1. June, 2009 SSC-2009-Vancouver1 Authentic Statistics Education Larry Weldon Simon Fraser University Canada Larry Weldon Simon Fraser University Canada Updating the Apprenticeship Model

2. The Problem Adaptation of course content to practitioner needs June, 2009 SSC-2009-Vancouver2 Since most students are practitioners of statistics, not statistics teachers or statistics consultants ….

3. STAT Service Course Complaints  Not enough examples in student’s area of interest  Too much focus on calculations that software can accomplish  Inference logic is too difficult for our students  Too abstract – motivation is obscure  Not enough examples in student’s area of interest  Too much focus on calculations that software can accomplish  Inference logic is too difficult for our students  Too abstract – motivation is obscure June, 2009SSC-2009-Vancouver3

4. The basics via textbooks  Histograms, measures of center and spread  Simple probability models  Estimation  Hypothesis testing  Regression and Anovar  Histograms, measures of center and spread  Simple probability models  Estimation  Hypothesis testing  Regression and Anovar June, 2009SSC-2009-Vancouver4 But are these enough? And, are they the most basic?

5. Examples of omitted “basics”  analyzing population data  software options, help sources  graphical analysis & presentation  smoothing  simulation & calibration  dealing with apparent outliers  verbalization of stat logic  … and much more …  analyzing population data  software options, help sources  graphical analysis & presentation  smoothing  simulation & calibration  dealing with apparent outliers  verbalization of stat logic  … and much more … June, 2009SSC-2009-Vancouver5

6. How does a student learn these practical strategies?  Through live data analysis projects with expert statistical advice  Incremental basics better than basics all at once?  Through live data analysis projects with expert statistical advice  Incremental basics better than basics all at once? June, 2009SSC-2009-Vancouver6

7. June, 2009SSC-2009-Vancouver7 Undergrad Stats Ed Proposal Immersion in Data Analysis, with Guidance and Feedback, will promote a more Useful Knowledge of Statistics than a Logical Sequence of Technique Presentations Immersion in Data Analysis, with Guidance and Feedback, will promote a more Useful Knowledge of Statistics than a Logical Sequence of Technique Presentations A return to Apprenticeship Education, but making use of modern resources (statistical software and electronic communication.)

8. June, 2009SSC-2009-Vancouver8 From ICOTS2 (1986) "Using the practical model [of teaching statistics] means aiming to teach statistics by addressing such problems in contexts in which they arise. At present this model is not widely used." (Taffe 1986) “Experiential Education”

9. June, 2009SSC-2009-Vancouver9 Status in 1996  Hands-on activities  Working in small groups  Frequent and rapid feedback  Communicating results  Explaining reasoning  Computer simulations  Open questions real settings  Learning to work co-operatively  Hands-on activities  Working in small groups  Frequent and rapid feedback  Communicating results  Explaining reasoning  Computer simulations  Open questions real settings  Learning to work co-operatively In discussing what helps students learn, [David Moore (1996)] listed the following: Phillips - ICME 8 Do we incorporate all these features???

10. June, 2009SSC-2009-Vancouver10 Obstacles to Implementation Domination of Old-Math Culture in Stat Ed Suppression of Context Institutional Disincentives to Curriculum Change Publishers Reluctance to Innovate Use Math but Reject Math Culture … e.g. statistics is judged by ability to extract info from context Promote Experiential Courses - Instructor Is Guide Find a new role for existing textbooks – as reference, rather than as a course sequence Overcoming These Obstacles

11. June, 2009SSC-2009-Vancouver11 An Example: Gasoline Consumption Each Fill - record kms and litres of fuel used Smooth ---> Seasonal Pattern Any pattern?

12. June, 2009SSC-2009-Vancouver12 Suggests follow-up  1. How do you choose the amount of smoothing to produce useful information?  2. How do you learn why a seasonal pattern occurs?  1. How do you choose the amount of smoothing to produce useful information?  2. How do you learn why a seasonal pattern occurs? Point is … New theory is best introduced through data exploration.

13. June, 2009SSC-2009-Vancouver13 Intro to smoothing with context …

14. Role of Context? June, 2009SSC-2009-Vancouver14 Necessary for the extraction of useful information Necessary for arousing student interest in statistical theory

15. A More Traditional Intro to Theory of Smoothing June, 2009SSC-2009-Vancouver15 Introduce technique then provide example

16. June, 2009SSC-2009-Vancouver16 Illustration of Effect

17. Real Data Example June, 2009SSC-2009-Vancouver17

18. June, 2009SSC-2009-Vancouver18 Data Analysis -> Stat Theory  Using applications to illustrate theory (is common approach)  Using applications to construct theory (is proposal here)  Using applications to illustrate theory (is common approach)  Using applications to construct theory (is proposal here) Best Approach for undergraduate stats?

19. June, 2009SSC-2009-Vancouver19 Arms and Hands Exercise  Ways to cross arms and to fold hands (MacGillivray (2007))  Related?  Related to Gender?  Ways to cross arms and to fold hands (MacGillivray (2007))  Related?  Related to Gender? Theory Learned? Formulation of Data-Based Question Summary of Categorical Variable Relationships Illusions of Randomness …. (more)

20. June, 2009SSC-2009-Vancouver20 Some Experiential Learning Courses (SFU)  STAT 100 - Statistics Appreciation Course  STAT 300 - Statistics Verbalization  STAT 400 - Data Analysis  STAT 100 - Statistics Appreciation Course  STAT 300 - Statistics Verbalization  STAT 400 - Data Analysis More details at www.stat.sfu.ca/~weldon

21. June, 2009SSC-2009-Vancouver21  Experiential learning has potential to –Motivate student inquiry into stat theory at all undergraduate levels –Encourage authentic learning of stat theory  Experiential learning has potential to –Motivate student inquiry into stat theory at all undergraduate levels –Encourage authentic learning of stat theory

22. June, 2009SSC-2009-Vancouver22 Objections to Experiential Learning  1. Chaotic collection of techniques (No general framework for applications)  2. Lack of complete coverage of basics  1. Chaotic collection of techniques (No general framework for applications)  2. Lack of complete coverage of basics Some New Technologies can help

23. June, 2009SSC-2009-Vancouver23 Rodney Carr Deakin U Demo in PP

24. Summary Rodney Carr’s Power Point Macros provide a way to construct electronic notes that: 1.Can make clear the links among non-sequential items 2.Can be used on-computer or online, and by the lecturer or the student When applied to a Case Study approach to basic stats, has the potential to : 1. Maintain motivation with focus on real-life problems 2. Enhances focus on stat. concepts and techniques 3. Provides useful contextual information

25. June, 2009SSC-2009-Vancouver25 Textbook as Reference  Textbook for topic sequence? NO.  Textbook for reference, cases for sequence  Electronic textbooks particularly useful here (e.g. Stirling(2002) CAST - Computer Assisted Statistics Teaching.)  Textbook for topic sequence? NO.  Textbook for reference, cases for sequence  Electronic textbooks particularly useful here (e.g. Stirling(2002) CAST - Computer Assisted Statistics Teaching.)

26. June, 2009SSC-2009-Vancouver26 Math as an “simplifier”  Identify Common Approaches (e.g. regression, residual plots, conditioning, …)  Compare and Contrast Methods (e.g. hypoth tests vs CIs, parametric vs non-parametric, …)  Discuss role of models (simpler than reality, simulation role, independence, …)  … Anything that clarifies and reduces ambiguity  Identify Common Approaches (e.g. regression, residual plots, conditioning, …)  Compare and Contrast Methods (e.g. hypoth tests vs CIs, parametric vs non-parametric, …)  Discuss role of models (simpler than reality, simulation role, independence, …) …… Anything that clarifies and reduces ambiguity

27. June, 2009SSC-2009-Vancouver27 The aggregate of guided data analysis experiences is what practitioners actually need to learn Experiential learning is Authentic Learning

28. June, 2009SSC-2009-Vancouver28 Teaching vs Learning  Teachers can encourage authentic learning  Difficult to arrange in conservative depts  Difficult to do with large classes  Difficult for teachers without practical exp’ce  Nevertheless, a worthwhile goal.  Teachers can encourage authentic learning  Difficult to arrange in conservative depts  Difficult to do with large classes  Difficult for teachers without practical exp’ce  Nevertheless, a worthwhile goal.

29. June, 2009 SSC-2009-Vancouver29 Thanks for listening. Follow-up (weldon@sfu.ca)weldon@sfu.ca www.stat.sfu.ca/~weldon Follow-up (weldon@sfu.ca)weldon@sfu.ca www.stat.sfu.ca/~weldon The End

30. June, 2009SSC-2009-Vancouver30

31. June, 2009SSC-2009-Vancouver31 Good Ideas from ICOTS2 (1986) "The interplay between questions, answers and statistics … if students have a good appreciation of this interplay, they will have learned some statistical thinking, not just some statistical methods." (Speed 1986)

32. June, 2009SSC-2009-Vancouver32 Quotes from ICOTS2 (1986) … while most statistics professors like statistics for its own sake, most students become interested in statistics mainly if the subject promises to do useful things for them. …. Only then do most students seem to become sufficiently intrigued with statistics to want to learn about statistical theory." (Roberts 1986)

33. June, 2009SSC-2009-Vancouver33 Quotes from ICOTS2 (1986) "The development of statistical skills needs what is no longer feasible, and that is a great deal of one-to-one student-faculty interaction..." (Zidek 1986)

34. June, 2009SSC-2009-Vancouver34 Implications from ICOTS2  Use Context to teach theory (Taffe)  Whole process of data-based Q&A (Speed)  Abstractions do not motivate (Roberts)  Teacher-student interaction needed for useful learning of statistics (Zidek)  Use Context to teach theory (Taffe)  Whole process of data-based Q&A (Speed)  Abstractions do not motivate (Roberts)  Teacher-student interaction needed for useful learning of statistics (Zidek)

35. June, 2009SSC-2009-Vancouver35 Context vs Abstraction  Which is more interesting to students?  Example of a new item of stat theory “Zipf’s Law” chosen for obscurity!  Which is more interesting to students?  Example of a new item of stat theory “Zipf’s Law” chosen for obscurity!

36. June, 2009SSC-2009-Vancouver36 “Theory”: Zipf’s Law  An empirical finding of relative sizes of things  Frequency * rank = constant  An empirical finding of relative sizes of things  Frequency * rank = constant Total Freq = 300 Constant=100

37. June, 2009SSC-2009-Vancouver37 Population*Rank = Constant? CANADA

38. June, 2009SSC-2009-Vancouver38 Population*Rank = Constant? CANADAU.S.

39. June, 2009SSC-2009-Vancouver39 Population*Rank = Constant? CANADA WORLD

40. June, 2009SSC-2009-Vancouver40 Examples of Experiential Learning Courses (SFU)  STAT 100 - Statistics Appreciation Course –Survival analysis, Randomized Response, …  STAT 300 - Statistics Communication –Verbal explanations of stat theory and practice –Oral presentation of summary of official data  STAT 400 - Data Analysis –Data exploration by graphics and simulation –Comparison of parametric and non-par methods –Rescue of (almost) hopeless cases  STAT 100 - Statistics Appreciation Course –Survival analysis, Randomized Response, …  STAT 300 - Statistics Communication –Verbal explanations of stat theory and practice –Oral presentation of summary of official data  STAT 400 - Data Analysis –Data exploration by graphics and simulation –Comparison of parametric and non-par methods –Rescue of (almost) hopeless cases More details at www.stat.sfu.ca/~weldon

41. June, 2009SSC-2009-Vancouver41 Suggests Follow-up 1.Why is WORLD different? 2.To which kinds of counts does Zipf’s Law apply? Point is: Contextual Introduction conveys understanding of theory wheras Theory alone conveys ‘theory’ but not understanding (Even with confirming example)