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Authentic Statistics Education

Authentic Statistics Education. Updating the Apprenticeship Model. Larry Weldon Simon Fraser University Canada. The Problem. Since most students are practitioners of statistics, not statistics teachers or statistics consultants …. Adaptation of course content to practitioner needs.

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Authentic Statistics Education

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

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

  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 SSC-2009-Vancouver

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

  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 … SSC-2009-Vancouver

  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? SSC-2009-Vancouver

  7. 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 A return to Apprenticeship Education, but making use of modern resources (statistical software and electronic communication.) SSC-2009-Vancouver

  8. 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” SSC-2009-Vancouver

  9. Status in 1996 In discussing what helps students learn, [David Moore (1996)] listed the following: • 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 Do we incorporate all these features??? SSC-2009-Vancouver Phillips - ICME 8

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

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

  12. 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? Point is … New theory is best introduced through data exploration. SSC-2009-Vancouver

  13. Intro to smoothing with context … SSC-2009-Vancouver

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

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

  16. Illustration of Effect SSC-2009-Vancouver

  17. Real Data Example SSC-2009-Vancouver

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

  19. Arms and Hands Exercise • 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) SSC-2009-Vancouver

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

  21. Experiential learning has potential to • Motivate student inquiry into stat theoryat all undergraduate levels • Encourage authentic learning of stat theory SSC-2009-Vancouver

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

  23. Rodney Carr Deakin U Rodney Carr Demo in PP SSC-2009-Vancouver

  24. Summary Rodney Carr’s Power Point Macros provide a way to construct electronic notes that: Can make clear the links among non-sequential items 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 Enhances focus on stat. concepts and techniques Provides useful contextual information

  25. 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.) SSC-2009-Vancouver

  26. 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 SSC-2009-Vancouver

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

  28. 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. SSC-2009-Vancouver

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

  30. SSC-2009-Vancouver

  31. 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) SSC-2009-Vancouver

  32. 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) SSC-2009-Vancouver

  33. 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) SSC-2009-Vancouver

  34. 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) SSC-2009-Vancouver

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

  36. “Theory”: Zipf’s Law • An empirical findingof relative sizes of things • Frequency * rank = constant Total Freq = 300 Constant=100 SSC-2009-Vancouver

  37. Population*Rank = Constant? CANADA SSC-2009-Vancouver

  38. Population*Rank = Constant? CANADA U.S. SSC-2009-Vancouver

  39. Population*Rank = Constant? CANADA WORLD CANADA SSC-2009-Vancouver

  40. 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 More details at www.stat.sfu.ca/~weldon SSC-2009-Vancouver

  41. Suggests Follow-up Why is WORLD different? 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) SSC-2009-Vancouver

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