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