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  Variables student selects often survey based constructs  Survey design  Sampling  Regression analysis t-tests  Variables student selects  Designs Independent samples Dependent samples

Make It Real Sample Activities from Our Workshop for Teachers of AP Statistics

Workshop Goals: Mirroring Phases of the Project Participants create surveys: DDevelop quality research ideas DDesign their variables and constructs P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 – 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 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  : Control groups by instructor  : 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 = 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:  Significance: p = Self-Efficacy for Statistics  Pretest:59.64  Posttest:  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 = )  SE for General Statistical Tasks ( p = ) Little or No Improvement  SE for t-test Techniques ( p = )

Subscales: Content Knowledge Regression Techniques  Moderate Gains ( p = ) T-test Usage  Moderate Gains ( p = ) 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 “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.” “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.”

Materials Developed (Web-Based) Instructor Guide  Project overview Timelines Best practices  Student handouts  Evaluation rubrics Student Guide  Project Guide Help for each project phase  Technology Guide  Variables and Constructs

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  northgeorgia.edu/~djspence/nsf/ northgeorgia.edu/~djspence/nsf/ Instructional Materials Home  Contact Us  Dianna:  Brad:  Robb: