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Collaborative Research:
Adaptation & Implementation of
Activity & Web-Based Materials
Into Post-Calculus Introductory
Probability and Statistics Courses
Tracy Goodson-Espy
M. Leigh Lunsford
Ginger Holmes Rowell
3/15/2002
NSF DUE-0126716
Project* Objectives
• To improve post-calculus students
learning of probability & statistics.
• To provide students with better
preparation for their future careers in
mathematics & statistics, mathematics
education, and computer science.
*This project is partially support by the National Science Foundation. The
project starts in June, 2002 and continues through August, 2004.
3/15/2002
NSF DUE-0126716
The Materials for A&I
• “A Data-Oriented, Active Learning, PostCalculus Introduction to Statistical
Concepts Methods, and Theory (SCMT)”
• A. Rossman, B. Chance, K. Ballman
• NSF DUE-9950476
• “Virtual Laboratories in Probability and
Statistics (VLPS)”
• K. Siegrist
• NSF DUE-9652870
3/15/2002
NSF DUE-0126716
Statistical Concepts Methods, and Theory
(SCMT): A Small Sample of Materials
Activity
Context
Randomization
Test
Friendly
Observers
Randomization,
simulation, p-value
Uses cards (23 per student) and Minitab to
simulate a randomization test to estimate pvalue from a 2x2 table for a psychology study.
Equal
Likeliness
Random
Babies
Sample space, long-run
relative frequency,
random variable,
expected value,
simulation
Uses index cards (4 per student) and Minitab
to simulate the matching problem and
develops probability calculations with equally
likely outcomes.
Fishers
Exact Test
Friendly
Observers
Counting rules,
hypergeometric
probabilities
Exact probabilities for simulation in
Randomization Test
General
vs.
Specific
The
Birthday
Problem
Applications of counting
techniques, complement
rule
Does calculations for the birthday problem
(using a spreadsheet) contrasting any
birthday vs. a specific birthday
Probability
Rules
100 top films,
2000 Michigan
primary
Variety of basic
probability rules
Discovery approach through two-way tables
and some Venn diagram. HW is very
interesting
3/15/2002
Concepts
Description
NSF DUE-0126716
Virtual Laboratories in Probability &
Statistics: An Example
Games of Chance
Contents
1. Poker
2. Poker Dice and Chuck-a-Luck
3. Craps
4. Introduction
5. Roulette
6. The Monty Hall Problem
7. Lotteries
8. Notes
Applets
•
Poker Experiment
•
Poker Dice Experiment
•
Chuck-a-Luck Experiment
•
Craps Experiment
•
Roulette Experiment
•
Monty Hall Game
•
Poker Experiment Applet
Monty Hall Experiment
3/15/2002
NSF DUE-0126716
A Collaborative Approach
A&I Materials into Post Calculus Prob/Stat Courses
Athens State Univ.
Middle Tenn. St. Univ.
M. Leigh Lunsford
Ginger Holmes Rowell
Univ. of Alabama, Huntsville
Tracy Goodson Espy
Provide Objective Independent Assessment of A&I
3/15/2002
NSF DUE-0126716
The A&I Cycle
Receive Training
on New Materials
Develop Best
Practices for Use
of Materials Co-jointly
Materials
VLPS
Use Materials
in Courses
SCMT
Provide Feedback to
Material Developers
3/15/2002
Evaluate A&I
Refine Adaptation
Use Independent
Assessment Results
to Improve A&I
NSF DUE-0126716
Assessment of A&I of Materials
• Will Use an Action Research Model*
– What is the problem? I.e., what is not
working in the classroom?
– What technique can be used to address the
learning problem?
– What type of evidence can be gathered to
show whether the implementation is
effective?
– What should be done next, based on what
was learned?
*1999 - R. delMas, J. Garfield, B. Chance
3/15/2002
NSF DUE-0126716
Project Goals and Outcomes
•
The development of post-calculus probability and statistics courses that
produce well-educated students.
•
The integration of technology and group-based activity work into the
courses for the purpose of enhancing student learning.
•
The enhancement of student communication skills through oral and written
reports and presentations.
•
The improvement and implementation of non-traditional assessment
techniques for evaluating students.
•
A contribution to the mathematics community discussion/research
concerning what topics/materials/methods should be included in reformoriented probability and statistics courses to improve overall student
understanding of the subject.
3/15/2002
NSF DUE-0126716
Dissemination
• Presentations at Professional Conferences
• In-Service Training for High School Statistics
Teachers (Spring 2004)
• Summer Workshop for College Faculty
(Summer 2004)
• Papers in Mathematics Education Journals
• Project Website:
http://www.athens.edu/NSF_Prob_Stat/
3/15/2002
NSF DUE-0126716