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The effects of online courses for student success in basic skills mathematics classes at California community colleges

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The effects of online courses for student success in basic skills mathematics classes at California community colleges

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Content THE EFFECTS OF ONLINE COURSES FOR STUDENT SUCCESS IN BASIC SKILLS MATHEMATICS CLASSES AT CALIFORNIA COMMUNITY COLLEGES by Jason Goering Rey A Dissertation Presented to the FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF EDUCATION August 2010 Copyright 2010 Jason Goering Rey ii DEDICATION The completion of this dissertation is dedicated to my loving husband, Mr. Robbie Rey, for standing beside me throughout the long process of graduate school and writing this dissertation. The long nights he spent alone watching television on the couch, cleaning our home, and otherwise ensuring me undisturbed study and writing time did not go unnoticed or unappreciated, nor did the dinners served to me at my desk, constant pot of coffee at the ready, and words of encouragement when I was feeling down. Without his unwavering support and encouragement, I would have never been able to finish this long journey. He is as much responsible for this degree as I. Thank you for all of your love, help and support though this process. For everything you have done I am forever grateful. I love you! iii ACKNOWLEDGMENTS My gratitude is offered to Dr. Guilbert Hentschke, my Advisory Chairman, for his advice and continual encouragement through the dissertation process; my advisory committee members, Dr. David Dwyer and Dr. Melora Sundt, whose insight and advice proved invaluable during the process. For their combined efforts on my behalf, I am grateful. I am thankful for Melissa Bater for her assistance in the midnight hours of this dissertation helping me ensure grammar and formatting were correct. Without her expertise I would not have been able to complete this on time. I would also like to thank David Torres, Dean of Institutional Research, and Raj Bajaj, Dean of Institutional Reporting and & Academic Services, of Riverside Community College District. They provided me the data set with that allowed me to begin my study during a time when budget cuts and furloughs had pushed others to be unwilling to work with me. iv TABLE OF CONTENTS DEDICATION ii ACKNOWLEDGMENTS iii LIST OF TABLES vi ABSTRACT viii CHAPTER ONE: INTRODUCTION TO THE STUDY 1 The Growth of Distance Education 2 Basic Skills Mathematics 9 The Problem of Online Basic Skills Mathematics 12 Research Questions 15 Significance of the Study 17 CHAPTER TWO: REVIEW OF RELATED LITERATURE 19 Introduction 19 Background 19 Basic Skills Mathematics in Community Colleges 22 Learning Management Systems 26 Online Mathematics 27 The Effect of Online Mathematics on Cognition 31 Online versus Face-to-Face Education 35 Student Factors on Success and Persistence 36 Conclusion 38 CHAPTER THREE: RESEARCH DESIGN AND METHODOLOGY 41 Introduction 41 Data And Data Collection 46 Data Refinement 48 Data Analysis 49 Significance of the Study 51 Limitations 52 v CHAPTER FOUR: ANALYSIS OF DATA 54 Part One 55 Part Two 59 Summary of Statistically Significant Findings 68 CHAPTER FIVE: FINDINGS, CONCLUSIONS, AND IMPLICATIONS 70 Findings 72 Conclusions 74 Implications and Future Research 77 REFERENCES 81 vi LIST OF TABLES Table 1.1 Growth of Distance Education in California’s 4 Community Colleges Table 3.1 Final Database Information and Coding 49 Table 3.2 Online vs Face-to-Face comparison database 50 Table 4.1 Online vs Face-to-Face pass rates including drop/withdraw 55 Table 4.2 Online vs Face-to-Face pass rates excluding drop/withdraw 56 Table 4.3 Elementary Algebra Grades – Disaggregated by online and 58 face-to-face pre-algebra class and pre-algebra grade earned Table 4.4 OL/F2F – Elementary algebra grades 59 Controlling for pre-algebra grades Table 4.5 Summary of instructor responses and number of students 60 affected Table 4.6 Summary of students’ use of components, disaggregated 61 by pre-algebra grade earned Table 4.7 Summary of students’ use of components, disaggregated 62 by elementary algebra grade earned Table 4.8 Correlation Matrix – Components with persistence for all 63 online pre-algebra students Table 4.9 Correlation Matrix – Components with persistence for 64 online pre-algebra students who passed vii Table 4.10 Correlation Matrix – Components with pre-algebra grades 66 Table 4.11 Correlation Matrix – Components with Elementary 67 Algebra grades for all students who took pre-algebra at RCCD viii ABSTRACT Online education is a modality of teaching that has proliferated throughout higher education in such a rapid form and without any guidelines that its quality and merit is largely unknown, hotly debated, and still evolving. Institutions have used online education as a method of reducing costs and increasing enrollments and students have flocked to online classes for their convenience and often perceived ease. This is very apparent in California’s community colleges were students are filling online course offerings in record numbers. Many studies and analyses have been done citing the relative equivalence of online education to traditional face-to-face education and sometimes the relative superior learning outcomes of online courses. This study examined the correlations between taking basic skills mathematics courses online versus face-to-face and student success and persistence. Additionally, five common online course components were identified and analyzed to determine if these components correlated to students success or persistence in of online classes. Contrary to what much of the literature says, the difficulties associated with effective communication of mathematics topics and ideas via the Internet had no noticeable negative correlations with learning outcomes or persistence. Students who began their basic skills mathematics in an online pre-algebra class tended to persist at higher rates and earn higher grades than students who began in a traditional face-to-face pre-algebra course. This positive effect of the online classes diminished very quickly and within two classes of the online class has been completely lost. It seems that the quality ix of education gained from online basic skills mathematics courses is relatively equivalent to face-to-face courses. Five common course components were analyzed in the study and it was found that only the required use of discussion boards had a significant effect on persistence and success. The use of exclusively multiple-choice examination, mathematics display software, and video lectures for delivering content had no significant effect on either persistence or success. The fifth component, the implementation of proctored examinations, was too new at Riverside Community College District and no longitudinal was available for analysis. The significance of the required use of discussion boards likely lies in keeping students engaged in the class and not in the discussion board use itself. The medium of delivery is likely to be inconsequential to the quality of education, but the quality of the class is more likely linked to variations in teacher quality. 1 CHAPTER ONE INTRODUCTION TO THE STUDY Education using the Internet as the primary method of delivering instruction, communication, and assessment (commonly referred to as Online Education) has proven to be arguably the fastest and most disruptive innovation in the history of education. In its relatively short lifespan (about 20 years), online education has gained a significant foothold in higher education and is proliferating throughout K-12 systems of education nationwide. The quality of online education is hotly debated with staunch arguments on both sides. Researchers and laymen alike have offered predictions ranging from online education being nothing more than a fleeting fad that educators and students will soon tire of, to online education so revolutionizing education that all traditional forms (i.e. face-to-face classrooms) will soon become obsolete and irrelevant. A more accurate prediction is likely a balance of the two as students and institutions take advantage of both systems to suit their individual educational needs. This study consciously avoids the temptation to engage in the debate over the ultimate future of online education instead choosing to accept that both online and traditional face-to-face modalities are sufficiently established within the higher education infrastructure and neither is likely to be eliminated within the foreseeable future. This study makes a comparison of student persistence and success when beginning remedial college mathematics in an online format versus a face-to-face format, then examines current online classes in a attempt to tease out successful practices and strategies. Students at Riverside Community College District, located in Southern California, are 2 tracked from pre-algebra to elementary algebra, these classes are then examined practices and technologies that correlate to students’ successful learning of and progression through basic skills mathematics. Growth of Distance Education Distance education is hardly a new phenomenon in higher education. Rather, it dates back at least one hundred years to the earliest correspondence courses (U.S. Department of Education, 2009), relying on postal mail, and later on fax, television broadcast, and tape/DVD as the content medium. While many have offered slightly differing definitions of distance education, the technologies used have changed, and the medium of delivery changed; the overriding theme is that the students and instructor are separated by distance. Garrison (1985) proposed three generations to describe the evolution of distance education. Generation 1 (Correspondence) is characterized by slow asynchronous communication between the students and instructor primarily by postal mail. Students generally work independently, there is very little cost to the institution, and courses typically have a high attrition rate. Generation 2 (Teleconferencing) provides synchronous communication between students and instructor as well as among students. It requires students and instructors to “attend” class at the same time, typically has low attrition rates, and is similar in style and composition to traditional face-to-face instruction. Generation 3 (Microprocessor Based) is a result of the advent and expansion of the personal computer and widespread access to the Internet; leading to nearly endless opportunities for both synchronous and asynchronous communication, multi-media presentations of concepts, and rapid dissemination of information. Today the vast 3 majority of all distance education is generation 3 and is growing at a pace faster than any other form of education throughout history (Allen & Seaman, 2008). The form of distance education at institutions of higher education with content delivered primarily via postal mail, fax, television broadcast, telephone, and tape/DVD saw relatively little success or consumer demand in academe (Garrison, 1985; Moore, 1989). Catering primarily to students who had little or no opportunity to attend or to have access to traditional institutions of higher education, distance education existed in the periphery of higher education rather than as an equivalent option (Simonson & Bauck, 2003). From the mid-1980’s to the present, the growth and proliferation of personal computers and access to the Internet has provided the platform upon which distance education has grown from a fringe element of higher education to a major part of the higher educational infrastructure in the United States. In fact, from Fall 2002 to Fall 2007, U.S. online enrollment grew 146% from about 1.6 million students to about 3.9 million students (Allen & Seaman, 2008, p.5). During the same time period, overall higher education enrollment grew only 8% from about 16.6 million to 18.0 million students (Allen & Seaman, 2008, p.5). During the Fall 2007 term, online course enrollment accounted for nearly 22% of all higher education enrollments in the United States (p.5). A large portion of this growth is attributable to associates institutions (most prominently Community Colleges) which teach about 37% of the US higher education student body but account for over half of all higher education enrollments (p.6). The 2008 Distance Education Survey shows that nearly 74% of community colleges now offer an entire degree program online, up from 67% the prior year (Lokken, 2009). 4 The growth of online education is especially evident within California’s Community College System. According to data collected and made available by the California Community Colleges Chancellor’s Office (http://www.cccco.edu/ ChancellorsOffice/Divisions/TechResearchInfo/MIS/DataMartandReports/tabid/282/ Default.aspx), in the decade between the 1997 – 1998 and 2007 – 2008 academic years, full-time equivalent student (FTES) enrollment in California’s Community Colleges increased 25.93% overall. During the same time period, distance education FTES enrollment increased 1,362.75% (see table 1), the vast majority of this growth is due directly to the rapid increases in the number of online course offerings. Unfortunately, incompatible record keeping systems among colleges have clouded this data making the difference between hybrid courses (courses taught partially face-to-face and partially online) and online courses virtually indistinguishable. Additionally, the data provides no aggregation between types of distance courses (online, tele-courses, courses by postal mail, etc.). Nevertheless, it remains a safe assumption that the vast majority of this growth is due directly to the growth of online course offerings. Table 1.1 Growth of Distance Education in California’s Community Colleges Academic Year 1997-1998 2007-2008 % Change Total FTES 887,768.19 1,117,959.86 + 25.93% Distance Ed FTES 6,328.42 92,568.90 + 1,362.75% Percent DE 0.71% 8.28% + 1,091.55% Source: California Community Colleges Chancellor’s Office (http://www.cccco.edu/ SystemOffice/Divisions/TechResearchInfo/MIS/DataMartandReports/tabid/282/Default.aspx) This expansion of distance/online education is predicted to continue in the coming years, albeit at a slower pace, and will continue to make online education an ever 5 increasingly prominent part of the core higher education infrastructure (Johnson, Levine, & Smith, 2009). Johnson et al. further suggest that with the growth in use of mobile technology devices, such as iPhones and Blackberrys, the future of distance education will see a shift from computer based instruction/learning to mobile learning (2009). The fact that online education has grown so fast and will likely continue to grow should come as no surprise to anyone familiar with today’s college-age youth, a generation of individuals who grew up using the Internet, and who now use it as their primary source of social networking as well as news and information. In a typical online course, students can log-in to the course site and read content and/or view videos on the subject matter, communicate with their instructor and fellow students, complete and submit work, and receive their grades. “Anytime-anywhere” (there is an Internet connection) has become the mantra for proponents of online education opening up access to higher education to individuals whose lives are incompatible with the traditional seat-in-a-classroom-during-business-hours version of higher education. This expanded access perfectly suits the typical online student who, Deirdre Folkers (2005) asserts, is female, between the ages twenty-five and forty-nine, and often has a job and familial responsibilities. Interestingly Allen & Seaman (2008) note just three years later that nearly one in five college students in the United States are enrolled in at least one online course. Many are also enrolled in traditional face-to-face courses as well. These studies illustrate the rapidly expanding demographic of students taking advantage of online education. 6 Many different reasons have been cited for the expansion of online education. Prominently administrative pressures on faculty to develop online courses and fringe groups of professors developing online curriculum on their own (Cox, 2005). For community colleges, these pressures are likely fueled by community colleges’ response to increasingly scarce fiscal resources (Olsen, 2000); competition with for-profit colleges and universities (Cox, 2005; Folkers, 2005); the breakdown of geographically protected service areas by the virtually unlimited reach of the Internet (Folkers, 2005); and, more recently, rising unemployment coupled with rising fuel costs (Allen & Seaman, 2008). Community Colleges around the world now find themselves in competition for the same geographically disconnected students as all other colleges with online course offerings, placing them within a new frontier or business model to which they are unaccustomed (Folkers, 2005). The growth of online education fits Clayton Christensen’s (2008) model of a disruption innovation in education. The innovation first caters to a largely underserved population (students unable to access higher education via traditional face-to-face models), while slowly developing and improving or waiting for technology to emerge. Eventually the mainstream population adopts the new innovation over the old. According to Christensen’s model, eventually a disruptive innovation (i.e. online education) gains a sufficient foothold in the education market and, as it evolves over time, changes the fundamental beliefs on how education is delivered. Levine and Sun (2002) suggest the Internet and online learning will ultimately change the entire landscape of higher education with three types of institutions emerging: brick, click, and 7 brick and click. The brick universities will remain the traditional universities delivering face-to-face instruction to students who want the traditional college experience and have the ability to attend. The click universities will be virtual universities delivering instruction electronically to those who cannot attend traditional universities or who choose to get their higher education via an alternate format. Most universities, however, will fall into a third category that blends face-to-face and electronic delivery of instruction to their students allowing students to take advantages of the benefits of both: brick and click. Numerous researchers believe online education is already changing how education is viewed by offering a creditable alternative to the dominant face-to-face instruction that traditional institutions have employed for centuries (Allen & Seaman, 2008; Cox, 2005; Engelbrecht & Harding, 2005; Trinkle, 2005; Zemsky & Massey, 2004). The growth in popularity of online classes coupled with their growing acceptance and legitimacy (as evidenced by the accreditation and enrollment growth of completely online for-profit institutions like the University of Phoenix Online and Capella University) have forced institutions to examine their educational methods and to evaluate whether their classes are better or as good as their online counterparts. Institutions must realize that students want (or need) the option of online education, and they will enroll in the colleges and universities that provide it. Sixty-one percent of community college students surveyed in the 2008 Distance Education Survey stated that their college was not offering sufficient online courses to meet demand (Lokken, 2009). 8 Zemsky and Massey (2004) argue that the promises that fueled the online education explosion have never come to fruition. They believe that short of another technological revolution online education will eventually loose its cool-factor and fade to the background like most other educational fads. What is agreed upon is that online education currently has expanded access to higher education to many students who are unable to access traditional forms of higher education. Online education provides prospective students with a wealth of alternate opportunities to access courses, programs, and colleges and is ultimately forcing a reevaluation of face-to-face educational practices and outcomes (Christensen, 2008). This new modality of education and learning has and will likely continue to have a dramatic effect on how higher education is viewed and provided. Early developers of online courses (and many still today) used the Internet simply as a means of extending the reach of their traditional methods of teaching (Buschel, 2008; Zemsky & Massey, 2004). No differentiation was made between strategies teaching face-to-face versus teaching online. Lectures, usually in the form of written text, were posted on the Internet for students to review, followed by assignments from the textbook (Allen, 2003). Very little, if any, interaction was available for students to communicate with other students, and students communicated with instructors either via email, telephone, or by visiting the campus. Online classes, however, provide increased opportunities for meaningful interaction among students, between students and instructor, as well as between students and content beyond the capability of the traditional face-to-face classroom (Bueschel, 9 2008; Christensen, 2008; Engelbrecht & Harding, 2005; Hughes, McLeod, Brown, Maeda, & Choi, 2007; Pyon, 2008; Stary & Totter, 2006; Wolf, 2008). Additionally, the capacity for computers to share in the mundane work of grading, record keeping, even some interaction and feedback (Christensen, 2008; Engelbrecht & Harding, 2005) opens the potential for increases in course size, thus making online education a potentially attractive opportunity for administrators facing increasingly scarce resources (Cox, 2005; Mupinga & Maughan, 2008). Clayton Christensen (2008) suggests that online education is poised to completely dominate the education industry in the way the personal computer took over the computing industry. Others assert that the promises of online education have not come to fruition, will never gain sufficient support to replace traditional face-to-face education, and will ultimately fade away as another educational fad (Mellon, 1999; Zemsky & Massey, 2004). What is indisputable, however, is that online education has gained a significant foothold in American (and worldwide) higher education and, therefore, warrants the same critical attention and improvement efforts as traditional face-to-face education modalities. Basic Skills Mathematics In California, basic skills courses are explicitly defined by law in section 55002(b) of Title V as courses in reading, writing, computation, and English as a Second Language which are designated by districts as non-degree applicable credit. In addition, in the widely distributed and read Basic Skills as a Foundation for Student Success in California Community Colleges (Center for Student Success, 2007), commonly referred 10 to as the Poppy Copy, basic skills are more broadly defined as “those foundational skills in reading, writing, mathematics, and English as a Second Language, as well as learning skills and study skills which are necessary for students to succeed in college-level work” (p.13). In mathematics courses at California Community Colleges, this generally refers to any mathematics class below Elementary Algebra, the mathematics requirement for graduation with an Associates Degree for all students who entered college prior to the Fall 2009 semester. The Associates Degree graduation requirement changed to Intermediate Algebra beginning with all students entering in the Fall 2009 semester. The Board of Govenors of the California Community Colleges voted to raise the Mathematics (and English) requirements one level on Sepember 11, 2006. This action was taken in response to faculty complaints that the graduation requirements were too low as well as to better coordinate Associates Degree requirements with transfer requirements to California’s state university systems (Bogue-Feinour, 2006). Continually Americans are told by popular media sources and prominent political figures of American’s decline in educational dominance, particularly in mathematics and applied sciences. The data seem to contradict these assertions however. According to the National Center for Educational Statistics (NCES), the National Assessment of Educational Progress (NAEP) shows educational progress for both 9- and 13-year olds as well as a constant level of achievement among 17-year olds from 1973 through 2007 (Planty et al. , 2009, p.35; Rampey, Dion, Donahue, 2009, p. 29). The NCES further reported that the 2007 Trends in International Mathematics and Science Study (TIMSS) 11 showed the United States was one of only eight countries that displayed improvement from 1995 – 2007 (Planty et al., 2009, p.36). Despite these facts, American’s K-12 educational infrastructure is promoting students who lack the very basic mathematics skills necessary to be successful in many careers or college programs. This is evident in California where the California High School Exit Exam (CHASEE) requires of students only mathematics skills at a Junior High School level for High School graduation (http://www.cde.ca.gov/ta/tg/hs/ overview.asp). Furthermore, the University of California (UC) and California State University (CSU) systems are being overwhelmed with students who cannot perform academically at the level required and are seeking alternative methods of providing remediation to their students (Olsen, 2000). The California State University at Long Beach has openly stated that, due to the overwhelming need for mathematics remediation by its students and the lack of funds to provide this remediation, the University has been forced to utilize online remediation programs that allow for large class sizes with minimal instruction (Olsen, 2000). Proposed budget cuts to Higher Education in California are likely to exacerbate the situation in the coming academic years. A recent Los Angeles Times article reported that a University of California panel was considering increasing its number of online offerings to reduce costs and increase university efficiency (Gordon, “UC panel discusses proposals to make university more efficient,” 2010). In California community colleges the situation is more extreme; students taking placement exams test into remedial/basic skills mathematics courses at close to a ninety percent rate (Moore & Schlock, 2007, p. 14). This indicates that the vast majority of 12 entering community college students are deficient in the mathematics skills considered prerequisite for any college level science or mathematics class. Scholars, legislators, school officials, and constituents are engaged in constant debate over the cause of this problem and how it should be fixed. Schools, teachers, students, parents, and society are all blamed in various degrees for the situation. Given the current state of this debate, the political climate, and deep budget cuts, there is no reasonable expectation for a remedy anytime soon, thus colleges and universities will be left to remediate more students than ever before. The Problem of Online Basic Skills Mathematics The rapid growth of online education and the increasing need for mathematics remediation have resulted in growing numbers of online basic skills mathematics course offerings. However, this growth has occurred so fast that online course technology has yet to adequately address the unique requirements for communication and teaching mathematics (Smith, Torres-Ayala & Heindl, 2008). Furthermore, the faculty who develop and teach these classes are often given no special preparation or training for developing and teaching online classes (Mupinga & Maughan, 2008). These faculty generally use what they know about effective face-to-face instruction in their online courses; however, those skills and practices often do not effectively translate to the online environment (Bernard et al., 2004). Hundreds of articles and reports have been published chronicling no significance difference between distance education and traditional face-to-face education (Russell, 2001; http://www.nosignificantdifference.org, April 2009). This research however, 13 misses its mark when applied to teaching basic skills mathematics due to its focus almost exclusively on transfer level classes and very rarely on mathematics at all. These articles rely on simple comparisons of course grades and exam results to assess learning. However, the purpose of a non-credit basic skills course is not to pass but to equip students with those skills necessary to be successful in subsequent courses. Communication difficulties created by the unique language and the symbolic and graphic nature of mathematics conveyed via a medium not designed for such communication create unique challenges in the online environment unseen by most other disciplines (Smith & Ferguson, 2004; Smith, Torres-Ayala, Hendel, 2008). Researchers have found that one major advantage of online courses is the special opportunity for student-to-student and student-to-instructor communication. That collaboration leads to the advanced construction of knowledge and a deeper understanding of the material (Schrum & Hong, 2002; Mansour & Mupinga, 2007; Buschel, 2008; Pyon, 2008). The argument is that online communication, which is generally text based, requires thinking through the material and questions more thoroughly than verbal face-to-face communication, forcing online students to clearly articulate their thoughts and meaning in writing in plain text. For this communication to work, however, an effective method of two-way communication between both parties is required, something most basic skills students are likely to have a difficult time with because of the complex multiple meanings a single mathematics symbol carries (Aiken, 1972). Students are enrolled in a basic skills mathematics course because they do not understand the fundamental properties of mathematics. It cannot be expected that these students will be able to effectively 14 communicate those complicated concepts (or their misunderstanding of those concepts) using text. There exist both several programs for displaying mathematics in its standard symbolic form and a commonly understood set of keyboard workarounds (using keyboard symbols to horizontally display mathematical concepts differently from how they would normally be displayed) that allow for digital communication of mathematics. Most instructors and high level mathematics students have little trouble negotiating the complicated programs or keyboard workarounds used for displaying mathematics on the Internet. Basic skills students on the other hand have trouble negotiating such communication strategies (Smith & Ferguson, 2004), mitigating the unique advantages of such student-to-student and student-to-instructor communication provided by the online environment. Literature suggests that despite the technological problems communicating mathematics via the Internet online mathematics courses are at least as effective as face- to-face classes for specialty courses like Statistics for Engineers, (Adams, Glenn, Adams, 2006; Gundy, Morton, Liu, Kline, 2006) and for graduate level mathematics classes (Schrum & Hong, 2002). However, literature is lacking on how basic skills mathematics students are performing in online courses. A vast library of literature exists detailing the special needs of basic skills students and the different teaching strategies for teaching these students in face-to-face courses (Center for Student Success, 2007). However, little is known about how these basic skills students are coping with the known difficulties 15 expressing mathematics symbols, graphs, charts, and concepts via the Internet (Smith & Ferguson, 2004). Another problem with current research and literature is its definition of success in terms of course retention, success rates, assessment exam results, and faculty and student satisfaction. While these are all indicators of a successful online basic skills course, none truly measure whether a student has successfully mastered the “learning skills and study skills which are necessary for students to succeed in college-level work” (Center for Student Success, 2007, p. 13). If providing the foundational skills necessary for students to succeed in college level work is the goal, a truer measure of success is whether or not students are succeeding in subsequent mathematics courses and persisting though college mathematics, i.e. if students are succeeding in college-level work. The sequential nature of mathematics education and its pedagogical structure lend themselves relatively easily to investigation of this type of question. As a result, this study will define success not in the traditional success of “C” grade or better but as earning a “C” grade or better in both the basic skills course as well as in the subsequent mathematics course. While still not a perfect measurement of learning, this definition of success can help to tease out whether students are exiting their class with the knowledge intended. Research Questions Despite the known difficulties of teaching mathematics online and the fundamental importance of students mastering basic skills topics, no literature is available to inform practitioners of effective practices being used in online basic skills mathematics classes. 16 This study seeks to identify how well students who take a basic skills course online are successfully persisting through the subsequent course versus their counterparts in traditional face-to-face courses. Furthermore within online classes, it seeks to identify what strategies are employed and are correlated to successful persistence through the next course. To do this, two fundamental questions are raised: 1. Is there a statistically significant difference in persistence, retention, and success for basic skills students who begin taking pre-algebra online versus face-to-face? 2. Which software and/or strategies being used are correlated with basic skills mathematics students’ successful completion of online basic skills mathematics courses? Successful completion of a basic skills course in California Community Colleges is defined in the Basic Skills as a Foundation for Student Success in California Community Colleges (Poppy Copy) as more than earning a passing grade but as gaining those “learning skills and study skills which are necessary for students to succeed in college-level work” (Center for Student Success, 2007, p. 13). For that reason, this study looks not only at student performance in pre-algebra classes but also at relationships between online and face-to-face pre-algebra and student performance in the subsequent elementary algebra class. Additionally, components of online pre-algebra classes are examined for correlations between those components and students performance. In building an online mathematics course, G. Donald Allen (2003) asserts there are four aspects of online course development: interactivity, assessment, mathematical typography, and course operation. To address these four aspects, the five common 17 components of online classes examined in this study are: (1) the use of video lectures to deliver content , (2) required use of discussion boards, (3) student use of mathematics display software, (4) the use of exclusively multiple-choice exams, and (5) the use of proctored examinations. The use of video lectures to deliver content reflects the growing trend of using videos in online courses to deliver content as opposed to the prior method of instruction requiring students to read text from their computer screen (Allen, 2003; Munpinga & Maughan, 2008; Johnson, Levine, & Smith, 2009). Required use of discussion boards and students’ use of mathematical display software address interactivity, including student-to-student and student-to-teacher, in communicating mathematical concepts. Finally, the use of exclusively multiple-choice exams and proctored examinations address types of assessments as well as issues of course integrity. Significance of the Study Basic Skills mathematics serves as a gatekeeper in many students pursuit of higher education, especially those pursuing degrees in the STEM (science, technology, engineering, and mathematics) (Center for Student Success, 2007). If the United States is going to increase the numbers of students entering those fields, then the first step is getting more students to persist through their basic skills coursework! As budgets become increasingly tight and students increasingly demand online course offerings, more and more basic skills students are taking their coursework online. Online education has grown and proliferated throughout higher education to a point that most colleges and 18 universities offer an online curriculum, many offering entire degree programs online, and those who don’t are planning to in the near future (Allen & Seaman, 2008). These facts indicate that educators should expect more and more students to be taking basic skills mathematics online, and as yet there exists little research to help guide colleges, instructors, and students in the successful implementation these classes. Ideally, this study will help to guide colleges and instructors in setting up and implementing their online basic skills programs in a manner which is most beneficial to the students. 19 CHAPTER TWO REVIEW OF RELATED LITERATURE Introduction This literature review brings together several different topics to gain insight into the effects of teaching basic skills mathematics online and questions several common practices and components of online mathematics courses. Starting with the background and rapid growth of online education, a discussion of basic skills education in community colleges, and a brief overview of learning management systems, it sets the stage for a discussion of teaching mathematics online. The research on online mathematics is explored along with its effect on mathematics cognition, followed by a discussion of the research comparing online and face-to-face educational modalities. Finally, a conclusion ties these topics together into an argument supporting the research questions in this study: (1) Is there a statistically significant difference in persistence, retention, and success for basic skill students who begin taking pre-algebra online versus face-to-face? and (2) Which software and/or instructional strategies being used are correlated with basic skills mathematics students’ successful completion of online basic skills mathematics courses? Background The development of online courses lacks the standardization and tradition of face- to-face education developed over hundreds of years (Lucas, 2006). Over that time, various pedagogical practices have gained wide acceptance, e.g. hour-long lectures, 20 regular class meetings, small group discussions, homework assignments, and semester and quarter length courses. On the other hand, institutions developing online courses rely on a consortium of faculty members who volunteer (or are persuaded) to experiment with the development and implementation of online courses (Cox, 2005). Often these faculty members are given no special preparation or training to develop these courses (Mupinga & Maughan, 2008), leaving them to invent (or mimic face-to-face formats) and later to discover what an effective online class looks like on their own. Consequently, no standardized or agreed upon pedagogy exists for teaching online courses (Engelbrecht & Harding, 2005), indicating a need for additional research to develop such a pedagogy. Rather than taking heed of the past successes and failures of colleges throughout history, colleges are rapidly and idiosyncratically developing and adopting a myriad of online teaching strategies without a well-developed, research-based, pedagogical framework. Stella and Gnanam (2004) claimed that, thus far, there exists no established quality assurance mechanisms specifically for online education, nor is there even agreement within academia as to what quality assurance means for online education. Simonson and Bauck (2003) have further noted the increased recognition of the need for policies to guide the growth and expansion of online education from institutions and faculty. This indicates a recognition from the academic community of the potential problems with the rapid and haphazard expansion of online courses and programs. Despite the recognition of a need for quality standards and guidelines specific to online education, online programs are being developed and expanded at a whirlwind pace presumably using the standards of traditional face-to-face education as a guide. 21 Furthermore, accrediting agencies have no special guidelines for evaluating the quality of online education at colleges and universities; and hence, institutions like the University of Phoenix Online and Capella University have been accredited under the same quality assurance standards as traditional face-to-face universities. The State of Florida runs the Florida Virtual School (FLVS) offering an fully online alternative to traditionally face-to- face K-12 education for Floridians. Most recently, the U.S. Department of Education (2009) released a meta-analysis of online learning studies finding that, while few rigorous studies of the effectiveness of online learning for K-12 students exists, students who took all or part of their class online performed better on average than students in traditional face-to-face classes. For many students, online courses are often perceived as an easier and quicker path to completing coursework. For colleges, particularly those with limited physical space and resources, online courses are often seen as a method to enroll additional students without requiring additional physical space. Remediation online, thus, is seen as a way to increase the capacity and ability of a college or university to enroll students who are unready for college level coursework (Cox, 2005; Mupinga & Maughan, 2008). Remarkably, some universities have publicly stated that using online coursework to help students catch up in mathematics is a financial necessity (Olsen, 2000). Olsen points to the California State University at Long Beach as an example of universities using automated remediation systems and large online class sizes to provide necessary remediation in a cost-effective manner. No statistics have been offered showing how 22 those students perform after this online remediation versus the traditional face-to-face format. As online course offerings have become common at colleges, community colleges have found themselves in competition for students they have never competed for. The Internet transcends their traditional geographic service areas creating a worldwide marketplace for colleges to complete for student enrollment (Cox, 2005; Folkers, 2005). This provides incentives for community colleges to grow their online programs by reaching out to students unavailable to them using traditional face-to-face instruction. Furthermore, as student demand for online courses grows among community college students (Lokken, 2009), community colleges that do not grow their online programs risk losing students in their geographic service area to outside colleges offering substantial online programs. Thus, despite the technological challenges of teaching online mathematics, community colleges find themselves in a position where not increasing online numbers is detrimental to their programs and continue to grow their online offerings. Basic Skills Mathematics in Community Colleges Basic Skills in California’s community college system are “those foundational skills in reading, writing, mathematics, and English as a Second Language, as well as learning skills and study skills which are necessary for students to succeed in college- level work” (Center for Student Success, 2007, p.13). In mathematics, these classes are arithmetic and pre-algebra, with Elementary Algebra being the mathematics requirement for earning an Associates Degree for students who entered prior to the Fall 2009 23 semester. For students first enrolled in Fall 2009 or later, the requirement was raised to Intermediate Algebra (Bogue-Feinour, 2006). With this change, the retention of learned skills becomes more important as students must proceed further in mathematics as a minimum requirement for graduation. In California’s community colleges, entering students test into basic skills/remedial mathematics courses at a rate of almost ninety percent (Moore & Schlock, 2007). These students face a long road to graduation and/or transfer to four-year universities. College Algebra is the lowest transfer-level mathematics course; students in basic skills classes must progress through three semesters of mathematics before they have met the prerequisites for College Algebra. Remediation time is especially long for students who want to major in a STEM (science, technology, engineering, and mathematics) field. For example, a typical STEM field student is required to take calculus as a freshman in college. The ninety percent of community college students who test into basic skills/remedial mathematics must take a minimum of four mathematics courses as prerequisites (Elementary Algebra, Intermediate Algebra, Trigonometry, and Precalculus) before becoming eligible for freshman calculus. This course of study takes four semesters potentially adding two years to a student’s college career. In their study of online mathematics courses, Smith et al (2008) conducted interviews with twenty experienced online mathematics instructors, followed by a more widely distributed questionnaire to validate themes and assumptions drawn from the interviews. These mathematics instructors consistently described the biggest challenges in teaching mathematics, across all modalities, as: (1) abstract concepts, (2) the sequential 24 nature of mathematics, (3) the need for instructor modeling of problem solving, (4) visual-spatial components, (5) the use of a unique set of symbols, and (6) academic integrity. The abstractness of mathematics makes teaching and learning mathematics a challenge because students must interact with the concepts regularly and relate them to practical, concrete examples in order to construct a working knowledge of the subject matter. Students have little motivation to complete coursework when it seems irrelevant to their educational pursuits. Typical remedial courses bear “little relation to the regular college courses for which they were preparing students” (Fenwick, 1994, p.8). Smith et all (2008) further noted the difficulties mathematics instructors have convincing their students not only to read the textbook but to read and work through (i.e. with a pencil and paper) the concepts simultaneously. Additionally mathematics instructors indicated that, because of the abstractness of mathematics, most students were math-phobic and have already “turned off what they have to learn” (p. 71); thus, teaching basic skills mathematics is much more than teaching the mathematics concept as so much as selling its value to students. The sequential nature of mathematics creates a situation where, if students miss particular concepts at an early level in the sequence, they will not have the prerequisite knowledge to build new concepts upon, making the more complex topics much more difficult to understand. Concepts and techniques build on earlier concepts and techniques with each level of mathematics providing the foundation upon which the next will be built. Thus, basic skills mathematics courses are building the foundation up on which all 25 other mathematics will rest. Students who do not build this foundation face disadvantages not only in all future mathematics courses, but in all science classes where mathematics is used heavily. Instructor modeling and student mimicking are the standard pedagogical model for teaching and learning mathematics especially for the visual-spatial components of mathematics. Students need to be shown using manipulatives, drawings, and examples the concepts and procedures of practicing and communicating mathematics. This is followed by students working problems, instructors providing feedback on their work, and students making any necessary adjustments and/or corrections to their understanding and/or skills. The traditional face-to-face course is modeled around this method with instructors lecturing and students practicing their understanding and skills with classwork and homework. Academic integrity is a problem all disciplines struggle to maintain and mathematics is no exception. In a 2004 study, Smyth and Davis found that, among junior college students, nearly 74% of respondents had witnessed cheating and 45.6% confessed to cheating at least once (p. 72). Additionally, they found that nearly half of all respondents viewed cheating to be socially acceptable that college was a game and students were justified in playing the game to their greatest perceived advantage. Aiken noted that students in classes with impersonal teaching styles tend to rationalize cheating as a way to beat the system (1991). This makes online classes where students and instructor potentially never meet particularly susceptible to cheating. Students may feel justified in cheating because the “classroom” is non-existent and the ability of instructors 26 to monitor cheating is diminished dramatically by the distance between students and instructor. The sequential nature of mathematic and the fact that mathematics is prerequisite knowledge for most science courses makes ensuring academic integrity a heightened concern for mathematics instructors. A student not understanding the causes of the second World War and cheating in his World History class may not negatively effect his or her ability to understand the concepts in another history class. A student who does not understand how to add fractions and cheats in his or her arithmetic class is assured that, without first revisiting and learning fractions, he or she will not be successful in an algebra class or any science class using algebra. Learning Management Systems Most online courses today are delivered using a commercial Learning Management System (LMS) (Lokken, 2009). They typically consist of methods for student-to-student contact and student-to-instructor interaction driven primarily by text. For both financial and practical purposes, institutions tend to purchase a one-size-fits-all LMS for all departments and disciplines within a college to use simultaneously (Smith & Ferguson, 2004). The 2008 Distance Education Survey, conducted among U.S. community colleges revealed that fifty nine percent of colleges use Blackboard/WebCT, down from seventy seven percent the preceding year (Lokken, 2009). Thirty seven percent of colleges further reported they were considering switching LMSs within the next couple years, but no rationale was given for this consideration. This may be a result 27 of cost, convenience, or possibly a recognition that certain disciplines (i.e. mathematics) have had difficulties with their existing systems. While most LMSs often seem well suited for most disciplines (including English, psychology, history, and other writing/text based courses), mathematics faculty face many special challenges that are either not addressed at all or not addressed well by current LMSs (Smith, Torres-Ayala & Heindel, 2008). Communicating mathematics requires the ability to read and write (type in the case of an online course) nuanced mathematics symbols; the text based LMS provide little opportunity for this to occur. When they do, the programs are either difficult to understand or overly cumbersome to be used effectively. Online Mathematics Mathematics faculty were initially slow in developing online courses; they tended to use the Internet as a method of information distribution (i.e. syllabi, homework assignments, worksheets, and grades) rather than as a medium for instruction and/or interaction (Buschel, 2008). Allen (2003) asserts this was largely due to difficulties of communicating mathematics online and the overwhelming amount of time and effort it takes to produce text using mathematics symbols. As computer and online technologies have improved, communication of mathematics concepts has become somewhat easier; although it remains difficult and time consuming. As a result of these improvements, mathematics courses have gained, increased prominence in online education as instructors put in the extra time to create online content. Today online mathematics courses are still considered among the most difficult to develop and teach (Lokken, 2009) 28 yet have become common course offerings at nearly every community college in California. This is especially true for basic skills/remedial courses as colleges and universities struggle to find cost effective ways to remediate the growing numbers of students underprepared for college level mathematics (Olsen, 2000). In 2008, Smith et al found that according to online mathematics instructors the two primary hurdles for overcoming challenges of teaching mathematics in the online environment are (1) the lack of dynamism and (2) the inherent difficulties in communication with diagrams and mathematics notation over the Internet. As described previously, teaching mathematics is a very dynamic activity requiring modeling by instructors and many trial attempts by students coupled with quick, accurate and understandable feedback from the instructors. This is especially true of basic skills students who are often learning the basic definitions, rules, procedures, and notation of mathematics. The asynchronous nature of most online mathematics courses (Smith & Ferguson, 2004) slows this vital communication often making students wait hours or even days for corrective feedback or answers to even simple inquires causing students to quickly become distracted and unmotivated. Face-to-face instruction provides class time for student interaction with the instructor and amongst themselves, to get many of their basic questions answered immediately. In their study of e-learning literature and subsequent consultation with online learning “experts”, Schrum and Hong (2002) found motivation to be among the seven most significant characteristics of successful online students. This makes any obstacles to student motivation a significant disadvantage for online mathematics education versus 29 a more traditional face-to-face education. Since basic skills mathematics students tend to be math-phobic and enroll in mathematics courses already turned off to what they need to learn (Smith et al, 2008), increasing motivation to study and learn becomes a particular challenge and slow communication of online instruction is likely to further exacerbate these problems. Communication of mathematics concepts and symbols using current technology presents an additional challenge for teaching and learning mathematics online. Often described as like a foreign language (Smith et al, 2008), the notation, symbols, and words of mathematics carry heavily nuanced meaning. Simple placement of a symbol can dramatically change the meaning of what is written; students often misunderstand. This problem is further advanced by the fact that, when translated into words or text, two different meanings are often said in the same way. For example, consider the phrase “negative two squared”. This is exactly how one would say both ! "2 2 and ! "2 ( ) 2 , however the meaning of these two expressions is dramatically different. The expression ! "2 2 means ! "2#2 ="4 while the expression ! "2 ( ) 2 means ! "2 ( ) "2 ( ) =4. The addition of parentheses and placement of the exponent dramatically change the value of the expression, yet the words are not changed at all. This common misunderstanding among basic skills mathematics students is difficult to detect and correct in the online environment. Current LMSs have made advances incorporating mathematics symbols and notation into communication tools. However utilization of these tools often requires a steep learning curve, and they tend to be very technical and often complicated to use 30 (Smith & Ferguson, 2004). For advanced users and higher level mathematics (i.e. college level) students these math notation tools may constitute a resource for instructors. They encourage students to think more about what they are typing and to understand the meaning behind the symbols they are using. A basic skills student, however, has little familiarity with the meaning behind the mathematics symbols and their nuances. These students are often just learning the language of mathematics, hence mitigating any advantages of these tools. In fact, if instructors are not careful, student misunderstandings could be reinforced setting them up for future difficulties. Smith & Ferguson (2004) found that the most commonly used mathematics notation tool by LMSs (mathml) was actually counter intuitive to use. In many cases, to get the proper notation using the computer requires the user to make several key-strokes and mouse clicks in reverse order from the way an individual would write the same idea by hand. Consider for example the process for entering the fraction “one-half” into a Backboard posting using WebEq powered by mathml: (1) the user must make sure the curser is in the exact spot where the fraction is to be entered, (2) use the mouse to click the “insert equation” button, (3) use the mouse to click the fraction button on the popup window, (4) use the mouse to click the curser into the numerator, (5) use the keyboard to enter the number 1, (6) use the mouse to click the curser into the denominator, (7) use the keyboard to enter the number 2, (8) and finally use the mouse to press the “insert equation” button. The resulting display will look something like <equn_001> leaving the user to remember what each equation stands for. A preview is available, but adjustments cannot be made in that mode. 31 As a result, many online mathematics instructors avoid using such programs all together and opt instead to use the symbols available on a standard QUERTY keyboard (Smith et al, 2008). These workarounds can be complicated for students to understand, particularly for basic skills mathematics students. Consider for example entering the number “one and a half” using only symbols on the standard QUERTY keyboard. By convention this would be entered as 1 – space - 1 - / - 2 and would look like 1 1/2. A simple enough workaround until confusion arises around the difference between the two distinct numbers one and a half (1½ ) and eleven-halves (11/2). To the trained observer, or mathematician, the difference is obvious. One-and-a-half looks like 1 1/2, while eleven-halves looks like 11/2, the difference being the space between the two 1’s in the numbers. It would be inappropriate to assume a basic skills mathematics student new to learning fractions is able to readily distinguish between the two very different numbers effectively. The Effect of Online Mathematics on Cognition Moore introduced the three types of interaction most commonly referred to in online education research in 1989: (1) learner-to-content, (2) learner-to-learner, and (3) learner-to-instructor interaction. Hillman, Willis & Gunawardena (1994) argue that a fourth type of interaction, (4) learner to interface must be considered. Forcing a student to use, or interact with, a complicated and difficult to use interface requires of students a set of skills and a level of understanding that have little to do with the actually mathematics concepts and learning expected of the course. This situation is actually 32 analogous to students taking two courses simultaneously. The first course is a computer course to learn the intricacies of the user interface or LMS, and the second course is to learn the actual intended content of the course (Hillman et al, 1994). Furthermore, a significant body of literature and college documents exist that suggest students must master using the online environment and LMS prior to being able to comprehend the new knowledge intended in the course (Schrum & Hong, 2002). The time a student spends on learning the technology is lost for teaching and learning the intended content of the course. This technological hurdle adds an additional and unnecessary cognitive burden on the basic skills students while providing no additional benefit. Instead this is one more additional interaction obstacle (Moore, 1989) for students to overcome. Cognitive load theory suggests that when cognitive load is shifted from the intended topic to compensate for needed concentration on non-germane topics, like working with the LMSs interface, it reduces students’ available working memory resources to engage in the content of the course (Paas, Rnekl & Sweller, 2003). Some advances have been made to reduce this extraneous cognitive load by making the programs easier and more intuitive for students to use. However, these advances compromise the semantic mathematical meanings of technical mathematics jargon (Smith & Ferguson, 2004; Smith et al, 2008). Interactive discussion boards and digital white boards can be implemented and may be appropriate for online discussions and collaboration. However within the LMS’s programming, the distinction between mathematical text and diagrams is lost (Smith & Ferguson, 2004) making obsolete tools like automated grading provided by advances in digital computers. Thus the advantage to 33 institutions of increasing class sizes is diminished. Additionally, such programs have not been full integrated into LMSs’ programming but are, instead, additional or stand-alone programs students must download and install onto their computers. This adds cost and the necessity for additional technical prowess on the part of the instructor as well as assumptions of technological expertise of the basic skills student. In general, programs that allow student-to-student and student-to-instructor interaction using mathematics symbols and diagrams in a natural and intuitive way provide an enriching learning experience. Instructors, researchers, and students alike have reported that online discussions facilitate a deeper understanding and more thoughtful responses than discussions occurring in a face-to-face classroom (Schrum & Hong, 2002; Mansour & Mupinga, 2004; Buschel, 2008; Pyon, 2008). They argue that students must make a concerted effort to understand the mathematics before they are able to articulate their thoughts in text or on a discussion board using symbols at all. The argument has also been made that unless these discussions are graded and count as a part of the students’ grade more motivated and articulate students will dominate the conversations, and the rest of the students will either passively observe or become disconnected from the conversation (Taylor, 2002). This observation leads to the additional argument that those students who dominate the conversation without external motivation would have been successful in the course even without the discussions, hence such discussions have added nothing to the value of the course or learning experience for the majority of students. 34 Presentation, understanding, and development of diagrams to represent mathematics concepts is widely considered the optimal method of mentally organizing and comprehending concepts. Those concepts are then applied to understanding and solving more advanced problems. Diagrams can help students to take the abstract concepts of mathematics and mentally organize them in a more concrete and understandable manner by making them tangible and meaningful. Larkin and Simon (1987), in their study comparing comprehension between groups using diagrammatic representations of information versus text based paper-and-pencil representations of the same information found diagrammatic representations to be superior. In particular they identified the following three reasons for diagrammatic superiority: (1) diagrams can group information, making problem-solving inference easier, (2) diagrams typically group information around a single element, and (3) diagrams automatically support a large number of perceptual inferences easily understood by humans. Roth and Bowen (2003) found similar results in their study and suggested that the quality of a scientist may depend on that individual’s ability to develop and understand charts and diagrams representing complex concepts and ideas. Since these conceptual skills are generally learned in basic skills mathematics courses, it is imperative that students are working with and can understand information presented via charts, diagrams, and graphs. This, unfortunately, remains the most difficult method of communicating mathematics. 35 Online versus Face-to-Face Education Many papers have been written and research done comparing students’ outcomes in online versus face-to-face versus hybrid courses. Russell reviewed hundreds of these studies and found “no significant difference” in the outcomes between online and face-to- face courses (2001). In a recent meta-analysis and review of online learning studies, the U.S. Department of Education found that online and hybrid courses produced higher student learning outcomes than did face-to-face courses. The vast majority of these studies contained small sample sizes and narrowly focused their definition of success on grades earned the class being studied. The question of evaluation methods and whether or not the class produced an advantage or disadvantage for the students’ long term educational careers is largely left unexplored. The concept of mathematics education online is another sector of online education research that has largely been unexplored, the vast majority of online education research focusing on classes other than mathematics and the sciences. What research does exist on online mathematics education tends to focus on supplemental courses to majors other than mathematics, i.e. statistics for engineers (Adams, Glenn, Adams, 2006; Gundy, Morton, Liu, Klien, 2006), online students at four year-year colleges and universities, and graduate-level coursework (Schrum & Hong, 2002). Using these studies to make claims about basic skills mathematics seems inappropriate because of the differing levels of mathematical sophistication between such students and basic skills mathematics students. In his 2001 dissertation study, Dooley (2001) examined a large sample of students taking elementary algebra at Pasadena City College. He compared the results of students 36 who took traditional face-to-face elementary algebra courses with students who took a computer mediated learning (CML) course. His study revealed that the CML students scored more poorly than their face-to-face counterparts, but interestingly he found that when students enrolled in the subsequent intermediate algebra course, the advantage for face-to-face students had diminished. His analysis produced no rationale for the initial difference in grades and subsequent lack of difference but, never-the-less, uncovered an interesting question most researchers have overlooked: What are the long term effects of taking classes online? Are the advantages or disadvantages in outcomes a result of differing evaluation methods, instructional methods, quality of students or instructors, or is online education a superior or inferior medium for the long-term success of students? Student Factors on Success and Persistence Students themselves bring to the classroom factors that research has linked to student success and persistence in post-secondary education. In the discussion of their review of research on online teaching, Tallent-Runnels et al. (2006) assert that the understanding of students’ goals, needs and motivations is a basic tenet in both traditional and online instructional design. Particularly at community colleges, students enter college for a wide range of reasons with differing preparation, resources and abilities. Tallent-Runnels et al. found in their review that online students typically are older (in their late 20’s and early 30’s), typically are white, and are roughly split evenly between men and women (2006). Studies have mixed results when looking at students success and persistence in terms of age and gender. According to Goldstein & Perin 37 older students consistently outperform younger students in college classrooms and performance studies looking at gender vary too widely to make any conclusions (2008). Wassmer, Moore, and Shulock (2004) examined institutional level data from 108 community colleges and found that institutions with younger student populations had on average higher transfer rates than institutions with older student populations. They further found that females were less likely to transfer due to familial responsibilities. Not considered, however, was whether these students had intended to transfer, thus making a broad assertion about older students and females and transfer/persistence rates not possible. Students who enrolled in college immediately after high school, enrolled full- time, and attended continuously had higher persistence rates in Wassmer, Moore & Shulock’s study (2004). They further noted that Latino and African-American students are more likely to vary from this non-traditional enrollment pattern in so much as they enroll part-time and take frequent periods away from school. After controlling for both academic preparation and socioeconomic status, Wassmer et al. they found institutions with high Latino populations have lower transfer rates across the 108 community colleges studied. Similar results were found by Zajacova, Lynch, and Espenshade (2005) who found that full-time students were had consistently higher GPA’s than part-time enrolled students. These results agree with Tinto’s (1975) Student Interaction Theory. Students are more likely to persist when involved in the college and its activities. Part-time students are likely to have other factors in their personal lives that inhibit full-time enrollment and 38 prevent active involvement in college activities. Student Interaction Theory, however, it is based on traditional college-aged students and may not be applicable to the typical online students whose motivations and maturity may produce differing results from a typical college-aged student. Conclusion The rapid and haphazard growth of online education has vastly outpaced the ability of researchers, educators, and institutions to establish effective and agreed upon set of pedagogical practices for online education. This growth in online education has show signs of slowing, indicating a market saturation point may be nearing, but has given no indications of a reversal. In fact, it is likely to further expand as advances in technology, the current economic downturn and related budget problems, and an renewed G.I. Bill drive a multitude of under-prepared students back into classrooms across the nation (Johnson et al, 2009). The community college will be the starting point for many of these students as four-year colleges and universities cut back enrollment and remediation services to cope with decreasing budgets and rising operational costs. This means that community colleges will find themselves providing remediation for more students than ever before and are likely, due to their own economic constraints, to do much of this online. Because mathematics acts as a gatekeeper for students who want to pursue degrees in mathematics or the sciences, it is important that colleges have a firm understanding of the effects of offering basic skills mathematics online and to know 39 effective strategies for teaching mathematics online well. While the vast majority of research on online education indicates that there is either no significant difference between online and face-to-face education (Russell, 2001) or that online education produces slightly superior student learning outcomes (U.S. Department of Education, 2009), little of this research focuses on mathematics or the longitudinal effects on student persistence or success. For students taking a basic skills mathematics course online, the research seems to indicate a disadvantage. Online communication of mathematics concepts is difficult (Allen, 2003, Smith & Ferguson, 2004; Smith et al, 2008). Most LMS’s have text-based discussion boards and overly difficult to use mathematics display software that would allow students to display mathematics ideas in the proper notation. (Looken, 2009; Smith & Ferguson, 2004). According to research, the popular use of discussion boards produces negligible additional learning only influencing how students interact with each other and the material (U.S. Department of Education, 2009). Furthermore, cognitive load theory suggests that the complications of posting mathematics to discussion boards reduces students’ available working memory to process the mathematics (Paas, Renekl, & Sweller, 2003). Also noted by the U.S. Department of Education’s meta-analysis is the lack of effect of adding media to online classes (2009). This gives rise to the question of the effectiveness of popular trends in video lectures and demonstrations in online classes. Such activities are often expensive to produce and host online and consume a large amount of instructor time that could possibly be better spent on instruction. In an 40 increasingly flashy world of electronic devices and competition to attract students world- wide to online courses, it remains unknown if students will enroll in an equally or more effective online course without videos and flashy demonstrations. Finally, left out of the research on online courses are concerns over evaluation methods and academic integrity. Cited as one of the top concerns among mathematics instructor (Smith et al, 2008), academic integrity is increasingly difficult to preserve in the online environment. Many instructors use multiple-choice exams because of students difficulty entering mathematics online (Smith et al, 2008). Many institutions and instructors are now requiring students to take paper examinations proctored either on campus or by a neutral third party. This phenomenon is easily verified by looking through college course catalogs but remains relatively absent in the literature. With the knowledge that enrollments are on the rise, budgets are shrinking, and students are in need of more remediation than ever before, it is time for research to begin looking at the long-term effects of taking basic skills mathematics online as well as common course components and evaluating their relative effectiveness. 41 CHAPTER THREE RESEARCH DESIGN AND METHODOLOGY Introduction The rapid growth of online education coupled with the extreme need for mathematics remediation in higher education, particularly at community colleges, has spurred the growth of online basic skills mathematics courses over the past decade. The general consensus among researchers is that online education is, on average, as at least as good as face-to-face education (Russel, 2001; U.S. Department of Education, 2009). Mathematics is a unique case and research has been conducted pointing out many of the challenges teaching mathematics online. Problems with effective communication are at the core of these difficulties; technology has yet to develop an effective method of communicating using mathematics symbols in a simple and efficient way. On the other hand, case studies have been published highlighting specific successes teaching mathematics online (Adams, Glenn, Adams, 2006; Gundy, Morton, Liu, Kline, 2006; Russell, 2007; Schrum & Hong, 2002) Those studies focus primarily on high-level undergraduate, graduate, or specialty mathematics courses. Basic skills mathematics is likely most effected by the difficulties pointed out by researchers yet has been largely overlooked by them. In fact, in his dissertation study of elementary algebra students at Pasadena City College, Allen Dooley found that student use of computer mediated learning software had a grade disadvantage in elementary algebra when compared to students who took the class face-to-face (2001). He further found no link between computer skills and confidence to the grades earned in a computer 42 mediated learning course indicating that the grade disadvantage was not linked to inadequate computer skills. The disadvantage was gone, however, when students persisted to the subsequent intermediate algebra course leaving a fundamental question about the education students got from the computer mediated classes. Why did students score worse in their online class yet begin the next class seemingly equally prepared? Throughout the literature online education has been both criticized and praised. Additionally, the strategies, technologies, and practices of online instructors have been criticized and praised for a variety of reasons. The aim of this study is to narrow the focus on online education research to a well-known and expanding difficulty in higher education: basic skills mathematics. It is taken at face value that most research indicates “no significant difference” exists in outcomes of online versus face-to-face modalities of education (Russell, 2001). The literature review revealed several aspect of online mathematics education that have been largely unexplored but have the potential to influence student success and persistence in online basic skills mathematics classes. The popular trend of adding media to online classes typically comes in the form of video lectures to deliver content. The U.S. Department of Education indicates the addition of media has little effect on outcomes and can actually have a negative impact (2009). Tallent-Runnels et al. (2006) reported that delivering content via video enhanced recall better than still slides but that narration in the video caused learners to split their attention and lowered performance. Discussion boards are present in nearly all online class designs. The U.S. Department of Education indicates these have a positive effect on results but as a result of keeping 43 students engaged in the material rather than as an effect of the discussion boards themselves (2009). Discussion boards, therefore, provide the opportunity for enhancing learning but are not necessarily a guarantee that learning will be enhanced. When mathematics display software is integrated into online communication, in discussion boards or otherwise, cognitive load theory indicates that students may suffer as a result of limited working memory available to dedicate to understanding mathematics concepts (Paas, Renekl, & Sweller, 2003). When cognitive load is increased during instruction, learner understanding of complex concepts like mathematics is hindered (Tallent-Runnel, 2006). This extraneous cognitive load is a result of the difficulties associated with using currently available mathematics display software (Looken, 2009; Smith & Ferguson, 2004). Cited as one of the top concerns among mathematics instructors (Smith et al, 2008), academic integrity is difficult to ensure in the online environment. Many instructors use multiple-choice examinations because of the difficulties associated with students entering mathematics online (Smith et al., 2008). Instructors fear students will be able to solve the problems but not enter the correct answer in a correct and/or understandable manner. Multiple-choice exams, however, provide students with the opportunity to test the possible choices to find the correct answer rather than actually solving the problems allowing students to score relatively well on assessments without actually having an understanding of the material. In addition to the methodology of multiple-choice exams is the problem of ensuring the student taking an assessment is actually the student who is enrolled in the course. As a result, many departments and 44 institutions have begun requiring proctored examinations for their students allowing for institutions to verify the identity of the test-takers. This test taker verification has become such a problem that new accreditation regulations by the Accrediting Commission for Community and Junior Colleges (ACCJC) now requires community and junior colleges to verify the identity of their online students. This study takes a look at the longitudinal effects of taking pre-algebra online versus face-to-face and examines course components for correlations to success and persistence. This study poses two basic research questions: 1. Is there a statistically significant difference in persistence, retention and success for basic skills students who begin taking pre-algebra online versus face-to-face? 2. Which software and/or instructional strategies being used are correlated with basic skills mathematics students’ successful completion of online basic skills mathematics courses? For the sake of practicality the components, practices, or strategies are summarized as the following: 1. The use of video lectures to deliver content. 2. The required use of discussion boards by students. 3. Student use of mathematics display software to display mathematics in proper notation. 4. The exclusive use of multiple-choice exams 5. Proctored examinations. 45 Any videos, animations, or movie lectures are considered the use of video lectures. This may include the instructor recording a lesson himself or herself, animated lectures produced by outside proprietary services, or freely available videos available on the Internet. The required use of discussion boards means giving credit for participation on class discussion boards. No distinction is made between the amounts of required participation. Student use of mathematics display software is considered any software used by students to display mathematics concepts and ideas in correct notation digitally. Proctored examinations deals primarily with examination security and the growing concern that the students taking the class are actually doing the work for themselves. In addition to research overlooking basic skills mathematics courses, success has largely been defined around pass rates, retention, examination results, and faculty and student satisfaction. Few studies have considered student performance in terms of learning outcomes and persistence through a sequence. Basic skills courses at community colleges are non-transferable and are intended to convey “those foundational skills in reading, writing, mathematics, and English as a Second Language, as well as leaning skills and study skills which are necessary for students to succeed in college-level work” (Center for Student Success, p.13). Performance in a single class is therefore not a adequate measure of success in basic skills mathematics courses. These classes are aimed a filling a void in student understanding and skills to facilitate later success. Given the sequential nature of mathematics curriculum, performance in subsequent mathematics courses for which the basic skills classes are prerequisites is an appropriate measure of success in a basic skills mathematics course and will be considered in this study. 46 To answer the questions posed using the success criteria explained above, a quantitative analysis study was chosen. A large database of numerical/quantifiable data at the institutional and class level was gathered and a broad picture of the relationships between online basic skills classes, their components, students success, and persistence is built. Data And Data Collection The original intent of the study was to include nine different community colleges throughout the State of California. These colleges were identified as generating at least 250 full-time equivalent students (FTES) taking online non-transferable mathematics courses during the Fall 2008 semester (http://www.cccco.edu/SystemOffice/Divisions/ TechResearchInfo/MIS/ DataMartandReports/tabid/282/Default.aspx). Assuming three unit courses, this meant that each school had 2,430 individual student enrollments in online non-transferable mathematics courses during the Fall 2008 semester, and it was likely that a range of different instructors would have taught them. As data collection began, the State of California was fully entrenched in a deep recession that resulted in large cutbacks at both the individual colleges as well as in the California Community Colleges Chancellor’s Office. This resulted in reduced staff and furloughs which further resulted in waiting lists for data, unanswered phone calls and emails, and denials for data requests citing lack of resources to collect and code the data to protect individual identities. Neither the individual colleges nor the State Chancellor’s Office were willing to gather the data and ensure student confidentiality was maintained. 47 Personal relationships were leveraged within the Riverside Community College District, however, and 20,928 individual student records for students taking pre-algebra and elementary algebra were collected from the three-college district. This was a database of all students who had taken either or both of the courses during the time period beginning with the Fall 2005 semester and ending in the Spring 2008 semester. The RCCD Institutional Research Department provided a database of students each identified with specially coded identification numbers to mask the identity of individuals; the semester they took the course; the course they took (pre-algebra or elementary algebra); the online status of the course (either online or face-to-face); the course code; and, the grade earned. From this database, a list of all course codes for all online pre-algebra courses was generated. Using the district’s published course schedules, the instructors who taught these online courses were identified. Twenty-seven online pre-algebra courses were taught by seven different instructors during the time period investigated. Each instructor was initially contacted via email and asked six questions. The first five were limited to yes or no answers; asking the instructors if they used the following components in each of the online classes they taught: (1) video lectures to deliver content, (2) the required use of discussion boards by students, (3) student use of mathematics display software, (4) exclusively multiple-choice examinations and/or quizzes, and (5) proctored examinations. The sixth question was open-ended: asking if there was anything further they had done had made a significant impact in their online classes. For those who didn’t respond to the initial email, personal phone calls were 48 made and answers collected verbally. Eventually all seven instructors responded and questions were answered for all twenty-seven courses taught. Data Refinement The data collected included all students who had taken pre-algebra and elementary algebra any time during the 2005-2006, 2006-2007, or 2007-2008 academic years. In addition to securing useful data, this request also yielded data not useful to this study, including many students who did not take pre-algebra. However, the request was intentionally framed to consume the least amount of time on the part of RCCD’s institutional research department. Using Microsoft Excel, the data was restructured to a database of students who had taken pre-algebra at RCCD using the following steps: 1. All students who had taken elementary algebra without first taking pre-algebra were removed. 2. All repeated attempts at either pre-algebra or elementary algebra were removed, leaving only students who had taken pre-algebra but did not move on to elementary algebra (either because of a failing grade or for an unknown reason) and students who took pre-algebra and subsequently took elementary algebra. After this was completed 4,664 student records remained in the database. Table 3.1 summarized the data recorded for each student record and how it was coded in the database. 49 Table 3.1 Final Database Information and Coding Data Possible Entries/Coding Student ID Number Generated by RCCD’s Institutional Research Department. Pre-algebra grade A=4, B=3, C=2, D=1, F=0, DR=0, W=0 Online or Face-to-Face Online = 1, Face-to-Face = 0 - Required use of Discussion Board - Use of Mathematics Display Software - Exclusively Multiple Choice Exams - Proctored Exams - Video Lectures Component not used = 0 Component used = 1 Pre-algebra class was not online = 999 Elementary Algebra Grade A=4, B=3, C=2, D=1, F=0, DR=0, W=0 NoPass (did not pass pre-algebra) NoCont (passed pre-algebra but did not move on) Data Analysis Data analysis was done in two distinct parts. The first part was a comparison of student persistence and performance while taking pre-algebra online versus face-to-face and, subsequently, enrolled in elementary algebra after taking pre-algebra either online or face-to-face. The second part is an analysis of the five components of online pre-algebra classed considered in the study, analyzing any relationships and correlations to persistence and performance in pre-algebra online and the subsequent elementary algebra course. In part one, chi-square tests are used to test for statistically significant relationships between pre-algebra online versus face-to-face and whether or not a student persisted through pre-algebra, then on to elementary algebra. Table 3.2 summarizes the 50 database used for this analysis. T-tests were used to test if the differences in grade point averages between students from online pre-algebra classes and face-to-face pre-algebra classes were statistically significantly different. Table 3.2 Online vs Face-to-Face comparison database Number Took Pre-algebra Online 834 Passed 591 Took Elem Algebra 440 Did not take Elem Algebra 151 Failed 182 Drop or Withdrew 61 Took Pre-algebra Face-to-Face 3,830 Passed 2,157 Took Elem Algebra 1,589 Did not take Elem Algebra 568 Failed 1,133 Drop or Withdrew 540 Part two of the study is an analysis of the five common course components considered in this study: (1) video lectures to deliver content, (2) the required use of discussion boards by students, (3) student use of mathematics display software, (4) exclusively multiple-choice examinations and/or quizzes, and (5) proctored examinations. A separate database was built from the one used in part one; only records of students who took pre-algebra online were used in the second database and part two of the study. Each online course was coded for each of the components, using a 0 to indicate the component was not used and a 1 to indicate the component was used. A Visual Basic script embedded in Microsoft Excel was then used to add columns for each component to all individual student records. Correlation matrices were then constructed using the SPSS statistical analysis software (version 17.0). Insufficient data was available on the use of 51 proctored examinations because RCCD had only recently begun requiring proctored examinations and was dropped from the study. The first matrix correlates the use of each component with students persisting through their pre-algebra course. Any student who earned a grade in the course, passing or not, was considered to have persisted through the course. Students who dropped or withdrew from the course were considered to have not persisted through the course. For the second matrix constructed, only students who passed pre-algebra with a “C” or better were considered. The matrix correlated the course components with the students persisting into elementary algebra. Any students who enrolled in an elementary algebra class were considered to have persisted to elementary algebra despite the grade they earned in the class. Students who did not enroll in elementary algebra at RCCD were considered to have not persisted, although some of those students may have enrolled in an elementary algebra at another institution. The final two matrices were constructed similarly to the first two replacing the persistence correlation with correlations to grades. Significance of Study This study examines the relationships between taking an online pre-algebra class versus a traditional face-to-face pre-algebra class with student performance and persistence through basic skills mathematics. Additionally it looks at the resources and methods currently being used teaching basic skills mathematics courses online. No experienced mathematics instructor would ever suggest using the same strategies for teaching an advanced mathematics and a basic skills class, yet the former dominates the 52 little research on online mathematics. To date, relatively little literature exists to inform the growing practice of teaching basic skills mathematics online. Ideally this study will give institutions and instructors an idea of the long-term relationship between teaching basic skills mathematics classes online and student performance and persistence. Additionally, it will provide insight into effective strategies for teaching those classes. Developers and instructors will have better understanding of how to effectively build and instruct basic skills mathematics. This research is by no means exhaustive, nor does it solve all of the problems associated with teaching basic skills mathematics online. What this study does do is recognize that thousands of students are enrolled in these courses and that very little research has been done on the relative effectiveness of this practice. This study hopes to takes some first steps toward what will ideally develop into a fruitful pattern of research. Limitations As with any study, there are limitations to the design and implementation. The data collected is limited to enrollment records in pre-algebra and elementary algebra, the semester enrolled, and the grade earned. Student characteristics with know correlations to student performance such as age, race and ethnicity, socioeconomic status, and academic preparation are not controlled for. Such unknown factors in this study are treated as a constant. Additionally, data on student enrollment patterns and past performance are unknown. Student GPA and full-time versus part-time enrollment status are know to be strong predictors of both student success and persistence. 53 Course design and quality are treated as a constant in this study. The U.S. Department of Education (2009) noted that course quality and teacher quality has a large impact on student outcomes. Tallent-Runnels (2006) noted, however, that course quality takes on a different meaning for different students who are taking the course for a variety of reasons. Students enrolling in community college classes may never intend to persist through into elementary algebra and, hence, could possibly skew persistence data. Many online students attend several different institutions as they seek course availability. It is unknown if a student who passes pre-algebra chooses not to persist to elementary algebra or whether they are simply taking it at another college. The database further does not allow for knowing whether or not students continued to enroll at RCCD but chose to take time away from mathematics with the intent to finish the mathematics sequence. 54 CHAPTER FOUR ANALYSIS OF DATA In this chapter, the findings are presented and analyzed within the context of the research questions posed in Chapter 1. This is done in two parts. The first part consists of a comparison of student persistence and performance when taking a face-to-face pre- algebra class versus an online pre-algebra class at the Riverside Community College District (RCCD). Records of all students who took pre-algebra and/or elementary algebra within the District between the Fall 2005 and Spring 2008 semesters were collected from RCCD’s Institutional Research Department. A total of 4,664 students took Pre-algebra during the indicated time period, 834 in an online course and 3,830 in a traditional face-to-face course. Of those, 2,748 students passed, 591 in online classes and 2,157 in face-to-face classes; 2,029 of them took elementary algebra at RCCD, 440 of them passing pre-algebra online and 1,589 passing pre-algebra in a traditional face-to- face course. Statistics are first presented followed by an analysis of these data. The second part consists of a presentation and statistical analysis of data collected on the five target components used in online pre-algebra classes combined with the student records dataset. Within the Fall 2005 through Spring 2008 time frame, 25 online pre-algebra classes were taught by 7 different instructors, consisting of 834 unique student records. All 7 instructors were initially contacted by email, and those who didn’t respond were subsequently contacted phone regarding their use of the five common course components studied: (1) video lectures to deliver content, (2) required us of discussion boards by students, (3) student use of mathematics display software, (4) exam 55 composition (multiple choice, free response, or a combination), and (5) proctored examinations within each of their sections. From this information, correlations were drawn as to which of these components made a significance difference in student persistence and student success in both the online pre-algebra class and the subsequent elementary algebra class. Part One Part One consists of a comparison of student persistence and performance when taking a face-to-face pre-algebra class versus an online pre-algebra class. For the purpose of quantifying grade records to make numerical statistical comparisons, letter grades were assigned numerical values in accordance with standard GPA practices: A = 4, B = 3, C = 2, D = 1, and F = 0. A total of 4,664 students were considered in part one: 834 took pre- algebra online and 3,830 took pre-algebra in a traditional face-to-face format. Of those, 61 dropped or withdrew from their online course and 540 dropped or withdrew from their face-to-face course, leaving 773 students who earned a letter grade in their online class and 3,290 students who earned a letter grade in their face-to-face class. Table 4.1 Online vs Face-to-Face pass rates including drop/withdraw Online Face-to-Face N % N % Took pre-algebra 834 3,830 Passed pre-algebra 591 70.9% 2,157 56.3% Took Elem Alg 440 52.6% 1,589 41.2% Did not take Elem Alg 151 18.1% 568 14.8% Failed pre-algebra 182 21.8% 1,133 29.6% Drop or Withdraw 61 7.3% 540 14.1% 56 Table 4.2 Online vs Face-to-Face pass rates excluding drop/withdraw Online Face-to-Face N % N % Took pre-algebra 773 3,290 Passed pre-algebra 591 76.5% 2,157 65.6% Took Elem Alg 440 56.9% 1,589 48.3% Did not take Elem Alg 151 19.5% 568 17.3% Failed pre-algebra 182 23.5% 1,133 34.4% Students who took pre-algebra online were less likely to drop or withdraw than those who took pre-algebra in a traditional face-to-face class. Online pre-algebra classes had an overall attrition rate of 7.3% while face-to-face pre-algebra classes had an attrition rate of 14.3%. A chi-square test revealed this relationship to be significant, ! " 2 1,N = 4,664 ( ) =28.09,p <0.01. Further investigation however, revealed the relationship between taking pre-algebra online versus face-to-face and persisting to elementary algebra was statistically insignificant. Of those students eligible to move on (those who earned a “C” grade or better in pre-algebra), 74.5% of those from online classes and 73.7% from face-to-face classes persisted to elementary algebra. For those students who did persist from pre-algebra to elementary algebra, students from a face-to-face pre-algebra class were more likely to drop their elementary algebra class than those from an online pre-algebra class. The elementary algebra attrition rate of students who took pre-algebra online was 10.9%, while their counterparts from face-to-face classes had an attrition rate of 23.0%. A chi-square test revealed this difference to be statistically significant, ! " 2 1,N =2,029 ( ) = 30.92,p <0.01. 57 Students who took pre-algebra online earned significantly higher grades than those who took pre-algebra face-to-face, t(4662) = 10.10, p < .01. The mean GPA for online pre-algebra students was 2.3 and for face-to-face students the mean GPA was 1.7. When all students who failed or dropped pre-algebra or chose to not continue to elementary algebra are removed from the database (leaving only students who too tracked students who took pre-algebra then moved into Elementary Algebra), the significance holds, t(2027) = 6.37, p < .01. The mean GPA for tracked online students was 3.2 while the GPA for tracked face-to-face students was 2.9. The focus of this study lies in the performance of students in an Elementary Algebra class after successfully completing pre-algebra. Table 4.3 is a summary of how these tracked students performed in Elementary Algebra after taking either an online or face-to-face pre-algebra class. To get a more in depth understanding of the longitudinal performance of these students, they are categorized first by the OL/F2F status of their pre-algebra class then further disaggregated by the grade they earned in that class. 58 Table 4.3 Elementary Algebra Grades – Disaggregated by online and face-to-face pre-algebra class and pre-algebra grade earned Pre-algebra Class & Grade N Mean GPA Median GPA % of Total N F2F A 437 2.25 3.00 21.5% B 612 1.25 1.00 30.2% C 540 .76 .00 26.6% Total 1589 1.36 1.00 78.3% OL A 182 2.99 3.00 9.0% B 165 1.68 2.00 8.1% C 93 .85 .00 4.6% Total 440 2.05 2.00 21.7% Totals A 619 2.47 3.00 30.5% B 777 1.34 1.00 38.3% C 633 .77 .00 31.2% Total 2029 1.51 1.00 100.0% Overall, there was a statistically significant difference in students’ elementary algebra grades after successfully taking pre-algebra online versus face-to-face, t(2,027) = 8.93, p < .01; students who successfully completed pre-algebra online earned an average GPA score 50.7% higher than students who successfully completed pre-algebra in a face-to-face course. This indicates that those students who passed pre-algebra online exited better able to utilize the skills learned in pre-algebra than those from a traditional face-to-face course. When the data were disaggregated by letter grade earned in pre- algebra, chi-square tests revealed the significance remained for students who earned an A or B in pre-algebra but not for students who earned a C. The Chi-Square tests are summarized in table 4.4. 59 Table 4.4 OL/F2F – Elementary algebra grades controlling for pre-algebra grades Pre-algebra Grade Value df Asymp. Sig. (2- sided) Pearson Chi-Square 41.397 6 .000 A N of Valid Cases 619 Pearson Chi-Square 21.014 6 .002 B N of Valid Cases 777 Pearson Chi-Square 5.939 6 .430 C N of Valid Cases 633 Students who earned an A or B in pre-algebra class online earned statistically significant higher grades in elementary algebra than their counterparts in face-to-face courses. The online versus face-to-face comparison produced no statistically significant difference in elementary algebra grades for students who earned a C in their pre-algebra course. Part Two The second part of the statistical analysis for this study involved integrating the student records from part one with the data collected from instructors of the 25 online pre-algebra classes involved in the study. Only those student records from students who took pre-algebra online were used in part two. Each instructor answered that he/she either did or did not use each of the 5 components of the study for each of the sections he/she taught. To allow for statistical analysis, answers were recorded as follows: 0 when the component was not used and 1 when the component was used. Table 4.5 summarizes the instructors’ answers in terms of the number of classes that used each component and the number of students who were involved with that component. 60 Table 4.5 Summary of instructor responses and number of students affected. Classes that used component Classes that did not use component Students that used component Students that did not use component Discussion Board 23 2 767 67 Mathematics Display Software 4 21 143 691 Multiple Choice Exams 13 12 400 434 Proctored Exams 0 25 0 834 Video Lectures 14 11 365 469 The majority of courses (92%) required students to post on discussion boards as part of their participation in the course. Few courses (16%) required students to use mathematics display software to communicate mathematics concepts. Multiple Choice examinations and the use of video lectures were split more evenly: 52% and 56% respectively. Proctored examinations have been employed within the past year and hence data for students who have taken those classes was unavailable at the time of this paper. Each instructor involved did, however, express anecdotal opinions that the new proctored examinations were cutting down on cheating in online classes. Table 4.6 provides a more detailed summary of the use of each component disaggregated by grade earned in the online pre-algebra class and table 4.7 provides a detailed summary of the use of each component disaggregated by grade earned the subsequent elementary algebra class. The coding of 0 for not used and 1 for used allows 61 the mean in the tables to be interpreted as the percentage of students who earned that grade who used the component. For example, in Table 4.6, 231 students earned an A in their online pre-algebra class, 95% of these students were required to use discussion boards as part of their class participation. Table 4.6 Summary of students’ use of components, disaggregated by pre-algebra grade earned Pre-algebra grade Discussion Boards Math Display Software Multiple Choice Exams N 231 231 231 A Mean .95 .18 .55 N 223 223 223 B Mean .92 .16 .61 N 137 137 137 C Mean .96 .12 .45 N 59 59 59 D Mean .90 .20 .49 N 9 9 9 Drop Mean .33 .00 1.00 N 123 123 123 F Mean .88 .24 .66 N 52 52 52 Withdraw Mean .90 .15 .50 62 Table 4.7 Summary of students’ use of components, disaggregated by elementary algebra grade earned Elementary Algebra Grade Discussion Boards Math Display Software Multiple Choice Exams Video Lectures N 104 104 104 104 A Mean .94 .16 .47 .00 N 112 112 112 112 B Mean .94 .13 .54 .00 N 74 74 74 74 C Mean .95 .14 .58 .00 N 35 35 35 35 D Mean 1.00 .23 .60 .00 N 5 5 5 5 Drop Mean 1.00 .00 .40 .00 N 67 67 67 67 F Mean .93 .21 .57 .00 N 43 43 43 43 Withdraw Mean .91 .12 .63 .00 An analysis between the five components studied and persistence through pre- algebra and elementary algebra was done by generating two correlation matrices: the first between the five components and the persistence through pre-algebra and the five components and the second between persistence to elementary algebra and the five components. No analysis was done correlating the five components and persistence through elementary algebra because no data was collected regarding the composition of the elementary algebra classes. All 834 students who enrolled in pre-algebra were used in the first correlation matrix, shown in table 4.8. After removing those students who did not pass or persist to elementary algebra were removed, 591 students remained for the second correlation matrix, shown in table 4.9. 63 Table 4.8 Correlation Matrix – Components with persistence for all online pre-algebra students Persistence Pearson Correlation 1 Sig. (2-tailed) Persistence N 834 Pearson Correlation .103 ** Sig. (2-tailed) .003 DisBoard N 834 Pearson Correlation .030 Sig. (2-tailed) .386 MathDisplay N 834 Pearson Correlation .012 Sig. (2-tailed) .738 MCExams N 834 Pearson Correlation -.006 Sig. (2-tailed) .852 VidLecture N 834 **. Correlation is significant at the 0.01 level (2-tailed). a. Cannot be computed because at least one of the variables is constant. 64 Table 4.9 Correlation Matrix – Components with persistence for online pre-algebra students who passed Persist to EA Pearson Correlation 1 Sig. (2-tailed) Persist to EA N 591 Pearson Correlation .001 Sig. (2-tailed) .982 DisBoard N 591 Pearson Correlation -.010 Sig. (2-tailed) .800 MathDisplay N 591 Pearson Correlation .004 Sig. (2-tailed) .919 MCExams N 591 Pearson Correlation -.002 Sig. (2-tailed) .967 VidLecture N 591 a. Cannot be computed because at least one of the variables is constant. **. Correlation is significant at the 0.01 level (2-tailed). There was no statistically significant correlation between students dropping or withdrawing from their online pre-algebra and the use of mathematics display software, video lectures for content delivery, or multiple choice examinations. The required use of discussion boards by students did have a statistically significant positive correlation with students persisting through their pre-algebra course. This relationship was verified as statistically significant using a chi-square test, ! " 2 1,N =834 ( ) =8.907,p <0.01. When the examination of the five course components studied was extended to persistence to elementary algebra there was absolutely no statistically significant 65 correlation found. Looking for correlations between the five components and student performance, a correlation matrix was created for the students’ pre-algebra and elementary algebra grades along with the four components being investigated (required discussion board posting, use of mathematics display software by students, exclusively multiple choice examinations, and video lectures). All 834 students who took pre-algebra online were used to create the matrix. The correlation matrix is given in table 4.10 showing only the columns correlating pre-algebra grades and elementary algebra grades with each other and the five components in question. A second matrix was then created to examine possible correlations between elementary algebra grades and the five components in question, this time only with students who passed pre-algebra and moved on included. The second matrix is given in table 4.11. 66 Table 4.10 Correlation Matrix – Components with pre-algebra grades Pre-algebra grade Elementary Algebra Grade Pearson Correlation 1 .584 ** Sig. (2-tailed) .000 Pre-algebra grade N 834 834 Pearson Correlation .584 ** 1 Sig. (2-tailed) .000 Elementary Algebra Grade N 834 834 Pearson Correlation .108 ** .069 * Sig. (2-tailed) .002 .048 Discussion Boards N 834 834 Pearson Correlation -.024 -.032 Sig. (2-tailed) .490 .358 Math Display Software N 834 834 Pearson Correlation -.003 .056 Sig. (2-tailed) .936 .109 Multiple Choice Exams N 834 834 Pearson Correlation -.026 -.076 * Sig. (2-tailed) .453 .029 Video Lectures N 834 834 **. Correlation is significant at the 0.01 level (2-tailed). a. Cannot be computed because at least one of the variables is constant. *. Correlation is significant at the 0.05 level (2-tailed). 67 Table 4.11 Correlation Matrix – Components with Elementary Algebra grades for all students who took pre-algebra at RCCD Elementary Algebra Grade Pearson Correlation 1 Sig. (2-tailed) Elementary Algebra Grade N 440 Pearson Correlation .021 Sig. (2-tailed) .666 Discussion Boards N 440 Pearson Correlation .002 Sig. (2-tailed) .963 Math Display Software N 440 Pearson Correlation .099 * Sig. (2-tailed) .038 Multiple Choice Exams N 440 Pearson Correlation -.083 Sig. (2-tailed) .081 Video Lectures N 440 *. Correlation is significant at the 0.05 level (2-tailed). a. Cannot be computed because at least one of the variables is constant. **. Correlation is significant at the 0.01 level (2-tailed). In agreement with earlier findings, there was a significant positive correlation between a student’s pre-algebra grade and their grade in the subsequent elementary algebra grade. There were no significant correlations between grades in either pre- algebra or the subsequent elementary algebra class and the use of mathematics display software. When all online pre-algebra students were considered, there were similarly no significant correlations between grades or the use of exclusively multiple-choice examinations. However, when only those students who passed pre-algebra online and chose to take elementary algebra were considered, a significant positive correlation was 68 found between the elementary algebra grades and the use of exclusively multiple-choice examinations in an online pre-algebra class. There was no significant correlation between the use of video lectures and pre- algebra grades, however, a significant positive correlation was found between the required use of discussion boards and grades in both pre-algebra and elementary algebra. When only considering student who passed pre-algebra and moved on to elementary algebra the significance was lost. Finally, while there was no significant correlation between the use of video lectures and pre-algebra grades, there was a small, but significant negative correlation between the use of video lectures in an online pre-algebra class and grades earned in an elementary algebra class. This correlation was lost when only considering students who passed and moved on to an elementary algebra class. Summary of Statistically Significant Findings Part one of the study revealed statistically significant relationships between taking pre-algebra online and both pre-algebra retention and grades. Online pre-algebra classes had higher retention than face-to face pre-algebra classes and students in online pre- algebra classes earned higher overall grades than students in face-to-face classes. This statistical significance extended into elementary algebra classes but only for students who earned an “A” or “B” in pre-algebra. Students who earned an “A” or “B” in pre-algebra were statistically more likely to earn a higher grade than their colleagues from traditional face-to-face classes, but for students who earned a “C” in pre-algebra, no statistically significant relationship was found. 69 Part two of the study revealed statistically significant correlations between pre- algebra grades and the required use of discussion boards by students. When discussion boards were a required part of the course, both retention and grades were higher. These relationships did not carry over to Elementary algebra persistence rates or grades. There was a weak, but significant positive relationship between the use of multiple-choice examinations in online pre-algebra and grades in the subsequent elementary algebra class. 70 CHAPTER FIVE FINDINGS, CONCLUSIONS, AND IMPLICATIONS Online education is the fastest growing modality for delivering education ever seen. In just a few decades online education evolved from the combination of a long established, but largely unpopular, system of distance education modalities (i.e. correspondence courses or tele-courses) and the advent and rapid proliferation of personal computers and the Internet. Online enrollments now account for more than one in five higher education enrollments in the United States (Allen & Seaman, 2008, p.5). At the same time, the need for mathematics remediation has never been higher for in coming college students. Nowhere is this need more obvious than in California’s Community Colleges where nearly 90% of incoming students test into basic skills/remedial mathematics (Moore & Schlock, 2007, p. 14). As would be expected, a result of this combination of growth trends is the rapid growth in basic skills/remedial mathematics courses taught online. The U.S. Department of Education recently published a meta-analysis and review of online learning studies, finding that online and hybrid classes produced stronger student learning outcomes than do solely face-to-face courses (2009, p.18). The goal of basic skills courses in California Community Colleges reaches beyond simply achieving an individual courses’ students learning outcomes, additionally aspiring to help students gain “learning skills and study skills which are necessary for students to succeed in college-level work” (Center for Student Success, 2007, p.13). These two points do not 71 necessarily intersect leaving a gap in the literature that serves as the target of the research in this dissertation. The main objective of this dissertation is to explore correlations between online classes and common online course components with student performance and persistence in basic skills mathematics courses. To do that, longitudinal student data was collected from Riverside Community College District consisting of all student records form all pre- algebra and elementary algebra courses taught at the three-college district. Student records were coded by the RCCD Institutional Research Department to mask the identity of individuals but still allow for tracking progress through basic skills mathematics. In addition to the records provided by the Institutional Research, all instructors who taught pre-algebra online were identified using published schedules and asked to identify whether or not they had used each of the five course components being studied: (1) the use of video lectures to deliver content, (2) required use of discussion boards, (3) student use of mathematics display software, (4) exclusively multiple-choice exams, and (5) proctored examinations. The study was done in two main parts. The first part was an analysis and comparison of students persistence and performance of students who took pre-algebra online versus face-to-face at Riverside Community College District. The primary unit of analysis in the first part was the online versus face-to-face status of the pre-algebra classes. Students’ persistence, grades in pre-algebra, and grades in the subsequent elementary algebra classes were all used as dependent variables. 72 The second part of the study consisted of evaluating the five common components of online mathematics courses identified in the study: (1) the use of video lectures to deliver content, (2) required use of discussion boards, (3) student use of mathematics display software, (4) exclusively multiple-choice exams, and (5) proctored examinations. Serving as the independent variables, connections and correlations were sought with the dependent variables: persistence and grades in pre-algebra online courses, persistence to elementary algebra and grades earned subsequent elementary algebra courses. Findings Initially looking at persistence and possible relationships to taking pre-algebra online versus face-to-face, it was found that students who took pre-algebra online were significantly less likely to drop and more likely to earn a grade than those who took pre- algebra in the traditional face-to-face setting. Interestingly, this relationship did not extend to students persisting into elementary algebra but did extend among those students who persisted into elementary algebra. Students who took pre-algebra online were significantly more likely to complete their elementary algebra course than students who had taken pre-algebra face-to-face. In both situations where a statistically significant relationship was found, beginning with an online pre-algebra course was advantageous and higher persistence rates were seen than when students began with a traditional face- to-face course. Extending the analysis to grades, students in online pre-algebra courses earned significantly higher grades than students from face-to-face pre-algebra courses. The 73 mean GPA for all online pre-algebra students was a 2.3, well within the “C” grade range and passing, while the mean GPA for all students in an face-to-face pre-algebra was not passing at 1.7. Significance held when considering only those students who passed pre- algebra and continued to elementary algebra with online pre-algebra students earning a “B” average of 3.2 and face-to-face students earning a “C” average of 2.9. Tracking those students to elementary algebra, it was found that students who had taken pre-algebra online had statistically significant higher grades in elementary algebra than students who had taken pre-algebra face-to-face. Disaggregating the data by pre- algebra grade, however, revealed that the significance was only true for students who earned an “A” or “B” in pre-algebra and not for students who had earned a “C”. Thus students who earned an “A” or “B” in their pre-algebra course tended to earn higher grades in elementary algebra after taking an online pre-algebra versus those who took a face-to-face pre-algebra course. For students who earned a “C” in there pre-algebra course, there no significant difference in elementary algebra grades after after pre-algebra online versus face-to-face. Analysis of the relationships between the five common course components studied and persistence reveals only the use of discussion boards in an online pre-algebra class was significantly correlated to completing an online pre-algebra class. No significant correlation was found between any of the other components and student completion rates in online pre-algebra classes. Furthermore, none of the five components studied were significantly correlated with student persistence to elementary algebra. 74 Examining grade performance in conjunction with the five components studied, the use of discussion boards again was the only component with a significant correlation. The use of discussion boards was positively correlated with higher grades in online pre- algebra classes. Similarly, the correlation did not extend into elementary algebra classes. Interestingly, where there was no correlation between the use of exclusively multiple- choice examinations and pre-algebra grades, there was a significant positive correlation between the use of exclusively multiple-choice examinations and grades earned in subsequent elementary algebra classes. Students who took an online pre-algebra class that used only multiple-choice examination for student evaluations earned higher grades in their elementary algebra classes. Conclusions Based on the sample of student data and information about the use of common online class components collected, several conclusions became apparent throughout the study. Initially, there is statistically significant evidence to support the claim that online classes for mathematics remediation have a place within the community college setting and are providing, on average, an equivalent educational opportunity (with respect to learning basic skills mathematics) as traditional face-to-face classes. Furthermore, Dr. A. Dooley found significant evidence that prior computer attitude and/or computer competency does not provide a relative advantage or disadvantage on success in basic skills mathematics courses (Dooley, 2001). This further reinforces the claim that 75 teaching basic skills mathematics online is at least as good as the traditional face-to-face methods of instructors and often superior. Students who enrolled in an online pre-algebra class were more likely to complete the class and for those who continued to elementary algebra were more likely to complete elementary algebra as well. The data in this study did not provide any evidence that students who took online pre-algebra classes were more likely to persist through the basic skills regime (i.e. into elementary algebra). This, however, is not evidence to the contrary either because, as Folkers pointed out, colleges offering online courses are competing in a world marketplace rather than the traditional geographic spheres of influence of traditional institutions (2005). This means that many students are likely attending several colleges, and it is likely that students who did not persist at RCCD from an online pre-algebra class did so at another institution. Students who took pre-algebra online also tended to earn significantly higher grades than their counterparts in face-to-face courses. Interestingly, when students were tracked into elementary algebra, those who had taken pre-algebra online only maintained their grade advantage if they earned an “A” or “B” grade in the pre-algebra class. For students who earned a “C” in pre-algebra, there was no significant difference in elementary algebra grades between students who had taken pre-algebra online versus face-to-face. This is evidence to support the claim that online mathematics classes provide superior educational opportunities for students who are inclined to excel and no relative advantage or disadvantage for struggling students. 76 When the results of this study are considered in conjunctions with Dooley’s 2001 dissertation, there is strong evidence that the effect of taking a basic skills class online is relatively short lived and does not extend far into a student’s educational career. Dooley found evidence that students who took Elementary algebra face-to-face had a relative grade advantage over students enrolled in a “Computer Mediated Learning” course but that this advantage did not extend into the subsequent intermediate algebra class (2001). These results support the evidence from this study that the positive effects seen in taking pre-algebra online seem to diminish into Elementary Algebra and, by extension, will be essentially absent when a students enrolls in Intermediate Algebra. The second part of this study was to look at common course components of online mathematics classes and look for correlations to students persistence and/or success. Surprisingly very few correlations were found between success these course components and either students persistence or success. The use of discussion boards in an online pre- algebra class was the only component correlated with both students persisting through pre-algebra and higher success rates. This correlation did not, however, continue with students into the subsequent elementary algebra class. This is likely because when groups of students are learning together online, support mechanisms generally influence only how students interact and not the amount they learn (U.S. Department of Education, 2009). Student interaction engages students in the class and material keeping them on task and helping them to self-monitor their own learning thus encouraging students to finish the course and study necessarily to earn a good grade. 77 Interestingly, the use of multiple choice examinations in an online pre-algebra class correlated positively with grades in the subsequent elementary algebra class. There was no correlation with grades in the pre-algebra class using the multiple-choice examinations. This may be as a result of very well written multiple-choice examinations that provide students with all common incorrect answers! This may force students to understand the mathematics in order to perform well on assessments but not provide for reverse engineering of answers and, hence, inflated grades. There is also the possibility of the small sample size of classes that did not use multiple-choice examinations creating a statistical anomaly. More research is needed to gain a greater understanding of this. Overall, teaching basic skills mathematics online provides no long-term advantage or disadvantage for students’ progression through mathematics. Any initial benefits realized quickly diminish in the next classes or two, leaving students on equal footing with their face-to-face counterparts. Exactly why this is the case cannot be determined from the data collected and is beyond the scope of this study, but strong evidence exists supporting the claim that teaching basic skills mathematics online is at least as effective as traditional face-to-face methods. Implications and Future Research The research and literature on online education spans the full spectrum of opinions and conclusions on the effectiveness of teaching online. In his research, Russell (2001) sites hundreds of studies showing “no significant difference” exists between the outcomes of online versus face-to-face classes. The recently released U.S. Department of 78 Education’s meta-analysis of online learning studies found that classes with online learning on average produce stronger learning outcomes than traditional face-to-face classes. The evidence in this study further supports this claim. What seems to be overlooked and needs to be strongly considered is that for online mathematics classes, this advantage seems to be lost within a semester of taking the online class. Thus to simply state that online education is producing stronger student learning outcomes may be misleading and even irresponsible. Why this is the case is unknown and unexplored; too many considerations have not been examined to make a determination on such a question. The evaluation methods of online classes versus traditional face-to-face methods may not equivalent. The fact that the online advantage quickly fades provides support to the argument that online students are being evaluated less rigorously than face-to-face students. Alternatively, it is well known that many students have a phobia of mathematics and taking assessments at a time of their choosing, in a location of their choosing may contribute to a comfort that influences their performance on exams. Also noted by the U.S. Department of Education is that the advantages observed for online learning conditions are likely not linked to the instructional medium but more likely linked to the extra time and thought instructors put into planning, designing, and implementing an online course (2009). This brings the discussion of course quality back to teacher quality. An evaluation of teacher quality is beyond the scope of this study, is filled with social and political constraints, and is likely to be a large part of the online advantage being seen. 79 Another piece of the puzzle arose when instructors were asked if there was anything further they would like to share about their online classes: it was mentioned that instructors were experimenting with student-paced courses. Students are allowed control of the class individually provided they meet specific deadlines and trip triggers that allow them to work ahead, i.e. a score threshold on a quiz, homework assignment, or examination. These comments are supported by findings that online learning can be enhanced by giving learners control of their interactions and allowing for self-monitoring of understanding (U.S. Department of Education, 2009). Future research in this area would be a valuable contribution to the literature on online education. Especially for community colleges with primarily commuter students and with growing numbers of working adults and parents returning to college; students have limited times to work on their classwork and may not always be able to follow schedules set but instructors. As indicated in chapter 3, limitations of this study include both the lack of student input and course quality considerations. Future research is needed to explore both of these variables. Research has shown online students tend to be older than traditional college students (Tallent-Runnels, 2006) and have familial responsibilities (Folkers, 2005). These students are likely to have a different set of goals, priorities, and motivations for enrolling in college. It is reasonable to assume that many of these students enroll in online classes because of the time constraints their personal and familial lives put on them. For just these students, would the findings in this study be the same or similar? Are these students the reason for the found advantage of taking online classes? 80 Students self-selecting into college classes prevents a true experimental study of to answer questions about students inputs; however, quasi-experimental studies similar to this one could help to tease-out whether the online classes are providing the advantages seen or if it is student quality. These questions could be explored by considering and controlling for known advantages and disadvantages of colleges students like age, race/ethnicity, socioeconomic status and academic preparation. Additionally, larger databases could allow researchers to consider student GPA, number of units attempted/completed, financial aid status, and whether or not students take mathematics in sequential semesters or with semesters off between math classes. Of interest is the design and composition of online classes. 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Abstract (if available)

Abstract Online education is a modality of teaching that has proliferated throughout higher education in such a rapid form and without any guidelines that its quality and merit is largely unknown, hotly debated, and still evolving. Institutions have used online education as a method of reducing costs and increasing enrollments and students have flocked to online classes for their convenience and often perceived ease. This is very apparent in California’s community colleges were students are filling online course offerings in record numbers.

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Asset Metadata

Creator Rey, Jason Goering (author)

Core Title The effects of online courses for student success in basic skills mathematics classes at California community colleges

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 06/04/2010

Defense Date 05/18/2010

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag community college,math,mathematics,OAI-PMH Harvest,online

Place Name California (states), Riverside (counties)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Hentschke, Guilbert C. (committee chair), Dwyer, David C. (committee member), Sundt, Melora A. (committee member)

Creator Email jasongpa@usc.edu,jasonrey1618@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3111

Unique identifier UC175563

Identifier etd-Rey-3788 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-332845 (legacy record id),usctheses-m3111 (legacy record id)

Legacy Identifier etd-Rey-3788.pdf

Dmrecord 332845

Document Type Dissertation

Rights Rey, Jason Goering

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu