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

h l i l h Iother two lectures in any class--even when I just get out of that class”


Recommendations

• TA & faculty training• Faculty Collaborationy• Empathy, Creativity, Shared responsibility• Exams & Laboratories for learning and testingg g• Less lecture, more class activities


Recommendations

• Understanding & Retention vs. width of exposure• More ‘Christopheran’ confrontationsp f• Increase the efficiency of the learning process• Communicate in writing, esp. with TAsg, p


Reference BooksTh Fifth Di i li P t M S (1990)• The Fifth Discipline-Peter M. Senge(1990)

• The 7 habits of highly effective people-Stephen R Covey (1989)R.Covey (1989)

• Enlightened Leadership-Ed Oakley and Doug Krug (1991)Krug (1991)

• Cognition-Margaret W. Matlin• 15 Proven ways to get your message across Ernest• 15 Proven ways to get your message across-Ernest

W. Brewer (1997)


Education

Statistical Thinking By Vinay Kulkarni