Transcript Document

Authentic Statistics Education
Updating the Apprenticeship Model
Larry Weldon
Simon Fraser University
Canada
June, 2009
SSC-2009-Vancouver
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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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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
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The basics via textbooks
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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?
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Examples of omitted “basics”
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analyzing population data
software options, help sources
graphical analysis & presentation
smoothing
simulation & calibration
dealing with apparent outliers
verbalization of stat logic
… and much more …
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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?
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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.)
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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”
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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
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Do we
incorporate
all these
features???
Phillips - ICME 8
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Obstacles These
to Implementation
Overcoming
Obstacles
Domination of Old-Math Culture in Stat Ed
Suppression
of Math
Context
Use
Math but Reject
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
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An Example:
Gasoline Consumption
Any pattern?
Each Fill record kms
and litres of
fuel used
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Smooth
--->
Seasonal
Pattern
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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.
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Intro to smoothing with context …
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Role of Context?
•Necessary for the extraction of
useful information
•Necessary for arousing student
interest in statistical theory
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A More Traditional Intro to
Theory of Smoothing
Introduce technique
then
provide example
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Illustration of Effect
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Real Data Example
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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?
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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)
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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
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 Experiential learning has potential to
– Motivate student inquiry into stat theory
at all undergraduate levels
– Encourage authentic learning of stat theory
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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
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Rodney
Rodney Carr
Carr
Deakin U
Demo in PP
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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
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.)
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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
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The aggregate of guided data analysis experiences
is what practitioners actually need to learn
Experiential learning is Authentic Learning
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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.
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The End
Thanks for listening.
Follow-up ([email protected])
www.stat.sfu.ca/~weldon
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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)
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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)
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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)
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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)
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Context vs Abstraction
 Which is more interesting to students?
 Example of a new item of stat theory
“Zipf’s Law” chosen for obscurity!
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“Theory”: Zipf’s Law
 An empirical finding
of relative sizes of things
 Frequency * rank = constant
Total Freq = 300
Constant=100
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Population*Rank = Constant?
CANADA
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Population*Rank = Constant?
CANADA
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U.S.
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Population*Rank = Constant?
CANADA
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WORLD
CANADA
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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
June, 2009
More details atSSC-2009-Vancouver
www.stat.sfu.ca/~weldon
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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)
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