authentic statistics education

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Authentic Statistics Education

Larry WeldonSimon Fraser University

Canada

Updating the Apprenticeship ModelUpdating the Apprenticeship Model

The Problem

Adaptation of course content to practitioner needs

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Since most students are practitioners of statistics,not statistics teachers or statistics consultants ….

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 Histograms, measures of center and spread Simple probability models Estimation Hypothesis testing Regression and Anovar

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But are these enough? And, are they the most basic?

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 … June, 2009 SSC-2009-Vancouver 5

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

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???

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Obstacles to ImplementationDomination 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

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An Example:Gasoline Consumption

Each Fill - record kms and litres of fuel used

Smooth--->SeasonalPattern

Any 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 …

Role of Context?

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•Necessary for the extraction of useful information

•Necessary for arousing student interest in statistical theory

A More Traditional Intro to Theory of Smoothing

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Introduce techniquethenprovide example

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Illustration of Effect

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 QuestionSummary of Categorical Variable RelationshipsIllusions 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 CarrRodney CarrDeakin U

Demo in PP

SummaryRodney Carr’s Power Point Macros provide a way to

construct electronic notes that:

1. Can make clear the links among non-sequential items2. 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 problems2. Enhances focus on stat. concepts and techniques 3. Provides useful contextual information

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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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Thanks for listening.

Follow-up (weldon@sfu.ca)www.stat.sfu.ca/~weldon

The End

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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 = 300Constant=100

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Population*Rank = Constant?

CANADA

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Population*Rank = Constant?

CANADA U.S.

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Population*Rank = Constant?

CANADACANADA WORLD

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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

More details at 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)