Authentic Discovery Learning Projects in Statistics

NCTM ConferenceApril 23, 2010

Dianna SpenceRobb Sinn

Department of Mathematics & Computer ScienceNorth 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: 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 ResearchExploratory 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: 50.42Posttest: 51.40Significance: p = 0.208

• Self-Efficacy for StatisticsPretest: 59.64Posttest: 62.57Significance: p = 0.032**

• Content KnowledgePretest: 6.78Posttest: 7.21Significance: 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 FeedbackStudent 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 GuideProject overview

• Timelines• Best practices

Student handoutsEvaluation rubrics

• Student GuideProject Guide

• Help for each project phase

Technology GuideVariables 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