Classroom Expectations

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					     Authentic Discovery Learning
            Projects in Statistics
                            NCTM Conference
                                April 23, 2010


                                Dianna Spence
                                    Robb Sinn

Department of Mathematics & Computer Science
       North Georgia College & State University
                           Dahlonega, Georgia
Agenda
• Overview of Project Scope and Tasks
   – Dianna

• Sample Classroom Activities
   – Robb

• Findings: Student Outcomes (Phase I)
   – Dianna

• Curriculum Materials Developed
   – Robb

• Future Directions
   – Dianna
NSF Grant Project Overview
•   NSF CCLI Phase I Grant:
    “Authentic, Career-Specific Discovery Learning
    Projects in Introductory Statistics”
•   Goals: Increase students’...
     knowledge & comprehension of statistics
     perceived usefulness of statistics
     self-beliefs about ability to use and understand
      statistics
•   Tasks:
     Develop Instructional Materials
     Develop Instruments
     Measure Effectiveness
Student Projects
•   Linear regression        •   t-tests
     Variables                   Variables
      •   student selects          •   student selects
      •   often survey            Designs
          based constructs         •   Independent
     Survey design                    samples
     Sampling                     •   Dependent
                                       samples
     Regression analysis
  Make It Real
 Sample Activities from
   Our Workshop for
Teachers of AP Statistics
Workshop Goals:
Mirroring Phases of the Project

• Participants create surveys:
    Develop quality research ideas
    Design their variables and constructs
    Practice writing good questions
• Surveys compiled, administered, and entered
  into Excel while participants are at lunch
• Participants return after lunch to analyze their
  research findings
• Participant teams present their findings and
  their own learning outcomes to the group
Points of Learning

• Scientific Method
    Where survey-based research fits
    Students become researchers
• Technology – Excel
• Statistics
    Regression analyses and analyzing relationships
    Presenting t-Test findings within context of
     discovery learning
• Brainstorming sessions on:
    Collaborative groups
    Assignment sheets, timelines, grading rubrics
Activity 1

• Consider the following survey-study variable
  idea:
    1. How much did you study last week _____ ?
    2. How many hours did you study last night?
            0 1 – 2 3 – 4 5 – 6 7 – 8 10+
•   What are some flaws?
•   Design your own “study” variable.
     Write a terse, clear question
     Suggest answer format
       •   Closed vs. open
       •   If closed, give categories
Variable Constructs
•   Our NSF grant supported the development a variables
    and constructs student help guide
•   Depression example
    Answer Choice Format:         Rarely       Often       Always


       1.   I do not get much pleasure or joy out of life.
       2.   Sometimes I feel sad, blue, or unhappy.
       3.   I often find it difficult to get out of bed in the morning.
       4.   Sometimes I feel like life is not going my way.
       5.   Sometimes I feel like crying.
       6.   I am not sure my life will improve in the future.
       7.   I often feel like my life really doesn’t matter.
Interesting Variable Ideas

• Number of text messages sent during class
• Age when you had your first real kiss
• Number of songs on your I-Pod / MP3 player
• Minutes spent getting ready each morning
• Number of “years old” for the car you drive most
  often
    Appears to measure SES
    Used in “Rich Kids” study ideas
Activity 2

• Develop a t-test study idea
    Brainstorm a variable you think will be different
     for two groups of students (at your school)
    Be ready to explain why you expect to find
     differences
• We give our students (and the workshop
  participants) these “rules of brainstorming”
    Lots of talking must occur
    Throw out 5 or 6 ideas: “popcorn”
    Choose a couple of good ideas and revise
• You have about 3 minutes
Next Step

• Turning students’ research ideas into high
  quality surveys
    We have found that teaching others to facilitate
     this portion of discovery is
      • The most difficult task
      • The most important task
    We both are adept at operationalizing opinions,
     activities, obsessions, and preferences
• High quality surveys
    Multiple drafts
    Tested with a few peers
    Critiqued at least twice by an instructor
Activity 3

• For the chosen topic, try operationalizing the
  variable idea
    Talk with 2 – 3 folks nearby
    Be clear and terse
    Suggest an appropriate answer format
• You have about 3 minutes
Research and Findings
        • Design of the Study
         • Student Outcomes
Phase I Research
Exploratory Study
• Compared student groups, AY 2006-2007
• Conducted prior to development of materials
• Used to validate instruments
Main Pilot of Materials
• 3 institutions
    university (3 instructors)
    2-year college (1 instructor)
    high school (1 instructor)
• Quasi-Experimental Design
    2007-2008: Control groups by instructor
    2008-2009: Treatment groups by instructor
Instruments Developed:
Content Knowledge
• Instrument
    21 multiple choice items
    KR-20 analysis: score = 0.63
• Exploratory Results
    treatment group significantly higher (p < .0001)
    effect size = 0.59
• Instrument shortened to 18 items for main pilot
Instruments Developed:
Perceived Usefulness of Statistics
• Instrument
    12-item Likert style survey; 6-point scale
    Cronbach alpha = 0.93

• Exploratory Results
    treatment group significantly higher (p < .01)
    effect size = 0.295
• Instrument unchanged for main pilot
Instruments Developed:
Statistics Self-Efficacy
• Beliefs in ability to use and understand statistics
• Instrument
    15-item Likert style survey; 6-point scale
    Cronbach alpha = 0.95

• Exploratory Results
    gains realized, but not significant
     (1-tailed p = .1045)
    effect size = 0.15

• Instrument unchanged for main pilot
Pilot Results: t-Tests
• Perceived Usefulness
    Pretest:      50.42
    Posttest:     51.40
    Significance: p = 0.208
• Self-Efficacy for Statistics
    Pretest:        59.64
    Posttest:       62.57
    Significance: p = 0.032**
• Content Knowledge
    Pretest:      6.78
    Posttest:     7.21
    Significance: p = 0.088*
Subscales: Statistics Self-Efficacy

• Strong Gains
    SE for Regression Techniques ( p = 0.035 )

    SE for General Statistical Tasks ( p = 0.018 )

• Little or No Improvement
    SE for t-test Techniques ( p = 0.308 )
Subscales: Content Knowledge

• Regression Techniques
    Moderate Gains ( p = 0.086 )

• T-test Usage
    Moderate Gains ( p = 0.097 )

• T-test Inference
    No Gain
Multivariate Analysis:
Content Knowledge
Multivariate Analysis:
Statistics Self-Efficacy
    Qualitative Findings:
    Participating Instructor Observations

•    Students need guidance with research question
•    Set Student Expectations
      Students underestimate time/effort required
      Students often unclear on exactly what to do once
       they have collected the data
      Students should be prepared for results that may be
       weak, non-significant, etc.
        • realistic view of statistics
        • avoid too much disappointment
Qualitative Findings:
Student Feedback
Student Quotes Shared by Instructors
    “While our results did not meet our initial expectations,
   this is not an utter disappointment. Before this project,
    statistics looked simple enough for anyone to sit down
  and do, but now it is evident that it requires more creativity
  and critical thinking than initially expected. Overall, it was
                     an edifying experience.”




        “The main thing that we have learned is that
       statistics take time. They cannot be conjured
        up by a few formulas in a few minutes. The
            time and effort that is put into a small
        research project such as this is significant.
       On a large scale, one can quickly understand
         the kind of commitment of money and time
          that is required just to obtain reasonable
                             data.”
 Materials Developed
 (Web-Based)


• Instructor Guide      • Student Guide
  Project overview       Project Guide
     • Timelines             • Help for each
     • Best practices          project phase
  Student handouts       Technology Guide
  Evaluation rubrics     Variables and
                           Constructs

 http://radar.northgeorgia.edu/~rsinn/nsf/
Future Directions

NSF CCLI Type II Grant
•   Proposal Submitted January 2010
•   Goals Include:
     Nation wide pilot
     Vertical Integration to early secondary
     Revisions to Materials
       •   Increased flexibility
       •   Accommodate early high school grades
     Qualitative Component
       •   More insight into instructor impact
     Advisory Panel of Statisticians & Educators
For more information

• Project Website
    http://radar. northgeorgia.edu/~djspence/nsf/
• Instructional Materials Home
    http://radar.northgeorgia.edu/~rsinn/nsf/
• Contact Us
    Dianna: dianna.spence@northgeorgia.edu
    Brad:   brad.bailey@northgeorgia.edu
    Robb: robb.sinn@northgeorgia.edu

				
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