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«THE EFFECT OF STUDENT-DRIVEN PROJECTS ON THE DEVELOPMENT OF STATISTICAL REASONING by Melissa M. Sovak B.S. Mathematics, Carlow University, PA, 2003 ...»

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THE EFFECT OF STUDENT-DRIVEN PROJECTS

ON THE DEVELOPMENT OF STATISTICAL

REASONING

by

Melissa M. Sovak

B.S. Mathematics, Carlow University, PA, 2003

M.S. Computational Mathematics, Duquesne University, PA, 2006

Submitted to the Graduate Faculty of

the Arts and Sciences in partial fulfillment

of the requirements for the degree of

Doctor of Philosophy

University of Pittsburgh

UNIVERSITY OF PITTSBURGH

STATISTICS DEPARTMENT

This dissertation was presented by Melissa M. Sovak It was defended on July 16th 2010 and approved by Leon J. Gleser, Ph.D., Professor, Department of Statistics Satish Iyengar, Ph.D., Professor, Department of Statistics Henry Block, Ph.D., Professor, Department of Statistics Nancy Pfenning, Ph.D., Senior Lecturer, Department of Statistics Clement Stone, Ph.D., Professor, Department of Psychology in Education Dissertation Director: Leon J. Gleser, Ph.D., Professor, Department of Statistics ii Copyright c by Melissa M. Sovak iii

THE EFFECT OF STUDENT-DRIVEN PROJECTS ON THE

DEVELOPMENT OF STATISTICAL REASONING

Melissa M. Sovak, PhD University of Pittsburgh, 2010 Research has shown that even if a student passes a standard introductory statistics course, they often still lack the ability to reason statistically. Many instructional techniques for enhancing the development of statistical reasoning have been discussed although there is often little to no experimental evidence that they produce effective results in the classroom.

The purpose of this study was to produce quantitative data from a designed comparative study to investigate the effectiveness of a particular teaching technique in enhancing students’ statistical reasoning abilities. The study compared students in a traditional lecture-based introductory statistics course with students in a similar introductory course that adds a semester-long project. The project was designed to target three main focus areas found in an introductory statistics course: (i) distributions, (ii) probability and (iii) inference. Seven sections of introductory statistics courses were used. One section at each level served as an experimental section and used a five part project in the course curriculum. All other sections followed a typical introductory curriculum for the specific course level.

All sections involved completed both a pre-test and a post-test. Both assessments were designed to measure reasoning ability targeted by the project in order to determine if using the project aids in the increased development of statistical reasoning.

Additional purposes of this research were to develop assessment questions that target students’ reasoning abilities and to provide a template for a semester-long data analysis project for introductory courses.

Analysis of the data was completed using methods that included ANCOVA and continiv gency tables to investigate the effect of the project on the development of students’ statistical reasoning. A qualitative analysis is also presented to provide information on aspects of the project not covered by the quantitative analysis.

Analysis of the data indicated that project participants had higher learning gains overall when compared with the gains made by students not participating in the project. Results of the qualitative analysis also suggest that, in addition to providing larger learning gains, projects were also enjoyed by students. These results indicate that the use of projects are a valuable teaching technique for introductory statistics courses.

–  –  –

I would like to thank all the members of my committee for the time and effort that they put forth to make this dissertation a success. In particular, I would like to thank my advisor, Dr.

Gleser, for always being there to give great advice, constructive criticism and pep talks. I also extend my thanks to Dr. Pfenning, who spent a significant amount of time helping with the design of the study and the assessments used. To Dr. Iyengar, thank you for believing in me and always being encouraging. To Dr. Block, thank you for providing me with great suggestions and always being there to answer questions. I would also like to thank Dr. Stone, who provided insight into the educational research environment.

I also want to thank Laurel Chiappetta for inspiring the idea for this study through her own creative teaching methods, providing ideas for the project’s development and for providing me with a course section for my reliability analysis. I would like to extend gratitude to all of the instructors and students who participated in this study. Without your help and participation, this study would not have happened. My appreciation also goes to Mary and Kim who always have the answers to my questions (or at least will find the answer for me!).

To all of my family, thanks for all your prayers and support. In particular, to my grandma, Catherine, thank you for all your prayers and for insisting since I was a child that I would one day make a good teacher. Finally to my parents, thank you for supporting me and encouraging me while I went through this journey.





xiii 1.0 INTRODUCTION

Statistics education has long sought to provide reasonings on why students seem to miss big ideas in statistics and fail to be able to apply their knowledge to real world problems. In recent years, there has also been an attempt to not only identify why students have trouble comprehending and using statistical knowledge, but also to establish learning techniques that better equip students to develop statistical reasoning and to be able to apply this knowledge outside of the statistics classroom. Research into the area of learning techniques, however, is sometimes largely based on anecdotal studies, where authors recount their own experience with certain techniques in their own classrooms without providing any statistical evidence to support the success of the technique.

One such technique suggested to improve student learning is the use of a project. This technique comes in a variety of forms and has been suggested by a number of researchers.

However, again, no quantitative evidence has been provided to show the positive effects of the project on students’ understanding of statistical material. Producing quantitative experimental results to strengthen the qualitative claims made by other researchers is the purpose of this study.

–  –  –

The purpose of this study is to address whether or not a semester-long, student-driven data anaylsis project enhances students’ reasoning in the areas of distribution, probability, and inference.

The following research questions will be studied:

1. Does a student-driven project with interspersed feedback from the instructor have a significant impact on students’ conceptual understanding of distributions, probability, and inference?

2. What differences in the understanding of distributions, probability, and inference are there between students whose interaction with these topics occurs through a lecture, recitation, homework format and students whose interaction with these topics includes lecture, recitation, homework and student-led projects?

3. Are students who participate in the lecture, recitation, homework, plus project format better equipped to articulate statistical knowledge than students whose training does not involve a project?

1.2 CONTRIBUTION TO THE FIELD

There are three major contributions to the field of statistics education made by this study.

First, it aims to provide quantitative data obtained from a designed comparative study on the effect of the use of projects in an elementary statistics course. While the use of projects has been extensively discussed by other authors, no quantitative data has been provided to verify that projects have a positive effect on students’ learning. This study not only attempts to provide quantitative data to show the effect of projects, but also to provide information for instructors on what types of learning gains they can expect to see from students if they incorporate a project into their course.

Second, the study provides a template for a semester-long project in an elementary statistics course. The project protocol developed for this study seeks to incorporate all the major themes covered in an elementary statistics course. It also provides instructors with a grading scheme designed to reward students for developing statistical reasoning and connecting ideas in statistics as well as connecting statistical ideas to the larger context of the problem.

Finally, the study provides two assessment forms designed to assess statistical reasoning abilities. These forms focus on three key areas: displays and descriptives, classification of variables and inferential test selection. Because the questions on the forms require students to interrelate knowledge about types of variables, relationships between variables and other statistical information, they go beyond basic statistical literacy questions to assess reasoning skills.

1.3 LIMITATIONS OF STUDY

Several limitations should be considered as they pertain to this study. The sample chosen for this study was considered to be the most generalizable group available to the researcher at this academic level. However, this sample of students may not be entirely generalizable to students at other institutions or with different academic interests.

Second, the sample size may not be of an appropriate size to produce results of sufficient accuracy concerning the effect size. It also may not be large enough to produce the classically accepted power for statistical anaylsis. Also, percentage of students participating in each assessment and who completed both assessments varied. Table 1 shows the various percentages for participation for each course. As shown, the percentages for each section vary to a certain degree, with percentages for post-test participation consistently lower than pre-test participation. Also, percentages for students who completed both assessments is consistently lower than students completing just one form. Percentage of students participating is also listed in Chapter 4 when sample sizes differ from those shown in the table below. Also, Table 1 shows the time of each course section (day or night). At the STAT 1000 level, both sections were day sections. At the STAT 0200 level, the traditional and project sections were both night sections, while the Big Picture sections were all day sections. This difference should be noted since there may be differences between students who take day courses and students who take night courses. However, at each level, the project group and the traditional control group are directly comparable because they occur at the same time.

Finally, there may be variables that produce differences that were not measured in this study. Variables considered in this study included pre-test score, post-test score, difference of scores, year level of student, prior experience of student and instruction method. Other variables may also influence the outcome, but were not considered.

–  –  –

This dissertation is organized into five chapters. Chapter one provides a motivation for the research, an overview of the study, its contributions to the field, and a discussion of the study.

Chapter two reviews prior research into statistics education, including research about the three core reasoning areas of the project. It also focuses on pedagogical theory surrounding the use of projects in the classroom. Chapter three contains information about the methods used to analyze the data and why these methods were chosen. Chapter four presents the results of the analyzed data. Chapter five contains a discussion of the research findings, the implications of these findings and directions for future research studies.

–  –  –

In the last 20 years, the number of statistics courses taught on college campuses around the United States has risen dramatically. Many of these courses are designed to give students of varying backgrounds a basic understanding of statistical concepts. Despite a strong push to integrate statistics and probability into the K-12 classroom, these introductory courses are often a student’s first formal experience with statistics. Therefore, there has been a significant amount of literature produced concerning statistics education at the college level.

Prior to advancements in technology such as the graphing calculator and the personal computer, introductory statistics courses were primarily focused on teaching students how to perform calculations. However, with advancements in technology, this is no longer necessary in statistics courses of today and so the focus has shifted from learning how to complete complex calculations to learning how to reason statistically. This shift in the classroom has caused a shift in the focus of statistical education research. Much of the research deals with the educational issues that arise when educators try to teach

Abstract

concepts and students try to learn them [7].

Since the focus of research has shifted, it has become increasingly important to define what is meant by statistical reasoning and how it differs from statistical literacy and statistical thinking. Several studies attempt to define differences among the three; however, many authors still use these terms interchangeably. In recent years, there has been a considerable effort made to agree on definitions for these terms. The following definitions are the result of several papers written on the subject.

• Statistical literacy encompasses basic and important skills including being able to organize and display data appropriately and work with different data representations as well as understanding concepts, vocabulary and symbols [7]. It also includes the ability to interpret, evaluate and communicate statistical information and arguments [26].



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