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«FOSTERING MATHEMATICAL DISCOURSE IN AN ONLINE COLLEGE ALGEBRA CLASS by KIMBERLY NICOLE RICE BENNEKIN (Under the Direction of Patricia Wilson) ...»

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FOSTERING MATHEMATICAL DISCOURSE IN AN ONLINE COLLEGE

ALGEBRA CLASS

by

KIMBERLY NICOLE RICE BENNEKIN

(Under the Direction of Patricia Wilson)

ABSTRACT

Students are attracted to the convenience and the autonomy of taking online

classes, and, as a result, the demand for online classes is increasing at a much higher rate than traditional face-to-face classes. Researchers in mathematics education and online education agree that enhancing mathematical discourse and online interactions will improve knowledge construction, respectively. In this case study, I created a discussion board activity, with the intention of fostering more meaningful mathematical discourse in an online college algebra course. I completed the study in three stages. In the exploration stage, I collected data on students’ affective responses to mathematics and their current online course materials. In the development stage, I used this information to create a purposefully designed discussion activity. In the experimental stage, I administered the activity then analyzed the students’ discussion board postings. The week the purposefully designed activity was given, more meaningful mathematical discourse took place. This study provided some initial evidence that mathematical discourse can be fostered and enhanced in an online environment.

INDEX WORDS: mathematical discourse, online, interactions, learning, mathematics

FOSTERING MATHEMATICAL DISCOURSE IN AN ONLINE COLLEGE

ALGEBRA CLASS

by

KIMBERLY NICOLE RICE BENNEKIN

B.S., Spelman College, 1993 M.A., University of South Florida, 1995 Ed.S., University of Georgia, 2000 A Dissertation Submitted to the Graduate Faculty of the University of Georgia in Partial Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

ATHENS, GEORGIA

© 2013 Kimberly Nicole Rice Bennekin All Rights Reserved

FOSTERING MATHEMATICAL DISCOURSE IN AN ONLINE COLLEGE

ALGEBRA CLASS

by

KIMBERLY BENNEKIN

Major Professor: Patricia Wilson Committee: ChanMin Kim John Olive

Electronic Version Approved:

Dean of the Graduate School The University of Georgia May 2013

–  –  –

This dissertation is dedicated to my family. To my son, Asa, who has inspired me to do my best in everything I encounter. To my mother, Gloria, who helped me hold down the home front, doing whatever she could to help, as I balanced graduate school with working full-time. Last, but not least, to my husband, Mario, who always believed

–  –  –

I would like to take this opportunity to acknowledge faculty in the Department of Mathematics Education at the University of Georgia for your support. In particular, I would like to give special thanks to my major professor, Patricia Wilson, for providing me with guidance through my doctoral program. Her support and feedback from the beginning stages of designing my study to writing my results has been invaluable.

I would also like to thank ChanMin Kim for serving on my committee and for her support and guidance in the area of instructional design. Collaborating with her on various research projects allowed me to learn more about conducting research in an online environment. I will never forget the support she has shown me over the years.

Next, I would like to thank John Olive for serving on my committee, and providing helpful feedback and advice. You brought a wealth of information to the committee, and I was lucky to have you on my team. Thank you for your support and willingness to help me with whatever you could.

I would also like to thank Dorothy White, AnnaMarie Conner, James Wilson, Jeremy Kilpatrick, Leslie Steffe, and Robyn Ovrick, who all inspired me in some way to continue my work, not to give up, and believe in myself. Thank you all for your

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ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER

1. INTRODUCTION

Growth & Demand of Online Education

Quality Concerns

Purpose of the Study

Research Questions

2. LITERATURE REVIEW

A Review of Social Theories

A Review of Mathematical Discourse

Interactions in Online Learning

Designing Discussion Activities for the Online Mathematics Classroom

3. RESEARCH DESIGN AND METHODS

Setting

–  –  –

Instruments

Research Stages

Data Collection

Data

Summary

4. FINDINGS & INTERPRETATIONS

Findings

Interpretations

5. CONCLUSIONS

Overview of the Study

Conclusions

Implications for Teaching and Future Research

Personal Reflections

REFERENCES

APPENDICES

A ARCS MODEL SURVEY & MODIFIED FENNEMA-SHERMAN





INSTRUMENT, STUDENT SURVEY #1

B INTERVIEW PROTOCOL

C MODIFIED FENNEMA-SHERMAN SURVEY, STUDENT SURVEY #2

D INTERACTION ANALYSIS MODEL (IAM)

–  –  –

Table 1: Comparison of Mathematical Discourse Categories and Interaction Analysis Model Phases

Table 2: ARCS & Fennema-Sherman Survey Means and Standard Deviations (Exploration Stage)

Table 3: ARCS & Fennema-Sherman Survey Means and Standard Deviations (Experimental Stage, pre-survey)

Table 4: Connections between Data Sources & Research Questions

Table 5: Summary of Mathematical Discourse Posts coded within the IAM phases, weeks 1-7..

Table 6: Number of Posts Coded within Phases by Week

Table 7: Classification of participants’ weekly online discourse postings, weeks 1-7.....62 Table 8: Survey Means, Standard Deviations & Modes of Fennema-Sherman Survey (Experimental Stage, post-survey)…………

–  –  –

Figure 1: Model of Social Construction of Knowledge

Figure 2: Screenshot of Purposefully Designed Discussion Activity

–  –  –

Technology has changed our lives, allowing us to do things that were not imaginable even 25 years ago, personally and professionally. The introduction of technology into the classroom has had a large-scale impact on the way we teach and learn, directly and indirectly. For example, online courses for businesses, colleges and universities provided accessibility and a self-paced structure that enabled people to continue their education within the constraints of their daily lives. This chapter will showcase the growth and demand of online courses, quality concerns with creating online course components, and the need for research in the area.

Growth & Demand of Online Education Each year there are more students taking classes online and this number continues to rapidly increase. The number of students enrolled in online classes doubled between 1995–1998 (Wadsworth, L., Husman, J., Duggan, M., & Pennington, M., 2007). During the 1997-1998 academic year, 1.6 million students were enrolled in online courses (Institute of Higher Education Policy, 2000). In the fall of 2009, there were 5.6 million students taking at least one online course (Sloan Consortium, 2010), which equates to about thirty percent of all higher education students. In addition, “The twenty-one percent growth rate for online enrollments far exceeds the less than two percent growth of the overall higher education student population” (Sloan Consortium, 2010, p. 2).

Colleges also report that the decline of our country’s economy has created an increasing demand for online courses (Sloan Consortium, 2010). It is not unusual to expect people to return to school when the economy is bad for further training or to change career paths;

however, many of these people are not able to quit their jobs to attend school. Online classes are more accessible and appealing to students. Students are attracted to the convenience and the autonomy of taking online classes (Tallent-Runnels et al., 2006).

The appearance of this trend and the demand of accessibility have put pressure on colleges to provide more online course offerings (The Sloan Consortium, 2010).

Quality Concerns Even with the increased demand for online courses and the support of chief academic officers, many professors are still unconvinced about the quality of online instruction. Since the creation of online classes, their validity and effectiveness have been in question. There are some that believe the quality of online classes is deficient due to the lack of face-to-face interaction, i.e. lack of socialization (Allen & Seaman, 2003). There is a perception of isolation and inability to form student-teacher and student-student relationships. Some even go as far to say that they “doubt strongly that a totally virtual institution could demonstrate that it provides an education equivalent to that offered at traditional colleges and universities,” (Perley & Tanguay, 1999, p. B4).

Nish Sonwalkar (2008) states that one of the reasons online classes have been ineffective is because “there is no pedagogical framework provided for instructors to be effective online,” (p. 45). However, there has been ongoing research emphasis on creating standards for the design and implementation of online courses (Brown & Corkill, 2007;

Matsuo, Barolli, Xhafa, Koyama, & Durresi, 2008; Trotter, 2008a, 2008b). Even with researchers starting to take a general interest in online courses, there has not been much research on the design and implementation of course components specifically designed for online mathematics classes.

Many believe it is possible to educate a student in a totally online environment and still maintain, if not enhance, the quality of the instruction. Online interaction increases anonymity and gives all students a chance to be heard, in some cases, eliminating time constraints and reducing the fear of speaking in front of others (Fountain, 2006, p. 78). Sharon Fountain (2006) discovered that students, faculty and administrators concur that an increased amount of interaction is needed in online classes.

As a result, some believe that more research should be done on how interactions in online courses can impact learning outcomes. Instructional designers believe online courses created in a semi-structured format are ideal for promoting interaction and increasing learning outcomes (Woo & Reeves, 2007). Although her research supports face-to-face classroom discourse, Sfard (2001b) agrees that communication should also be the focal point of students’ mathematical learning. Combining the theories of both online learning and mathematics education will better prepare researchers for creating appropriate materials for online mathematics courses.

The Institute of Higher Education Policy’s (IHEP) study on the quality of online courses provides a good start to identifying needed research in this area. The IHEP is a non-profit organization dedicated to promoting success in postsecondary education world-wide. Their mission is to “increase access and success in postsecondary education around the world through unique research and innovative programs that inform key decision makers who shape public policy and support economic and social development” (IHEP, n.d.). The IHEP was commissioned by the National Education Association (NEA), the nation’s largest professional association of higher education, and Blackboard, Inc., a widely used Web-based platform provider for online education, to explore issues and examine benchmarks related to quality in online education. In 2000, the IHEP identified 24 benchmarks essential to quality assurance in online education. The benchmarks spanned 7 categories: institutional support, course development, teaching/learning, course structure, student support, faculty support and evaluation/assessment (IHEP, 2000). My area of interest falls within the teaching and learning category. The first benchmark under teaching and learning states, “Student interaction with faculty and other students is an essential characteristic and is facilitated through a variety of ways…” (IHEP, 2000, p. 2). Online interaction is an area identified to be in need of further investigation. The need to foster meaningful online student interaction is a familiar thread among online education researchers (Tallent-Runnels et al., 2006; Woo & Reeves, 2007). Gilbert and Dabbagh agree that “Despite a growing body of research on the instructional benefits of asynchronous communication, there is little research about the impact of the protocols and criteria that guide online discussions on meaningful discourse,” (Gilbert & Dabbagh, 2005, p.5).

Purpose of the Study This study investigated how to design course activities that enhance mathematical discourse in online mathematics courses. I used theories from both online education and mathematics education as a guide to design online activities that promote online mathematical discourse. There are many researchers who agree that mathematics is a social activity (Balacheff, 1990, Davydov, 1995, van Oers, 1996). In terms of online education, researchers agree that meaningful online student interaction has the ability to increase learning outcomes (Woo & Reeves, 2007). The goal of this study was to unite research in mathematics and online education by their common threads to design an online activity that will enhance meaningful online mathematical discourse. The research questions concentrated on the discourse patterns of students participating in an activity purposefully designed to enhance meaningful student interaction, i.e. online mathematical discourse. It also addressed the students’ perceptions of their discussion activities and their interactions.

Research Questions To examine the impact of a purposefully designed discussion activity on students’

online mathematical discourse, the following research questions were formulated:

1. What is the nature of the mathematical discourse of participants in an online

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