Arizona’s First University.
What Shall We Teach in
What Shall We Teach in
Statistics & Probability,
Statistics & Probability,
From a Distance?
From a Distance?
MATHEMATICS UA SCIENCE Walter W. Piegorsch Walter W. Piegorsch University of Arizona University of Arizona Tucson, AZ Tucson, AZQuantitative Literacy
Premise Premise Improve
Improve Quantitative LiteracyQuantitative Literacy in Statistics & Probability
in Statistics & Probability
Consequences Consequences Enhance understanding of Enhance understanding of
→
→ chance/random eventschance/random events
→
→ variabilityvariability
→
→ data analysisdata analysis
→
Background: Probability
Probability instruction includes: Probability instruction includes:
•
• random events (set theory)random events (set theory)
•
• axioms of probabilityaxioms of probability
•
• conditional probabilityconditional probability
•
• joint & marginal probability joint & marginal probability distributions
distributions
•
• multivariate probability distributionsmultivariate probability distributions
•
• hierarchical probability modelshierarchical probability models
•
Background: Statistics
Statistics instruction includes: Statistics instruction includes:
•
• random samplingrandom sampling
•
• study design/experiment designstudy design/experiment design
•
• data reduction and analysisdata reduction and analysis
•
• statistical inferencestatistical inference
•
• decision theorydecision theory
•
• phenomenological interpretation(sphenomenological interpretation(s))
Ö
Ö All are components of All are components of ““QL,”QL,” Quantitative Quantitative Literacy
Distance Education
We can enhance/improve statistical QL by offering We can enhance/improve statistical QL by offering
statistics & probability training
statistics & probability training at a distanceat a distance (
(““distributed instructiondistributed instruction””).). Consequences:
Consequences:
→
→ reaches a wider audiencereaches a wider audience
→
→ increases citizenry knowledge in increases citizenry knowledge in critical/high
critical/high-priority areas-priority areas
→
→ facilitates continuing educfacilitates continuing educ. “. “feederfeeder”” into into graduate programs
graduate programs
(In U.S., concept traces roots to 1800
Vehicles for Distance Ed.
Distribution vehicles for distance education: Distribution vehicles for distance education:
•
• radio, television, paper radio, television, paper ““correspondencecorrespondence”” courses
courses (now viewed as archaic)(now viewed as archaic)
•
• delayed videotape/CD/DVDdelayed videotape/CD/DVD
•
• direct video feeddirect video feed
→
→ ““hybridhybrid””: direct feed with live audience: direct feed with live audience
•
• live video streaming/live video streaming/webcastwebcast
→
→ also: “also: “hybridhybrid”” webcastwebcast
•
Distributed Statistics Instruction
Many U.S. universities adopt distance ed. for Many U.S. universities adopt distance ed. for delivering course content, including classes delivering course content, including classes
in statistics & probability. in statistics & probability.
•
• In some cases whole degree programs In some cases whole degree programs exist, typically M.S.
exist, typically M.S. (Stephenson, 2001)(Stephenson, 2001)
This prompts the question: can the wide range This prompts the question: can the wide range
of topics in statistics & probability be of topics in statistics & probability be
transmitted
transmitted andand digesteddigested effectively via effectively via distance ed.?
Cognitive Concepts
•
• Research has shown that students absorb Research has shown that students absorb advanced material best if certain learning advanced material best if certain learning principles are followed.
principles are followed.
•
• For distance ed., 2 important cognitive learning For distance ed., 2 important cognitive learning components are:
components are:
•
• Students learn best what they practice and Students learn best what they practice and perform on their own
perform on their own
•
• Learning is more effective when students Learning is more effective when students receive real
receive real--time feedbacktime feedback
(Lovett & Greenhouse, 2000) (Lovett & Greenhouse, 2000)
Student Satisfaction
•
• An additional concern is, how to achieve An additional concern is, how to achieve high student satisfaction?
high student satisfaction?
→
→ Not always easy in many math./stat. Not always easy in many math./stat. classes!
classes!
•
• As regards distance ed., students often As regards distance ed., students often desire (require!)
desire (require!) ““quality interaction with the quality interaction with the professor
professor”” (Tudor, 2006)(Tudor, 2006) Ö
Recap
Can we achieve Can we achieve
•
• students practice and perform new material students practice and perform new material on their own
on their own
•
• students receive realstudents receive real--time feedbacktime feedback
•
• students receive quality interaction with the students receive quality interaction with the professor
professor
in statistics & probability classes when taught at in statistics & probability classes when taught at a distance/online?
a distance/online? Answer: it depends! Answer: it depends!
Distance Education Needs
To meet these distance ed. goals, 21
To meet these distance ed. goals, 21stst century century
instruction must employ computer technologies:
instruction must employ computer technologies:
•
• Online textbooks (but: hardcopy also made Online textbooks (but: hardcopy also made available!)
available!)
•
• Online banks of exercises/problem setsOnline banks of exercises/problem sets
•
• Online homeworkOnline homework
→
→ Prompt gradingPrompt grading
→
→ Need: integrated course management Need: integrated course management system system more more ÖÖ Enhance Enhance student student practice practice Rapid Rapid feedback feedback
More Distance Education Needs
•• Use of software tools provides easier course Use of software tools provides easier course organization and operation
organization and operation (Tudor, 2006)(Tudor, 2006)::
→
→ allows for allows for ““automationautomation”” of many ongoing of many ongoing course activities
course activities
→
→ but: also increases but: also increases ““up frontup front”” cost to cost to instructor
instructor
•
• Must also provide flexible instructor access Must also provide flexible instructor access throughout course:
throughout course: →
→ EmailEmail
→
→ Online Online ‘‘ChatChat’’
→
→ Phone (tollPhone (toll--free?)free?)
“
Universality
This underlying paradigm for distance ed. in This underlying paradigm for distance ed. in
statistics & probability has been successful at statistics & probability has been successful at
a number of U.S. universities: a number of U.S. universities:
•
• Colorado State Univ.Colorado State Univ.
•
• Univ. of FloridaUniv. of Florida
•
• Iowa State Univ.Iowa State Univ.
•
• Univ. of South CarolinaUniv. of South Carolina
•
• many others...many others...
But, it
But, it’s ’s not always easy:not always easy:
→
→ certain courses lend themselves better certain courses lend themselves better to online/distance instruction
Successful Online Courses
Successful statistics courses taught online
Successful statistics courses taught online tendtend to be more methodological or applied:
to be more methodological or applied:
•
• Introductory statistics for nonIntroductory statistics for non--statisticiansstatisticians
•
• Linear regression methodologyLinear regression methodology
•
• ANOVA methodologyANOVA methodology
•
• Applied survey samplingApplied survey sampling
•
• Applied time series analysisApplied time series analysis
•
• Specialized topical courses (psychometrics, Specialized topical courses (psychometrics, business statistics, environmetrics, etc.)
Online Theory Courses
•• A nagging question: how to provide quality A nagging question: how to provide quality online/distance ed. for courses in the theory of
online/distance ed. for courses in the theory of
statistics or the theory of probability?
statistics or the theory of probability?
•
• Sometimes a blackboard is still the most effective Sometimes a blackboard is still the most effective way to explain the proof (
way to explain the proof (andand thethe stepssteps behindbehind) an ) an important theorem!
important theorem!
•
• Can we put a blackboard into a computer?Can we put a blackboard into a computer?
→
→ Yes: digital whiteboards exist. But they Yes: digital whiteboards exist. But they are expensive and still a very limited
are expensive and still a very limited
technology.
Digital Whiteboards
•
• Digital whiteboards can Digital whiteboards can take written material take written material from a specially de from a specially de- -signed whiteboard, signed whiteboard, convert it to digital convert it to digital information, and information, and transmit it over the transmit it over the WWW to a computer WWW to a computer user at a distant site. user at a distant site.
•
• But, they are more But, they are more useful as single useful as single
presentation aids than presentation aids than as at as at--aa--distance distance replacements for a replacements for a classroom blackboard. classroom blackboard.
MultiCast Technologies
•• A possible solution to the A possible solution to the ““blackboardblackboard”” problem is to stream a
problem is to stream a videocastvideocast of the of the
instructor at a large blackboard/whiteboard,
instructor at a large blackboard/whiteboard,
possibly with a second feed (
possibly with a second feed (““multicastmulticast””) of the ) of the actual on
actual on--board material using a digital board material using a digital converter.
converter.
•
• The technology exists, but can it be distributed The technology exists, but can it be distributed in a
in a costcost--effectiveeffective wayway to both the source to both the source universities
Hard Choices
•• ShortShort--cut solutions can seem costcut solutions can seem cost--effective, but effective, but a modern, complete, online curriculum
a modern, complete, online curriculum
eventually requires expensive technologies.
eventually requires expensive technologies.
•
• Must also consider cost of increased instructor Must also consider cost of increased instructor access and preparation.
access and preparation.
•
• Some Some hard choiceshard choices have to made by sponsoring have to made by sponsoring institutions before distance ed. for statistics &
institutions before distance ed. for statistics &
probability can become an effective reality.
Bibliography
Jordan, J., and Haines, B. (2006). The role of statistics
Jordan, J., and Haines, B. (2006). The role of statistics educaeduca- -tors
tors in the quantitative literacy movement. Journal of in the quantitative literacy movement. Journal of Statistics Education
Statistics Education 14, 14, http://www.amstat.org/publications/jsehttp://www.amstat.org/publications/jse/ / v14n2/jordan.html
v14n2/jordan.html..
Lovett, M.C., and Greenhouse, J.B. (2000). Applying cognitive Lovett, M.C., and Greenhouse, J.B. (2000). Applying cognitive
theory to statistics instruction.
theory to statistics instruction. American StatisticianAmerican Statistician 54, 19654, 196- -206.
206.
Stephenson, W.R. (2001). Statistics at a distance.
Stephenson, W.R. (2001). Statistics at a distance. Journal of Journal of Statistics Education
Statistics Education 9 (3), 9 (3), http://www.amstat.org/publications/jsehttp://www.amstat.org/publications/jse/ / v9n3/stephenson.html
v9n3/stephenson.html..
Tudor, G.E. (2006). Teaching introductory statistics online Tudor, G.E. (2006). Teaching introductory statistics online ––
Satisfying the students.
Satisfying the students. Journal of Statistics EducationJournal of Statistics Education 14, 14,
http://www.amstat.org/publications/jse/v14n3/tudor.html http://www.amstat.org/publications/jse/v14n3/tudor.html..
