Collaborative Research: Adaptation

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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

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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 supported by the
National Science Foundation. The project started
in June, 2002 and continues through August, 2004.
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The Materials for AI

• A Data-Oriented, Active Learning, Post-Calculus
  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

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Statistical Concepts, Methods, and Theory (SCMT)
A Small Sample of Materials
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Virtual Laboratories in Probability Statistics
An Example

• Games of Chance
• Contents
• Poker
• Poker Dice and Chuck-a-Luck
• Craps
• Introduction
• Roulette
• The Monty Hall Problem
• Lotteries
• Notes
• Applets
• Poker Experiment
• Poker Dice Experiment
• Chuck-a-Luck Experiment
• Craps Experiment
• Roulette Experiment
• Monty Hall Game
• Monty Hall Experiment

Poker Experiment Applet
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A Collaborative Approach
AI Materials into Post Calculus Prob/Stat Courses
Athens State Univ. M. Leigh Lunsford
Middle Tenn. St. Univ. Ginger Holmes Rowell
Univ. of Alabama, Huntsville Tracy Goodson Espy
Provide Objective Independent Assessment of AI
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Theoretical Orientation

• The project is based on an emergent
  constructivist perspective, meaning that
  mathematics learning can be characterized as both
  a process of active individual construction and a
  process of enculturation.
• This orientation emphasizes the importance of
  analyzing students individual mathematical
  activities as well as placing them in the context
  of the mathematical community in which they were
  developed. This is done through the use of a
  teaching experiment.
• Students individual constructive activities and
  their roles in social processes in the classroom
  act in a complementary way to enable student
  learning.
• 1995, P. Cobb

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Teaching Experiment Cycle
Class Implementation Feedback
Teaching Hypotheses Curricular Instructional
Choices
Instructors Reflections and Curricular
Modifications
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The AI Cycle
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Assessment of AI 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

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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
  reform-oriented probability and statistics
  courses to improve overall student understanding
  of the subject.

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Project Goals and Outcomes

• Goal The development of post-calculus
  probability and statistics courses that produce
  well-educated students.
• Outcome The project uses SCMT and VLPS for
  Three Different Types of Courses
• Athens State University - Mathematics 331Applied
  Statistics Probability (primarily an
  undergraduate probability course)
• Middle Tennessee State University - Math
  2050/Statistics 5140Probability Statistics
  (primarily an undergraduate course in inferential
  statistics)
• Middle Tennessee State University- Mathematics
  6350Probability and Statistics for Teachers

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Project Goals and Outcomes

• Goal The integration of technology and
  group-based activity work into the courses for
  the purpose of enhancing student learning.
• Outcome The project integrates selected SCMT
  and VLPS materials into the courses as well as
  using Mini-tab.
• Using these materials, students work in groups on
  discovery-based learning activities.
• The technology is integrated for three purposes
  1) a tool to help with computations, 2) a tool
  for visualization and 3) a tool for simulation.

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Project Goals and Outcomes

• Goal The enhancement of student communication
  skills through oral and written reports and
  presentations.
• Outcome Each of the courses included in the
  project requires multiple oral and written
  student reports and presentations that explore
  student understandings of the concepts covered in
  class and through the individual and group
  activities.

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Project Goals and Outcomes

• Goal The improvement and implementation of
  non-traditional assessment techniques for
  evaluating students.
• Outcome Each of the courses included in the
  project uses assessment methods in addition to
  traditional paper and pencil tests.
  Non-traditional assessments include written and
  oral reports, homework including the analysis of
  real data, written artifacts from lab activities
  and group work.

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Project Goals and Outcomes

• Goal A contribution to the mathematics community
  discussion/research concerning what topics/
  materials/methods should be included in
  reform-oriented probability and statistics
  courses to improve overall student understanding
  of the subject.
• Outcome While the project is on-going,
  preliminary results indicate that extensive
  inclusion of real-world examples, interactive
  lectures, student-active lab assignments,
  carefully crafted web-activities, and graded
  homework (that is connected to the previous
  items) result in improved student retention and
  mathematical understanding.

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Preliminary Survey Results

• Students in the project classes were given
  mid-term and final Class Activities Surveys.
  These surveys consisted of three parts
• Section One asked a series of questions
  concerning students beliefs concerning his/her
  understanding of specific mathematics concepts
  covered in the course such as sample space,
  conditional probability, independence of events,
  probability laws, etc. The student was asked to
  rate their understanding on a 1-5 scale(L-H).
• Section Two included a series of questions that
  asked students to rate the functioning of the
  class in terms of class dynamics, group dynamics,
  instructional strategies used, amount of
  technology used, and the effectiveness of the
  technology for conveying ideas.
• Section Three included open-ended questions that
  solicited student opinions.
• This survey was also given to pre-project classes
  in Spring 2002.

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Section One Results

• Table 1 shows the median student responses to
  Section One of the survey concerning student
  beliefs about their understanding of core
  material. (N14 in MA 331 at ASU N26 in MA 2050
  at MTSU)
• In order to test the validity of the students
  answers, students were also asked to evaluate
  their understanding of topics that were not
  covered in the course. We believe 95 of survey
  respondents provided valid answers concerning
  their beliefs about their own understanding.

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Section One Results - Table 1
5 High Knowledge 1 Low Knowledge
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Section One Results - Table 1
5 High Knowledge 1 Low Knowledge
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Section One Results - Table 1
5 High Knowledge 1 Low Knowledge
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Section One Results - Table 1
5 High Knowledge 1 Low Knowledge
As might be expected, the results seem to
illustrate the different content area emphases in
the two courses.
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Section Two Results - Table 2
5 Very Good 1 Very Poor
Due to cost and availability of Mini-tab
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Section Three Results

• Table 3 indicates the responses of the MA 2050
  class concerning the activities that they found
  to be most useful.

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Section Three Results-Table 3
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Section Three Results-Table 3
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Section Three Results-Table 3
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Section Three Results-Table 3
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Section Three Results

• The MA 331 (N14) class reported the following
  activities related to the following concepts to
  be the most helpful to their learning
• Basic Probability Rules
• Conditional Probability
• Hypergeometric probabilities
• Bayes Theorem
• Central Limit Theorem

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Further Data Acquisition

• During the spring term 2003, each project class
  will be observed repeatedly by the project
  evaluator. Individual videotaped teaching
  interviews will be conducted with selected
  students from each class and case studies will be
  developed from these interviews and the written
  artifacts of student work including, tests,
  homework, and reports.

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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/