Transcript slides - NCSU Statistics

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 topics
Learn normal distribution for first exam
• Then forget it
Learn confidence intervals for second exam
• Then forget it
Missing the big picture
Never see connection
Some 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 topics
Need to convey to students an overall
goal that motivates what topics will be
covered.
Possible Solution
Concept maps
Graphical organizer that shows topics
Presents course concepts and associated
links
Example: ST101
Topics covered
Sample Surveys
Errors in surveys
Experiments and
design
Question Wording
Histograms
Mean median mode
Standard Deviation
Normal Distributions
Sampling
Distributions
Basic probability
Confidence Intervals
C.I. for a mean
Hypothesis tests
Chi Square tests
Regression
Correlation
Two way tables
What links them?
Course Goal
Often not made explicit to students
Listed in syllabus and then forgotten
Example: ST101
Course Goal
ST101 is for non-scientific majors
Will not often use statistics in their fields
Understand 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.
Most often
includes
Sample Surveys
Also Includes
Scientific Studies
Course Goal: Understand Statistical Inference presented in the media.
Most often
includes
Sample Surveys
Also Includes
Scientific Studies
Tell about
Rules out chance in
Margin of Error
Statistical Significance
Course Goal: Understand Statistical Inference presented in the media.
Most often
includes
Sample Surveys
Non-random
samples
Random
samples
Also Includes
Scientific Studies
Randomized
Experiments
Non-random
experiments
Tell about
Rules out chance in
Margin of Error
Statistical Significance
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.
Most often
includes
Sample Surveys
Non-random
samples
Random
samples
Also Includes
Sometimes includes
Data Presentation and
Summary
Scientific Studies
Randomized
Experiments
Non-random
experiments
Tell about
Rules out chance in
Margin of Error
Statistical Significance
Includes
Means, Histograms, etc.
Course Goal: Understand Statistical Inference presented in the media.
Most often
includes
Sample Surveys
Non-random
samples
Random
samples
Also Includes
Sometimes includes
Data Presentation and
Summary
Scientific Studies
Randomized
Experiments
Non-random
experiments
Includes
Means, Histograms, etc.
Are used to picture
Distributions of Data
Tell about
Rules out chance in
A special case is
Normal Distribution
Margin of Error
Statistical Significance
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.
Most often
includes
Also Includes
Sample Surveys
Non-random
samples
Sometimes includes
Scientific Studies
Random
samples
Randomized
Experiments
Non-random
experiments
Includes
Means, Histograms, etc.
Are used to picture
Allow use of
Tell about
Data Presentation
and Summary
Rules of Probability
Distributions of Data
Rules out chance in
A special case is
Normal Distribution
Margin of Error
Statistical Significance
Course Goal: Understand Statistical Inference presented in the media.
Most often
includes
Also Includes
Sample Surveys
Non-random
samples
Sometimes includes
Data Presentation
and Summary
Scientific Studies
Random
samples
Randomized
Experiments
Non-random
experiments
Means, Histograms, etc.
Are used to picture
Allow use of
Tell about
Includes
Rules of Probability
Distributions of Data
Rules out chance in
Predict
A special case is
Is a good
model for
Distribution of a Statistic
Used to calculate
Margin of Error
Can show
Statistical Significance
Normal Distribution
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 phrases
In concise language
Show hierarchy
What topics are subtopics
Shown graphically
Course Goal: Understand Statistical Inference presented in the media.
Most often
includes
Also Includes
Sample Surveys
Non-random
samples
Sometimes includes
Data Presentation
and Summary
Scientific Studies
Random
samples
Randomized
Experiments
Non-random
experiments
Means, Histograms, etc.
Are used to picture
Allow use of
Tell about
Includes
Rules of Probability
Distributions of Data
Rules out chance in
Predict
A special case is
Is a good
model for
Distribution of a Statistic
Used to calculate
Margin of Error
Can show
Statistical Significance
Normal Distribution
Advantages for Course Planning
Help instructor visualize concepts
What 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 interrelationships
Emphasize key ideas
Advantages for Course Planning
Allow to think about order
What 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.
Most often
includes
Sometimes includes
Data Presentation
and Summary
Sample Surveys
Non-random
samples
Includes
Random
samples
Means, Histograms, etc.
Are used to picture
Allow use of
Tell about
Rules of Probability
Distributions of Data
A special case is
Predict
Distribution of a Statistic
Used to calculate
Margin of Error
Is a good
model for
Normal Distribution
Not Just a Course Outline
Syllabus/Course outline is linear
Can’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 map
Discuss with other instructors
Think about implications for teaching
Think about personal philosophy
Convey your understanding
Use it.
Emphasize key concepts and course goal.
Encourage students to use it.
Advantages of Concept maps
Visualize concepts
Most students are visual learners
More readily understand graphical
presentation
Connections are Explicit
Not a disconnected list of topics.
Cautions
Creation is not easy
Requires substantial though
Can be done in stages
Don’t try to fit in everything
Concentrate on the key topics
Not everyone has the same map
Even for the same course.
Other Uses and Ideas
Concept maps for assessment
Fill in the blanks
Draw from scratch
Use to arrange materials in online
course.
Extensive hyperlinks
Other Uses and Ideas
Hyperlinked on the web
Linked to learning objectives
Notes or presentations
Study guides
Images 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.org
US COTS
Put together concept maps for major
textbooks
Working with text authors
Course Goal: Understand Statistical Inference presented in the media.
Most often
includes
Also Includes
Sample Surveys
Non-random
samples
Sometimes includes
Data Presentation
and Summary
Scientific Studies
Random
samples
Randomized
Experiments
Non-random
experiments
Means, Histograms, etc.
Are used to picture
Allow use of
Tell about
Includes
Rules of Probability
Distributions of Data
Rules out chance in
Predict
A special case is
Is a good
model for
Distribution of a Statistic
Used to calculate
Margin of Error
Can show
Statistical Significance
Normal Distribution