Using Concept Maps in Planning an Introductory Statistics Course.
Roger Woodard
Missing the big picture
Most students in introductory statistics courses
See statistics as disconnected topicsLearn normal distribution for first exam• Then forget it
Learn confidence intervals for second exam• Then forget it
Missing the big picture
Never see connectionSome don’t associate 1.96 in margin of error with normal distribution
Bigger problem: Don’t understand where confidence intervals will be in their lives.
Why do I care?
Problem
Need to convey to students the interconnections of statistical topicsNeed to convey to students an overall goal that motivates what topics will be covered.
Possible Solution
Concept mapsGraphical organizer that shows topics Presents course concepts and associated links
Example: ST101
Topics coveredSample SurveysErrors in surveysExperiments and designQuestion WordingHistogramsMean median modeStandard DeviationNormal Distributions
Sampling DistributionsBasic probabilityConfidence IntervalsC.I. for a meanHypothesis testsChi Square testsRegressionCorrelationTwo way tables
What links them?
Course GoalOften not made explicit to studentsListed in syllabus and then forgotten
Example: ST101
Course GoalST101 is for non-scientific majorsWill not often use statistics in their fieldsUnderstand Statistics Presented in the Popular Press.
What is in the press?Surveys: Bush and Kerry tied for presidency.Scientific Studies: Grapefruit Fights Cancer
Example: ST101
How often do we see the normal distribution in Cosmo or USA Today?
Rarely
Why do students need to know about Normal distribution?
Course Goal: Understand Statistical Inference presented in the media.
Also IncludesMost often includes
Sample Surveys Scientific Studies
Course Goal: Understand Statistical Inference presented in the media.
Also IncludesMost often includes
Sample Surveys Scientific Studies
Margin of Error Statistical Significance
Rules out chance inTell about
Course Goal: Understand Statistical Inference presented in the media.
Also IncludesMost often includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Margin of Error Statistical Significance
Non-random experiments
Rules out chance inTell about
Course Goal: Understand Statistical Inference presented in the media.
Also IncludesMost often includes
Sample Surveys Scientific Studies
Margin of Error Statistical Significance
Rules out chance inTell about
Where are the other topics?
How do histograms, standard deviations and the normal distribution fit in?
Course Goal: Understand Statistical Inference presented in the media.
Also Includes Sometimes includesMost often includes
Data Presentation and Summary
Means, Histograms, etc.
Includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Margin of Error Statistical Significance
Non-random experiments
Rules out chance inTell about
Course Goal: Understand Statistical Inference presented in the media.
Also IncludesMost often includes
Sample Surveys Scientific Studies
Margin of Error Statistical Significance
Rules out chance inTell about
Course Goal: Understand Statistical Inference presented in the media.
Also IncludesMost often includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Margin of Error Statistical Significance
Non-random experiments
Rules out chance inTell about
Course Goal: Understand Statistical Inference presented in the media.
Also Includes Sometimes includesMost often includes
Data Presentation and Summary
Means, Histograms, etc.
Distributions of Data
Normal Distribution
A special case is
Are used to picture
Includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Margin of Error Statistical Significance
Non-random experiments
Rules out chance inTell about
Need connections
What connects these tools with “important things”?What are the links that make all of these part of statistics?
Course Goal: Understand Statistical Inference presented in the media.
Also Includes Sometimes includes Most often includes
Data Presentation and Summary
Means, Histograms, etc.
Distributions of Data
Normal Distribution
A special case is
Are used to picture
Includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Allow use of
Rules of Probability
Margin of Error Statistical Significance
Non-random experiments
Rules out chance in Tell about
Course Goal: Understand Statistical Inference presented in the media.
Also Includes Sometimes includes Most often includes
Is a good model for
Data Presentation and Summary
Means, Histograms, etc.
Distributions of Data
Normal Distribution
A special case is
Are used to picture
Includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Allow use of
Rules of Probability
Distribution of a Statistic
Margin of Error Statistical Significance
Non-random experiments
Predict
Used to calculate Can show
Rules out chance in Tell about
Concept Map
Identifies Sampling distributions as the link that holds everything together.
Throughout the course I stress this link.When talking about normal distribution foreshadow distribution of statistic.When working with p-values I bring them back.
Identifies dead ends
Characteristics of Concept Maps
Consist of propositions Key concepts together with linking phrasesIn concise language
Show hierarchyWhat topics are subtopics
Shown graphically
Course Goal: Understand Statistical Inference presented in the media.
Also Includes Sometimes includes Most often includes
Is a good model for
Data Presentation and Summary
Means, Histograms, etc.
Distributions of Data
Normal Distribution
A special case is
Are used to picture
Includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Allow use of
Rules of Probability
Distribution of a Statistic
Margin of Error Statistical Significance
Non-random experiments
Predict
Used to calculate Can show
Rules out chance in Tell about
Advantages for Course Planning
Help instructor visualize conceptsWhat do you want to focus on?What topics should you foreshadow?Which topics are superfluous?
Can be presented to students when finished.
Help them see the interrelationshipsEmphasize key ideas
Advantages for Course Planning
Allow to think about orderWhat is needed to support an idea?Can’t do Normal Distribution before standard deviation.Doesn’t dictate order
Course Goal: Understand Statistical Inference presented in the media.
Sometimes includes Most often includes
Is a good model for
Data Presentation and Summary
Means, Histograms, etc.
Distributions of Data
Normal Distribution
A special case is
Are used to picture
Includes
Sample Surveys
Non-random samples
Random samples
Allow use of
Rules of Probability
Distribution of a Statistic
Margin of Error
Predict
Used to calculate
Tell about
Not Just a Course Outline
Syllabus/Course outline is linearCan’t show cross links.Can’t show supporting concepts.
Syllabus/Course is not as concise Typically more verbose
Course outline still needed.Lists time order of the topics.
Creating a Concept Map
Identify course goal (or goals)Guided by course description or guidelines from course and curriculum committee.
Identify 4 to 7 key topics that are needed to achieve this goal.
Research shows that is max we can understand.Pick big ones
Creating a Concept Map
Identify linking phrases that connect concepts to the goal and to each other
Add sub topics and relation topics as needed.
Determine which topic is the focal point for the course, and how it relates to the course goal.Create graphic map with connections
Creating a Concept Map
Revise the mapDiscuss with other instructorsThink about implications for teachingThink about personal philosophyConvey your understanding
Use it.Emphasize key concepts and course goal.Encourage students to use it.
Advantages of Concept maps
Visualize conceptsMost students are visual learnersMore readily understand graphical presentation
Connections are ExplicitNot a disconnected list of topics.
Cautions
Creation is not easyRequires substantial thoughCan be done in stages
Don’t try to fit in everythingConcentrate on the key topics
Not everyone has the same mapEven for the same course.
Other Uses and Ideas
Concept maps for assessmentFill in the blanksDraw from scratch
Use to arrange materials in online course.
Extensive hyperlinks
Other Uses and Ideas
Hyperlinked on the webLinked to learning objectivesNotes or presentationsStudy guidesImages or Video
Further Development
Examine use of concept maps in TA training.
Do they teach better? More consistently?
Provide resources for instructors to build concept maps
CAUSEweb.orgUS COTS
Put together concept maps for major textbooks
Working with text authors
Course Goal: Understand Statistical Inference presented in the media.
Also Includes Sometimes includes Most often includes
Is a good model for
Data Presentation and Summary
Means, Histograms, etc.
Distributions of Data
Normal Distribution
A special case is
Are used to picture
Includes
Sample Surveys Scientific Studies
Non-random samples
Random samples
Randomized Experiments
Allow use of
Rules of Probability
Distribution of a Statistic
Margin of Error Statistical Significance
Non-random experiments
Predict
Used to calculate Can show
Rules out chance in Tell about
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