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Bendickson, Mary M.
The impact of technology on community college students' success in remedial/developmental mathematics
h [electronic resource] /
by Mary M. Bendickson.
[Tampa, Fla.] :
University of South Florida,
Thesis (Ed.D.)--University of South Florida, 2004.
Includes bibliographical references.
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ABSTRACT: Increased institutional accountability and fiscal constraints coupled with most community college students being required to take at least one remedial/developmental course indicates a need to find the best way to deliver these classes. Institutions are expanding alternate delivery formats to meet student expectations. Is using technology best for students in remedial/developmental courses? This study investigated effectiveness of technology-assisted instruction for remedial/developmental math in Florida community colleges. Technology has emerged as potentially enhancing student success; however, it is expensive. If research shows that students benefit from technology in remedial/developmental courses, then funds spent to provide instruction through technology are validated.However, if research does not show remedial/developmental courses with a technology component are more effective than courses delivered traditionally, then spending funds for technology in those courses becomes questionable. The research questions for this study asked whether the delivery format of gatekeeper remedial/developmental math courses varied by institutional size. Was there a relationship between student success and technology-assisted delivery of "gatekeeper" remedial/developmental math classes? The study asked if such a relationship existed when controlling for placement test scores. To answer these questions, the research compared student success rates in three delivery formats--traditional, hybrid, and computer-based. Results showed that small institutions favored traditional delivery of remedial/ developmental math. Medium institutions offered traditional and hybrid delivery in similar proportions while larger institutions favored hybrid delivery.Results also showed that students in traditional delivery sections were likely to be just as successful, or slightly more successful, than students in hybrid and computer-based delivery courses, Students with higher placement test scores in remedial/developmental math were clearly more successful in courses delivered via traditional instruction. Implications from this study suggest that the introduction of a technology component to remedial/developmental math courses does not seem to be more effective in helping students successfully pass remedial/developmental math classes. If an institution does not have funds to invest in technology for remedial/developmental math students, which may be especially true for smaller institutions, no harm is done in delivering instruction in remedial/developmental math via traditional methods. Students may actually benefit from the traditional delivery format in remedial/developmental math courses.
Adviser: Ignash, Jan M.
x Educational Leadership
t USF Electronic Theses and Dissertations.
The Impact of Technology on Community College StudentsÂ’ Success in Remedial/Developmental Mathematics by Mary M. Bendickson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Education Department of Adult, Career, and Higher Education College of Education University of South Florida Major Professor: Jan M. Ignash, Ph.D. Jeffrey D. Kromrey, Ph.D. Kathleen M. Moore, Ph.D. William H. Young, Ed.D. Date of Approval: June 25, 2004 Keywords: effectiveness, delivery format, instructional delivery, pre-collegiate, post-secondary Copyright 2004, Mary Bendickson
Dedication I dedicate this work to my mother and father, Edwina and John Griffin, for instilling in me a love for learning; to my husband, Jim, for unwavering support; and to my children, Ginny, Julie and Philip, who ha ve afforded me the time to pursue this endeavor as I spent countless hours as resear cher instead of mother. To my grandsons, Jared and Jack, I challenge you to continue this legacy. I also dedicate this work to my friends, who have listened to me and encouraged my efforts.
Acknowledgments I wish to acknowledge and express my a ppreciation for the professional assistance of my committee: Dr. Jan Igna sh, chair, Dr. Jeffrey Kromrey, Dr. Kathleen Moore, and Dr. William Young. I am thankful for the pati ence and guidance from Dr. Ignash, the support and gentle nudging from Dr. Kromrey and Dr. Moore, and the visionary thinking from Dr. Young. I am indebted to Dr. John Pezullo fo r his counsel, advice, and assistance through the whole process. I am thankful to Dr. Ed Dascher, who continues to remind me during each conversation that learning never stops. I am also appreciative to those who took the time to participate in the p ilot coding and proofreading. Additionally, I acknowledge and applaud the contributions that teachers of re medial/developmental math make in the lives of their students.
i Table of Contents List of Tables................................................................................................................. ....iii List of Figures................................................................................................................ ......v Abstract....................................................................................................................... .......vi Chapter One Introduction and Background.......................................................................1 Statement of the Problem.........................................................................................3 Significance of the Problem.....................................................................................5 Purpose.....................................................................................................................9 Research Questions....................................................................................10 Hypotheses.................................................................................................11 Definition of Terms....................................................................................12 Limitations and delimitations................................................................................18 Summary................................................................................................................21 Chapter Two Review of the Literature............................................................................23 Curriculum.............................................................................................................24 Studies by the Center for th e Study of Community Colleges....................24 Florida Curriculum Study..........................................................................27 Remedial/Developmental Education.....................................................................30 Teaching Approaches.................................................................................31 Student Success..........................................................................................33 Technology in Remedial/Developmental Courses.....................................35 Instructional Technology.......................................................................................37 Summary and Synthesis of Literature Review.......................................................43 Chapter Three Method.....................................................................................................45 Introduction............................................................................................................45 Research Design.....................................................................................................48 Population..............................................................................................................49 Instrumentation/Measures......................................................................................49 Procedures..................................................................................................51 Data analysis..............................................................................................53 Summary................................................................................................................54
ii Chapter Four Results........................................................................................................5 5 Summary of Data Collection.................................................................................55 Data Analysis: Quantitative design........................................................................62 Research Question 1..................................................................................62 Research Question 2..................................................................................76 Research Question 3..................................................................................78 Research Question 4..................................................................................88 Summary................................................................................................................90 Chapter Five Summary of Findings, Conc lusions, and Implications for Practice and Research............................................................................................................... ...92 Method summary...................................................................................................93 Summary of findings..............................................................................................93 Conclusions............................................................................................................98 Limitations.............................................................................................................99 Implications for practice........................................................................................99 State level implications............................................................................100 Institutional Implications.........................................................................101 Implications for research......................................................................................105 Summary..............................................................................................................107 References..................................................................................................................... ...109 Appendices..................................................................................................................... ..117 Appendix A: Configuration of Remedi al/Developmental Math Sequence.........118 Appendix B: Mathematics Courses Offered in Fall 2002 in Florida Community Colleges........................................................................................119 Appendix C. Coding Decision Rules...................................................................121 About the Author...................................................................................................End Page
iii List of Tables Table 1 CSCC Curriculum studies .........................................................................25 Table 2 Remedial/developmental course portion of all math courses in 2000.................................................................................................29 Table 3 Sections of all remedial/d evelopmental math courses offered in each delivery format by institutional size........................................64 Table 4 Distribution of deliver y formats in all remedial/ developmental math courses................................................................65 Table 5 Proportion of all remedial/developmental math sections by delivery format ...............................................................................66 Table 6 Distribution of all remedi al/developmental math sections by delivery format and course..............................................................67 Table 7 Proportion of gatekeeper courses compared to all remedial/ developmental math courses................................................................71 Table 8 Percentages of all remedi al/developmental math courses compared to gatekeeper remedial/developmental math courses by delivery format and institutional size.................................73 Table 9 Number of gatekeeper remedial/developmental math sections by in stitutiona l size................................................................74 Table 10 Average class size of ga tekeeper remedial/developmental math sections by delivery format.........................................................76 Table 11 Analysis of passing rates in gatekeeper sections of remedial/ developmental math by delivery format..............................................77 Table 12 Analysis of variance summary table Student success and delivery format in gatekeeper remedial/ developmental math sections...............................................................78
iv Table 13 Analysis of covariance su mmary table delivery format while controlling for CPT score in gatekeeper remedial/ developmental math sections..............................................................79 Table 14 Mean CPT score of gate keeper remedial/developmental math by delivery method.....................................................................80 Table 15 Mean placement test scores for each delivery format................................84 Table 16 Pass rates in sections when faculty members taught in multiple delivery formats...........................................................................89
v List of Figures Figure 1 Average class size in gate keeper remedial/developmental math classes.........................................................................................75 Figure 2 Comparison between CPT sc ore and pass rate by delivery method..................................................................................................81 Figure 3 CPT score and pass rates by de livery format for all gatekeeper remedial/developmental math sections...............................................83 Figure 4 Distribution of passing ra tes in three delivery formats..............................84 Figure 5 Correlation between CPT score and pass rate for traditional delivery sections of all gatekeeper remedial/developmental math....................................................................................................85 Figure 6 Correlation between CPT scor e and pass rate for hybrid delivery sections of all gatekeeper remedial/developmental math...................86 Figure 7 Correlation between CPT score and pass rate for computer-based delivery sections of all gatekeeper remedial/developmental math....................................................................................................87
vi The Impact of Technology on Community College StudentsÂ’ Success in Remedial/Developmental Mathematics Mary Bendickson ABSTRACT Increased institutional accountability and fiscal constraints coupled with most community college students be ing required to take at leas t one remedial/developmental course indicates a need to find the best way to deliver these classe s. Institutions are expanding alternate delivery formats to meet student expectations. Is using technology best for students in remedi al/developmental courses? This study investigated effectiveness of technology-assisted instruction for remedial/developmental math in Florida co mmunity colleges. Technology has emerged as potentially enhancing student success; however, it is expensiv e. If research shows that students benefit from technology in remedial/d evelopmental courses, then funds spent to provide instruction through t echnology are validated. However, if research does not show remedial/developmental courses with a technology component are more effective than courses delivered traditionally, then spe nding funds for technology in those courses becomes questionable. The research questions for this study asked whether the delivery format of gatekeeper remedial/developmental math courses varied by institutional size. Was there a relationship between student success and tec hnology-assisted delivery of Â“gatekeeperÂ” remedial/developmental math classes? The st udy asked if such a relationship existed
vii when controlling for placement test scores. To answer these questions, the research compared student success rates in three delivery formats--traditional, hybrid, and computer-based. Results showed that small institutions fa vored traditional delivery of remedial/ developmental math. Medium institutions offered traditional and hybrid delivery in similar proportions while larger institutions favored hybrid delivery. Results also showed that students in traditional delivery sections were likely to be just as successful, or slightly more successful, than students in hybrid and computer-based delivery courses, Students with higher placement test scores in remedial/developmental math were clearly more successful in courses delivered via traditional instruction. Implications from this study suggest that the introduc tion of a technology component to remedial/developmental math c ourses does not seem to be more effective in helping students successf ully pass remedial/developmental math classes. If an institution does not have funds to invest in technology for remedial /developmental math students, which may be especially true fo r smaller institutions, no harm is done in delivering instruction in remedial/developm ental math via traditional methods. Students may actually benefit from the traditional delive ry format in remedial/developmental math courses.
Chapter One Introduction and Background Community colleges are unique institutions in the American system of higher education primarily because of the comprehensiveness of the curriculum. The community college curriculum must reflect the needs of students and prepare them for their goals. Students who attend community colleges have various goals including preparation for transfer to a four-year institution, education for employment, or improvement of skills not mastered in high school. The curriculum c onsists of transfer general education, vocational, and developmental courses (Schuyler, 1999). While FloridaÂ’s community colleges have a large component of transfer courses, they also provide the first step into the college world for many students in remedial/ developmental (defined on p. 17) courses. St udents who score high enough on the college level placement test (defined on p. 12) may take courses at college level, but those who do not score high enough on the test may not ta ke courses at the college level. Since almost 60% of community college students in Florida are required to take at least one remedial/developmental course (Windham, 4), Florida community colleges must provide effective remedial/developmental programs. The Florida legislature has charged community colleges with sole responsibility for remediation: Â“Public postsecondary educ ational institution students who have been
2 identified as requiring additional preparation pursuant to subsection (1) shall enroll in college-preparatory or other adult educa tion pursuant to s. 1004.93 in community colleges to develop needed college-entry skillsÂ” (Assessment a nd Accountability, 2002, Chapter 1008, 4a). Beyond the fact that Fl oridaÂ’s statutory directive places the responsibility for remediation directly on th e community colleges in Florida, placement of remediation within commun ity colleges throughout the Un ited States is common. The 1995 National Center for Education Statistics (NCES) study found that state policies tend to name community colleges as the preferre d providers of remediation (USDE, 1995). The Florida statutory directive establis hes postsecondary remediation as a core part of the community college mission with li ttle prescriptive definition given to how remediation is to be provided. The lack of specific direction about the remedial/ developmental program has produced a wide variet y of course offerings in that portion of the curriculum. A study of the math courses o ffered at the 28 Florida community colleges shows the extent of math remediation needed. A quarter of the Fall 2000 Florida community college math course sections (Bendickson, 2000) were remedial/ developmental math classes offered in several formats. The community colleges must accommodate a large portion of students in remedial/developmental courses while operating with diminishing resources. In the academic year 2000-01, the state funded $4752 per FTE compared to $4340 per FTE in 2003-04 (Shugart, 2004). This is but one example of the diminishing resources. The combination of decreased funding and responsibility for remediation in the community colleges creates a necessity to maximize cost-effectiveness while still providing the needed remediation with maximum student success.
3 Technology has emerged as one possibility to enhance student success; however, technology is expensive. If research shows that students benefit from technology (defined on p. 17) in remedial/developmental courses, th en the funds spent to provide instruction through technology will be well spent. However, if research does not show remedial/ developmental courses delivered with a t echnology component more effective than courses delivered through traditional instruct ion, then spending funds for technology in remedial/developmental courses becomes questionable. Although there are multiple factors that influence the effectiveness of any instructional method, technology in instruction is one factor that can be controlled. The purpose of this research is to examine the effectiveness, as measured by student succ ess, of technology-assi sted instruction for remedial/developmental math courses in Florida community colleges. Statement of the Problem In addition to the fact that community colleges bear the responsibility of remediation in Florida, most Floridians believe that hi gh school graduates are not academically prepared to enter college. Th e public expects the community colleges to resolve this problem (Immerwahr, 2000). Th e publicÂ’s expectation that remediation should be offered in the community college s matches the legislatureÂ’s assignment of remediation to the community colleges. Because FloridaÂ’s community colleges are responsible for providing remediation at the college level, remedial/developmental math courses are offered at each of the stateÂ’s 28 community colleges. Two particular developments have occurr ed in Florida recently that make it necessary for community colleges to pay attention to remedial/developmental programs --
4 one legislative and the other fiscal. The firs t development is a legislative development and has far-reaching effects on the entire Florida public education system. The implementation of a seamless K-20 education sy stem in Florida with the passage of the Florida Education Governance Reorga nization Act of 2000 (House Bill 2263, 2000) changed the educational governance structure in Florida. The Act has focused attention on the missions of each segment of educati on in the state. While the K-12 schools and four-year colleges and universities have clar ity of mission (at least in the publicÂ’s mind), the community colleges must carve a unique and secure niche in the educational landscape. The Florida Reorga nization Act of 2000 establishe d the newly created Florida Board of Education as the sole governing body for public education in Florida. The new K-20 structure also empowered th e Board of Education to set standards and to coordinate with private education in the state. The Board of Regents and the State Board of Community Colleges were dissolved under the Florida Reorganization Act of 2000, placing university and community college govern ance at the local institutional level with Boards of Trustees. Although Florida statut e broadly assigns guide lines delineating the missions for universities, community colle ges, and K-12 schools, each level now has more latitude in providing instruction and services prev iously governed at the state agency level. This freedom has led to a perception of Â“mission squeezeÂ” in community colleges. However, one area remains inviolat e for community colleges. By statute (FL Stat. 1008) the responsibility fo r remedial instruction and se rvices is assigned to the community colleges. The second development is a fiscal devel opment concerning fiscal implications as a reduction in state dollars per student. Although the total state budget for community
5 colleges has recently shown an increase, th e effect of enrollmen t growth actually produced a drop in dollars funded per student The current state funding levels would require more than $100 million to restore funding levels to the levels of two years ago (E. Cisek, Vice Chancellor of the Florida Department of Education, Community College Office of Information and Finance, pe rsonal communication, March 31, 2003). The apparent increase in dollars decreased the sense of urgency in state funding. Newman (2003) painted a different picture. Â“The cuts in state appropriations are likely to do real harm to higher education.Â” Attention must be given to providing cost-effective delivery for remediation because funding for higher educa tion has not consistently kept pace with enrollment growth. This study will explore various ways that remedial/developmental math is offered in FloridaÂ’s community colleges and analyze on e factor that may be a realistic predictor of student success -delivery format. The re searcher expects to find courses delivered completely through technology; traditional in-class, lecture-based courses; and a hybrid of the two delivery methods. What delivery method for remedial/developmental math courses provides the best opportunity for success to the students who enroll in the courses? Significance of the Problem A central mission of the community college is to provide reme diation for students who are not prepared for college level courses. All expenditures in higher education must be justified because of the focus on qua lity, increased acco untability, and funding constraints. Declining funding and an assi gnment to provide remedial/developmental
6 courses make it critical to know how the cour ses should be structured to best serve both the institution and the student. Due to FloridaÂ’s legislative directive, there are significan t portions of the community college curriculum dedicated to remedial/developmental courses. In Fall 2000, more than 10% of the to tal community college credit curriculum in Florida was remedial/developmental course sections. Sin ce the state does not prescribe how remedial/ developmental math is to be offered, ther e is no common structure of those courses within the 28 Florida community colleges. Each of the 28 community colleges has its variation of the full remedial/ developmental track. A typical track for re medial/developmental courses in Florida community colleges includes MAT 0002, commo nly called College Preparatory Math, and MAT 0024, commonly called College Prepar atory Algebra. The MAT 0002 course is also offered as MAT 0002C and MAT 0024 as MAT 0024C; the C indicates that it is a combination course -part lecture and part laboratory formats. W ithout the C designation, MAT 0024 is a lecture course. There are some s ections identified in the printed schedules as C courses without any specification about how the laboratory portion of the class would be conducted. There are also combin ations of these two courses in which arithmetic and algebra are in one course often called Integrated Math and typically identified as MAT 0012, although other numbers may be used. MAT 0024, College Preparatory Algebra, is often the gatekeeper (defined on p. 14) remedial/developmental course because it concludes w ith the student taking the stat e exit exam. Regardless of the remedial/developmental track at a given inst itution, passing the state exit exam is the
7 single common requirement for a student to progress from remedial/developmental courses into college level math (defined on p. 12) courses. A question that flows from the extent to which technology is used in remedial/ developmental math relates to the size of the institution. Is it accurate to assume that larger colleges offer more sections in a grea ter variety of formats? Does the size of the institution affect the variety of remedial /developmental courses that it offers? Examination of the curriculum will likely re flect lecture-based, technology-assisted, and hybrid courses. It appears logical to assume that a larger institution will offer more sections, but do more sections translate to greater variety in format or simply more instances of a course in the same deliver y format? Does greater variety of delivery formats translate into improved student succes s? These results are important only if the delivery formats are found to be good predictors of student success. If delivery formats are good predictors of student su ccess and the research shows th at the larger institutions offer more sections in greater variety, does the conclusion follow that students in smaller colleges are at a disadvantage? The results may be informative to smaller colleges in their spending decisions and may also provide leverage for the smaller institutions to pursue increased funding. To know if particular students seem to be disadvantaged, it is important to provide measurable data, rather than anecdotal comments, when faculty and administrators are making decisions about the delivery format for remedial/developmental classes. While knowledge of any advantage or disadvantage du e to institutional size does not provide clear or easy answer s, that knowledge may be valuab le in choosing how to present particular classes at instit utions of different sizes.
8 Once taught in traditional cl assroom lecture format, remedial/developmental math courses began to change with the in crease of technology in the classroom. Computerassisted courses hybrid courses modular format courses and online courses (defined on pp. 12-15) have added to the element of change. Active promotion of academic software to community colleges by vendors has produced a plethora of remedial/developmental math courses being taught in a computer-a ided format. Colleges might not question the assertions of the vendors or seek out resear ch that shows whether or not the academic software formats are successful and beneficial to the studen ts. Colleges may also assume that such research has been done without taking the time to investigate a particular program. Developmental education programs must be evaluated to correctly assess the effectiveness of the program. Do the community colleges in Florida weigh the student outcomes in making the choices to use technology in remedial/developmental math classes? Although many educators have expected a transformation in education with the available burgeoning technology, there is not su fficient information readily available to support the difficult decisions that institutions face in choosing between delivery formats (Gilbert, 1996, pp. 412-413). Boylan (1999) de scribes the need for teachers in good remedial/developmental programs to emphasize outcomes. Each institution must rely on recommendations from faculty and administra tors within its own community to choose whether or not to incorporate technology and if so, how to best incorporate technology into its classrooms. Each of these reasons (size, cost, or lack of research on effectiveness) is sufficient alone to require a serious l ook at the various formats in which remedial/developmental
9 math is offered to community college students. It is imperative that community college administrators and math faculty members ha ve a firm understanding of expected success rates among the different instru ctional delivery formats for remedial/developmental math courses when making decisions on the delivery format to be used. Since there is such variety in the delivery of remedial/devel opmental math courses offered in Florida community colleges, this study will focus on one of the facets of those course offerings: What is the most effective delivery format in which to offer remedial/developmental courses? Questions driving this study cente r on assessing the effec tiveness of remedial/ developmental math courses offered through technology-assisted de livery formats. Purpose The purposes of this study are (1) to expl ore the range of reme dial/developmental math in FloridaÂ’s community colleges and any relationship that may exist between community college size and the variety of re medial/developmental math classes offered, (2) to explore the relationship that may exist between student success and the delivery format of gatekeeper remedial/developmental c ourses, (3) to explore the relationship that may exist between student success and the de livery format of gatekeeper remedial/ developmental courses while controlling for in itial placement test scores, and (4) to explore the relationship that may exist between student success and the delivery format of the gatekeeper remedial/developmental courses while controlling for in structor influence. The variables of initial placement te st score and instructor influence will be included in this study because they may influence the chan ces of student success and can be isolated to eliminate any influence on student success.
10 The reductions in state funding coupled with an increased focus on student retention and success provide th e impetus for pursuing these questions. It is important from a student services perspe ctive to have information on student success and retention in remedial/developmental courses. It is also important for academic administrators and instructors to have information on which deli very formats provide the best combination of cost effectiveness with the highest possibl e student success. This is not to say that selection of the delivery format is tota lly a financial questi on, but the academic administrator should be aware of comparativ e data when choosing the delivery formats for classes. While online and computer-based co urses may seem to be at the cutting edge of technology, they should not be employed for that reason alone. Any format should be used only if it is effective fo r students and within the fiscal constraints of the college. Research questions. To support this research, the sp ecific research questions are: 1) What remedial/developmental math courses are offered in FloridaÂ’s 28 community colleges? Does the instructi onal delivery format of the remedial/ developmental courses offered in Flor idaÂ’s 28 community colleges vary by institutional size? 2) Is there a relationship between student success (defined on p. 17) and the technology-assisted delivery format of the gatekeeper remedial/ developmental math classes in Florida community colleges? 3) Is there a relationship between student success and the technology-assisted delivery format of the gatekeeper remedial/developmental math classes in
11 Florida community colleges while cont rolling for initial placement test scores? 4) Is there a relationship between student success and the technology-assisted delivery format of the gatekeeper remedial/developmental math classes in Florida community colleges while cont rolling for instructor influence? Hypotheses. The researcher expects to find the following results to the research questions in this study: 1) There is greater variety in the instru ctional delivery formats of remedial/ developmental math offered by institution size in Florida community colleges. 2) There is a significant difference at th e .05 level in the student success rate relative to the variety of format s of remedial/developmental math. 3) There is a significant difference at th e .05 level in the student success rate relative to the variety of formats of remedial/developmental math while controlling for initial placement test scores. 4) There is a significant difference at th e .05 level in the student success rate relative to the variety of formats of remedial/developmental math while controlling for instructor influence.
12 Definition of terms. Definitions for terms used throughout this study are as follow: 1) Academic software -Any computer software program designed to support and/or deliver academic instruction is included in the academic software category. The variety of academic software includes programs that are designed for use with college level classes as well as remedial/developmental math, reading, and writing. 2) Accuplacer -ACCUPLACER is a set of eight multiple-choice computerized placement tests in a range of English a nd math subjects designed to determine whether or not a student has the skills to be successful in college level courses (Accuplacer, 2003). The tests were deve loped with the help of faculty committees and are produced by The College Entrance Examination Board. 3) College level mathematics -College level mathematics includes any math course that is designed to be transferable to other institutions and exists in the statewide list of transferable courses. Tr ansferability is verified by the statewide common course numbering list. Common course names and prefixes for these math courses are shown in Appendix B. 4) College level placement test -A common placement test has been used at all 28 community colleges since July 1995 and is required by Florida State Statue 240.117 (4)(a). The Florida College EntryLevel Placement Test (FCELPT) is the Computerized Placement Test (CPT ) that is part of the ACCUPLACER system. Written versions are available for institutions that do not have computer
13 testing laboratories available. There is a scale for conversion of scores from other standardized tests that are sometimes used for college placement. 5) Computer-based instruction -A course that is coded as computer-based instruction meets in a computer lab or other classroom equipped with computers and utilizes a commercial software packag e with a tutorial format that students may use in a self-paced timetable. Indi vidual instructors may incorporate minilectures to the class as needed, or provi de one-on-one instruc tion to students as needed, but the main mode of instructi onal delivery is via the computer. The primary distinction in a computer-based c ourse is the role of the faculty member. The role of the faculty member assigned to a computer-assisted course is one of management rather than whole class instru ction. A course considered to be in the category of computer-assisted instruction is not the same course as one offered as independent study. Independent study secti ons are not included in this study. 6) Credit courses -Credit courses are those that award credit, including both courses that are designed to be transferable and courses that carry only institutional credit and are not designed to be transferable. 7) Developmental courses -Based upon a holistic appr oach that includes all forms of learning assistance, counseling, academic advisement and coursework, developmental courses provide instru ction in the discipline as well as motivational and attitudinal aspects to e nhance student success in college. These courses include traditional academic di sciplines such as reading, writing, and math as well as courses in life skills -college success or study skills.
14 8) Gatekeeper course -A gatekeeper course is the most advanced remedial/ developmental course in each community college. The gatekeeper course contains the state exit exam. 9) Hybrid integrated course -A hybrid course is one th at combines traditional lecture-based instruction with computer -assisted instruction. The student may have choices of how and when to complete the assignments or the instructor may prescribe the parameters of acceptable methods and/or timetables for completion of assignments. Additionally, a course w ill be coded as hybrid if lecture and lab components are listed as co-requisite. Th e lecture and lab may be listed in the printed schedule as separate sections. These separate sections will not be coded separately, but as a hybrid course since both portions are required in the same semester. 10) Independent study -An independent study course is one in which the instructor allows the student to choose from opti ons to complete course requirements. These options are designed by the inst ructor. Independent study courses do not have specific meeting times or places. 11) MAT 0002 -The Florida statewide common co urse numbering office lists the course content for MAT 0002 as including Â“addition, subtraction, multiplication and division of whole numbers; fractions ; decimals; and percentsÂ” (Florida DOE, Statewide Course Numbering System section). 12) MAT 0024 -The content of this course incl udes Â“language and operation on sets, operations on signed numbers, solving lin ear equations and inequalities in one variable, adding, subtracting, and multiplying polynomials, factoring: greatest
15 common factor, differences of squares, trinomials, and by grouping, applications of factoring: solving equations and reducing algebraic fractions, integer exponents: definitions, properties, and si mplifying expressions with negative and zero exponents, simplifying, multiplying, addi ng and subtracting square roots of monomial expressions, gra phing ordered pairs and lines ; determining intercepts of lines and applications of the above topicsÂ” (Flori da DOE, Statewide Course Numbering System section). 13) Modular course -A modular course is one that allows a student to progress through the complete remedial/developmen tal math sequence without obstacles created by time-on-task demands or separa te course levels. The instruction is likely organized into self-paced units or m odules that students complete at their own pace during designated class days times, and meeting rooms. Time constraints may require that one semester is completed before advancing to the next step in the remedial/developmental math sequence. 14) Online course -An online course is one that may be completed solely through use of the worldwide Web. These courses may be based on a variety of distance learning packages or may be instructor-designed courses. 15) Preparatory math courses -Preparatory math courses are those math courses that are remedial or developmental. Thes e courses are not generally transferable between institutions. The terms remedial, developmental, and preparatory math are often used interchangeab ly although there are distin ctions between the terms. All remedial/developmental math course s taught in Florida community colleges are identified in Appendix B.
16 16) Remedial courses -Using the medical paradigm the term remedial implies a need to improve basic skills due to a deficit or lacking from prior educational experiences. 17) Remedial/developmental courses -Often used interchangeably, the many terms describing pre-collegiate c ourses are distinctive. R ecognizing philosophical differences and elements of validity that exist between the terms remedial and developmental (Ignash, 1997, p. 3), this st udy will use the hybrid term remedial/ developmental to represent those pre-colleg iate courses. Remedi al is a term often used in academic circles to describe student deficiencies, implying that something needs to be fixed (Cazarra, 1999). Remedial education only focuses on one facet of the individual student. C onversely, a holistic approach identifies these same courses as developmental. Developmental education addresses academic preparedness, diagnostic assessm ent and placement, development of general and discipline-speci fic learning strategies, and affective barriers to learning. Â“Developmental education includes, but is not limited to all forms of learning assistance . counseling . acad emic advisement . and coursework (National Association for Developmental Education, Definition section, 3). These distinctions highlight the one-dimen sional approach to remedial education compared to the holistic appro ach to developmental education. 18) Statewide exit exam -The statewide exit exam is written by a statewide group of instructors. Two forms of the test are written and each institution has the freedom to create its own test from within th e items provided. The institutions are given
17 the number of items to be tested from each skill area and the two forms have about 30% overlap. This test is rewritten annually, but the tests used in any particular year are made from the same bank of questions. The state exit exam is test is not normed (K. Fearon, Office of Assessment and School Performance, Florida Board of Education, pe rsonal communication, March 31, 2003). 19) Student success (defined for this study) -Although many other factors can be used to define student success, for this study, completion of the remedial/ developmental math sequence and passing the statewide exit exam constitutes student success. It is important to us e percentages of st udents passing the exit exam as the measure of student success, rather than measurin g student success by section because all sections are not the same size. Although there are differences in the 28 community colleges, students of ten must have a certain grade at the time of the final exam in order to take the exam. Each institution sets its required score for the student to be eligible to take the state exit exam. The statewide exit exam is often given as the final exam for the gatekeeper course, typically MAT 0024. A student must be successful in two st eps in order to achieve success. The student must be eligible to take the st ate exit exam by the standards set by the institution and must pass then the exam in order to enroll in college level courses. 20) Technology --Any computer-assisted instruct ion is considered to have a technology component. The technology compon ent is often based on a particular academic software program.
18 21) Traditional course -Any course offered at regularly scheduled times including an instructor and students without co ntaining a significant technology component is considered a traditional course. Limitations and delimitations A common measure of student success is a necessary limitation in this study. The only common thread among all 28 community colle ges is the state exit exam because the Florida community colleges vary in both th e number of courses required to exit the remedial/developmental sequence and in the nomenclature of the final course in the sequence. A second limitation of this study is the exclusion of non-credit remedial/ developmental courses. Non-credit refresher math courses may be available in continuing education departments of the colleges a nd may also be available through private enterprise. The materials covered by each of these other providers may duplicate the math presented in remedial/developmental math cour ses and thus may also have an effect on student success. A delimitation that may affect the re sults of the exam revolves around the administration of the exit exam. Each in stitution determines its own policies of administering, grading, and requiring a certain score in order to pass the exam. The state requires that each student earns a passing score on the exit exam, but does not define that passing score (K. Fearon, persona l communication, March 31, 2003). In the memorandum dated May 25th of 2002 and issued from the Division of Community Colleges, the specifications for passing the state exit exam are described.
19 Thomas Fisher, administrator of Assessm ent and Evaluation Services and Theresa Klebacha, Executive Vice Chancellor for Stude nt and Academic Success, describe the requirements: According to law, students must pass both the college remedial/developmental course and an Exit Test. As determined by the Council on Instructional Affairs, all Florida community colleges and Flor ida A & M University are required to administer the Florida College Basic Skills Exit Test as of the fall semester of 1999. The Exit Test is to be administered following the completion of the highest level of remedial/developmental coursework and prior to enrollment in college credit English or mathematics courses th at apply toward degree requirements. (Fisher & Klebacha, 2002) Further, the memorandum allows for institut ions to use the test forms provided by the state or to develop their own tests fo llowing a blueprint provided by the state using items from the state test bank. For instance, th e blueprint calls for a quantity of items of a given type, but does not provide specific it ems to be used on the exam (Fisher & Klebacha, 2002). A delimitation to be acknowledged is a cavea t to the definition of student success. Each institution has the responsibility to set th e standard to determin e student eligibility to take the state exit exam. For instance, Co llege A might require th at a student have a class average of at least 60 to qualify to take the state exit exam while College B requires that a studentÂ’s class average be at least 70 to take the same test. This is relevant information as it relates to student retention rates in remedial/developmental courses. For example, a student in College A with a cl ass average of 65 could pass the exam and
20 progress to college-level math by passing the state exit exam, while a student at College B with the same class average would not be able to take the exit exam. Simply being ineligible to take the state exit exam does not necessarily mean that the student at College B would not be able to pass the state exit ex am. If a student in College B could pass the state exit exam and is denied the opportunity to take it, that institutional standard could be the only insurmountable obstacle for that student In this example, the student in College B might not return to try again while the student in College A could progress through a full degree program. Another delimitation relates to the length of time that a particular software product is used at an institu tion and the method in which it is used. If College A has been using a particular product for several years and College B is using the same product for the first year, there might be differences in the degree of success that relate primarily to simply knowing the product. Also, if College A uses the product as the vendor intends for it to be used and if College B devises an alte rnate use of the same product, there might be differences in the effectiveness that relate to the differences in implementation. Either example could appear to produce greater success in College A when the reality is that the increased success is actually due to one of these factors instead. The fact that students do not always have a free choice in the delivery format of their section is a delimitation that would be diffi cult to measure. While it may be true that students tend to self-select the format that be st suits their individual strengths, true free choice would require that all institutions offer each delivery format and have unlimited seats in each delivery format. The large number of remedial/developmental math sections
21 reviewed will minimize the effect of the mode rating variables, inst ructor influence and initial placement test scores. Another major delimitation is geographic a nd situational. Each studentÂ’s available course choices are a factor of which instit ution serves his or her home district. Beyond the geographic delimitation, the only students at each institution who truly have a free selection in the formats that an institution o ffers are those who regi ster early enough that all delivery formats are available. Students may choose a class by the time/day it is offered or may even choose on the basis of a friendÂ’s selection rather than making choices based upon delivery format. Additionally, the students are limited by the scope of choices offered. Summary The purposes of this study are (1) to explore the remedial/developmental math offered in FloridaÂ’s 28 community college s with particular attention given to comparisons of institutional size and availabl e instructional delivery formats, (2) to explore the relationship that may exist between student succ ess and the technologyassisted delivery format of the gatekeeper remedial/developmental math classes in Florida community colleges and student succe ss, (3) to explore the relationship that may exist between student success and the delivery format of the gatekeeper remedial/ developmental math classes in Florida comm unity colleges while controlling for initial placement test scores and (4) to explore the relationship that may exist between student success and the delivery format of the gateke eper remedial/developmental math classes in Florida community colleges while cont rolling for instructor influence.
22 Chapter II reviews the literature relevant to this study and focuses on three areas: curriculum theory, theoretical background fo r remedial/developmental education in colleges and universities, and instructional delivery formats. The research focusing on each of these areas will be examined and compared. Chapter III discusses th e research questions and hypotheses, target population, participants, appropriate measures and proce dures, and methods of data analyses of the study.
23 Chapter Two Review of the Literature In order to effectively study the remedial /developmental mathematics education at the community college level with examina tion of the differences between delivery formats, the researcher must explore the lite rature in three areas: curriculum, remedial/ developmental education, a nd instructional technology. Re search on the first area, curriculum, is valuable for comparison between the curriculum of an institution and how well remedial/developmental classes provide th e needed skill enhancements for students. Research on the literature in the second area, remedi al/developmental education, describes the underlying philosophy that aff ects the delivery of effective remedial/ developmental education to meet the need s of under-prepared students (Payne & Lyman, n.d., 3), which raises questions about what particular factors ar e part of effective remedial/developmental courses. If student s do complete remediation in a reasonable period of time, what factors contribute to that success? Literature in the third area, instructional technology, offers a variety of ways to incorporate technology into the classroom. If there are ways to improve the percentage of students who complete remedial/developmental courses by investig ating classroom support through technology while maintaining the proven practices of remedial/developmental education, then
24 exploration of the combination of developm ental education with a technology component is worth consideration. Curriculum Research on community college curricula can be used to provide either a snapshot view or a longitudinal view when several studies are combined. Due to the number of studies on the curriculum in community coll eges that have been conducted, both views are available for further study. The community college curriculum has remained fairly consistent over time. Looking specifically at the math portion, which is the focus of this study, Schuyler (1999) reports th at the math portion of the to tal credit curriculum was consistently about 10% of the tota l curriculum since the 1930s (p. 4). Studies by Center for the Study of Community Colleges. The studies of community college curriculum that have b een conducted by the Center for the Study of Community Colleges (CSCC) at the Universi ty of California at Los Angeles under the direction of Arthur M. Cohe n have provided the foundation fo r further analytical studies on the community college curriculum. In additi on to a snapshot of the community college curriculum at a given point in time, the seve n different national st udies have provided a slightly different area of primary focus dependi ng on the specific priorities of the grants that funded the various projects: sciences, non-lib eral arts, transfer vs non-transfer, or an overview of the total curriculum.
25 The national studies began in 1975 with a grant from the National Endowment for the Humanities (Cohen & Ignash, 1994, p. 13) Additional studies of the community college curriculum were conducted during th e years following as cited in Table 1. Table 1 CSCC Curriculum Studies Date Sponsor No. of colleges in the sample Curri cula reviewed 1975 NEH 156 Humanities 1977 NEH 178 Humanities 1978 NSF 175 Sciences and Social Sciences 1983 Ford 38 All liberal arts 1986 Carnegie 95 All liberal arts 1987 Ford 109 Fine and Performing Arts 1991 NCAAT 164 All liberal arts Note. From Â“The total community college curr iculum,Â” by A.M. Cohen & J.M. Ignash, 1993, Probing the community college transfer function, p. 10. Reprinted with permission from the American Council on Education. In 1998, a comprehensive study examined the total curriculum of community colleges (Schuyler, p. 11). For the 1975 study and each subsequent national study, catalogs and schedules were gathered from a sample of colleges, a sample that was balanced by geographic region and institutional size. Course sections were coded and tallied according to a consistent coding scheme that Â“divides the liberal arts curriculum into six major disciplines: humanities, English, fine and performing arts, social sciences,
26 sciences, mathematics and computer sc iencesÂ” (Cohen & Ignash, 1992, p. 51). Each discipline was divided into 55 subject areas that were further divided into 245 sub-subject areas. For example, any sub-subject section of French was part of the subject area of Foreign Languages that was part of the broa d discipline of Humanities (Cohen & Ignash, 1992, p. 51). In each of these national curriculum studi es, course sections were coded and tallied with this coding scheme to examine the curricular offerings and trends across the nation using a sampling of colleges. To maxi mize consistency in the coding, each coding sheet was reviewed and random sections reco ded by a second researcher. All coders met on a weekly basis to discuss anomalies and ensure consistency across all coding. Brawer (1999) noted that 63% of the ma th courses in the 164 community colleges in the 1991 study were introductory and interm ediate courses (p. 22), while all math courses accounted for 12% of th e liberal arts courses. In the CSCC studies, the category of introductory and intermediate math incl udes courses at the remedial/developmental level and other math courses th at are at college level but do not fit into the category of advanced math or math for other majors. In the 1998 study, 59% of all math courses were introductory or intermediate and still accounted for 12% of the total li beral arts portion of the curriculum. In their 1991 national study, Cohen and Igna sh (1994) found that 16% of the math courses offered were remedial/developmental courses, 62% standard math courses, and 22% advanced math courses. Remedial/develop mental math, those courses that are basic and Â“below college-level prof iciency and which do not typica lly carry college transfer creditsÂ” (p. 14), were found at almost all institutions, regardless of size.
27 Florida curriculum study. In 2000-01, a team of seven Florida researchers conducted a study of the stateÂ’s community college curriculum similar to the CSCC national studies described above, with specific comparison to the na tional studies in 1991 and 1998. Following the pattern of the previous national studies, catalogs and Fall 2000 credit course schedules were collected from each of FloridaÂ’s 28 public community colleges. Each of more than 43,000 sections was coded by discipline, subject and subsubject area, following the coding scheme de veloped by CSCC and modified by the 1998 researchers. Each coding sheet was review ed by a second coder and random sections were recoded to maximize the consistency of the coding process and to maintain consistency with the previous studies. The integrity of the original CSCC coding system was maintained for accurate comparison betw een the Florida results and the national results. There is not a consistent pattern in the wa ys that the 28 Florida colleges show the remedial/developmental math courses in their schedules. Some of the schedules show the lecture course sections separate from corre sponding lab sections while others show the lecture and lab as one section with two components. Some schedules show one section of a single course that covers the entire spectrum of remedial/developmental math while other colleges show the remedial/developmenta l math sequence as mu ltiple sections of two or three courses, or any combination of these elements. Any section that was identified as a lab, self-paced, or independent study -that is without a definite time and meeting place or designated instructor -was not counted for consistency with the previous CSCC national studies.
28 The results of the Florida study differe d considerably in the proportion of remedial/developmental math from the two pr evious national community college studies largely because of the difference in how th e laboratory sections were counted. In 1986, 32% of the math courses were reported as remedial. The 1991 CSCC study shows that 16% of the math courses were remedial, refl ecting a dip from the previous studies. Cohen and Ignash (1994) attribute the dip in the 1991 study to the fact that more remedial courses were being offered in the laborato ry format and were not counted in the 1991 study. Â“Self-paced, individualized, and lab cour ses were not counted. A large number of remedial math courses were self-paced, indi vidualized, and lab c ourses; this would explain the low remedial math percentageÂ” (Cohen & Ignash, p. 17). If lab sections had been counted in the 1991 study, the percenta ge would have been higher. In the CSCC 1998 study, lab sections and tutori als were counted for remedial courses, showing that the remedial/developmental courses accounted fo r 32% of all math courses (Schuyler, 1999, p. 8). The Fall 2000 Florida study showed only 25% of all math courses were remedial/ developmental (Bendickson, 2002). This percen tage does not seem unusual compared to the percentage of math courses reported as remedial/development al in the 1998 national study until one considers the legislative mandate that all remediation in the state will be in the community colleges. Since all of FloridaÂ’s remediation is assigned to the community colleges, the researchers working on the study expected that there would be a larger proportion of remedial/developmental courses than the 32% in the national study.
29 Table 2 Remedial/Developmental Course Portion of All Math Courses in 2000 CSCC FL 1986 1991 1998 2000 Remedial/developmental percentage of all math courses 32% 16% 32% 25% A comparison of the percentages of th e remedial/developmental courses as a portion of the total curriculum is presente d in Table 2. Possible explanations for the discrepancy between 32% when all math cour ses were coded as remedial/developmental were reported in the 1998 national study and 25% reported in the Fall 2000 Florida study include an increase in the number of co mputer-assisted classes for remedial/ developmental math. The many ways that re medial/developmental math courses were presented in the Fall 2000 course schedules may explain the apparent dip to 25% from 32% reported in the 1998 national study, sin ce some sections were not counted to maintain consistency with the coding of the 1998 study. To preserve this consistency, there are a number of remedial/developmental math courses offered in formats that were not coded in the Florida study that were c ounted in the national study. Also, the number of hybrid sections may be greater in the Flor ida study than those in studies cited here due to inconsistencies in the ways that the cour ses are shown in the schedules. This lack of clarity in the actual number of sections of remedial/d evelopmental math that are technology-based or technology-assisted highlig hts the rationale to further examine this anomaly
30 Remedial/Developmental Education Remedial/developmental courses have been part of the collegiat e curriculum since the 17th century (Casazza, 1999). The National Center for Developmental Education (NCDE) at Appalachian State University has been a leader in studying remedial/ developmental education in college. There is extensive research by the NCDE and the National Association of Developmental Educ ators (NADE) on what constitutes effective developmental education. The NADE definition of developmental education is Â“a field of practice and research within higher edu cation with a theoretical foundation in developmental psychology and learning th eory. The NADE definition promotes the cognitive and affective growth of all postseconda ry learners, at all levels of the learning continuumÂ” (NADE website, definition page). To broaden knowledge, the effective remedial/developmental instructor must meet the needs of students who have Â“deficiencies in content know ledge and about the learning processÂ” (Stahl, Simpson, & Hayes, 1992, pg 4). Controversies surrounding the remedial/d evelopmental programs often show a lack of understanding of the programs. Ou tside the academic community, there is a prevalent mindset that remedial/developmental courses are a case of paying for the same training twice. It is not nece ssarily the same training when the student takes remedial/ developmental courses in the community colle ge. Secondary schools often allow students to graduate without the course work needed to prepare them for college. In this case, students may have received a high school di ploma, but without Al gebra and sufficient writing skills to place into college level read ing, writing, and math when they come to the community college. McCabe (2003) believes that we, as educators, must forget placing
31 blame for a studentÂ’s needing remediation and ac cept that it has become an essential part of higher education (p. 23). In response to some of the controve rsies surrounding remedial/developmental education, Colby & Opp (1987) called for entran ce and exit exams as well as integrated tutorial and lab experiences to maximize support for students while maintaining the integrity of the institution. Mandated entran ce and exit exams provide response to some concerns as researchers seek additional pred ictors of success in remedial/developmental courses. With declining numbers of student s passing the required exit exam, the Texas legislature considered eliminating the exit ex am as a requirement. A team led by Hunter Boylan reviewed the exit exam and found the test to be valid and reliable (Boylan & Saxon as cited in McCabe, p. 139). FloridaÂ’s ex it exam is mandatory, but has not been examined for validity and reliability. Teaching approaches. While courses for under-prepared students may have been largely remedial in nature in the beginni ng, a gradual shift occurred to modify the theoretical focus from remedial to developmental. Developmental educators began to look to psychological theories of Jerome Bruner and Jean Pi aget to link developmental education theory to cognitive and affective personality (McGrath & Spear, 1994). Following the humanistic views of Carl R ogers and Abraham Maslow, developmental educators identified a need for teachers to nurture each studentÂ’s individuality. In contrast, college remedial/development al programs often focus on the deficit model for instruction, implying that the stude nt is lacking knowledge. The skill and drill format, often a part of the remedial approac h, has been a primary teaching style in math
32 classes and tends to focus on fixing a pr oblem. Grubb (2001) repor ts that computer programs in remedial/developmental courses te nd to involve drills to teach a topic. Following the diagnostic test, discipline-base d remediation is ofte n used. Students are allowed to progress to a new topic only when they pass a test. Grubb (2001) suggests that the approach to remedial/developmental edu cation should be multi-f aceted rather than just a collection of skills and drills. GrubbÂ’s suggestion points to an approach that involves more than skills and drills in order for a technol ogy-based approach to provide the best support for those students, su ch as student-centered teaching, learning communities, and coherent philosophies across departments. Learning theories that addre ss how we learn include progr essivist thinking as well as a continual struggle between a developmen tal whole learner approach and a remedial discipline-based approach. The progressivist view identifies the natural stages that children encounter and responds with a stude nt-centered and problem-based approach. The progressivist educator supports the stages of cognitive development (Cazarra, 1999). Programmed instruction based on individual student need is one such approach. Programmed instruction is often utilized in remedial/developmental education following yet another model, the behaviorist model, w ith a basic assumption th at learners respond to external variables and can be expect ed to react in a ce rtain way. Programmed instruction may be built on expected responses Remedial/developmental instruction that follows the behaviorist model usually is self -paced or computer-assi sted instruction and often has an open-entry open-exit form at (McMillan, Parke, & Lanning, 1997, p. 25). Remedial courses in the open entry-open exit format may draw attention to a studentÂ’s
33 lack of the self-discipline necessary to su ccessfully complete any course that has no structured timetable. Student success. While the developmental weaknesses of the students who place into remedial/developmental courses may seem to be the reason for their weakness, Ley & Young (1998) report that a core deficit may be a lack of the ability to self-regulate in order to be successful in college. They repor t that the students who place into remedial/ developmental classes are not likely to have the self-discipline needed for success in college courses, which adds to the individua l studentÂ’s apparent developmental weakness. The need for self-regulation hi ghlights a potential misfit if a student who lacks this selfregulation skill enrolls in a section that is totally technology-based and requires that the individual student regulate s his/her own study needs. Another factor that may be a significant feature of a st udentÂ’s chance of success is the degree to which the student has control over the instruction. Computer assisted instruction has characteristics that may be indi cators of the potentia l effectiveness of a given program. Programs are either geared toward the learner having control over the program or the program controlling the learni ng process. There is research (Lawless & Brown, 1997, as cited in Lunts, 2003) to indica te that these controls may produce very different results. Learner control is seen if the student has the ability to change the program to match individual preferences or skill levels. Program control refers to a situation in which the student has no control over the program or its presentation (Lunts, 2003, p.1).
34 Williams (1996) points out that learni ng complex knowledge is made possible when the learner has the opportunity to par ticipate in the constr uction of how that knowledge is presented. Learners are more lik ely to influence the way that computerbased instruction affects them if they are gi ven interactive activiti es. College students, particularly remedial/developmental students, may not make good use of this ability to interact. If college students ar e allowed to have choice in th e amount of instruction they need, the least prepared students are the most likely to underestimate the amount of instruction that they really need (Willia ms, 1996, p. 959). Learner control in computerbased instruction may not be a positive fact or in student succe ss for all remedial/ developmental students. Recent research (as cited in Boylan & Saxon, n.d.) has identified several factors that contribute to successful remedial c ourses. Classroom and laboratory integration stimulate instructional and laboratory personne l to work together in collaboration. An institution-wide commitment and consistency of academic standards were found to strengthen remedial education programs. Learning communities, supplemental instruction, strategic learning, professional training, student orientation, and training in critical thinking are other factors that cont ribute to student success. Student success may increase when students have open access to de velopmental instruction. Â“Surveys indicate that 75 percent of developmental students enroll because of the flexible times for learning through the open labÂ” (McCabe, 2003, p.109). Other factors that contribut e to success of developmen tal programs are identified by Weissman (1995): remediation should be requ ired of students who are deficient in skills and should be required upon entering coll ege. Weissman recommends that students
35 who need some remediation should be a llowed to take colle ge-level courses simultaneously only if they continue the need ed remediation. But, any student who needs remediation in multiple areas such as r eading, writing, or math, should focus on the remediation needed before beginning co llege-level work (Weissman, 1995, p. 18). Some of the initial resear ch on effective methods for providing remediation was in the work of John Roueche. RouecheÂ’s ea rly studies (as cited in Boylan & Saxon, n.d.) show that successful techniques in remedial instruction include mastery learning and a degree of structure with a variety of t eaching methods. Courses should have a strong theory base, a clearly defined philosophy, and mandatory assessment and placement. Remedial/developmental programs that are centralized with c ounseling components, tutoring, and computer-based instruction were found to be the most successful (Boylan & Saxon, n.d., p.4). While much research exists to examine the effectiveness of given programs, there is no single answer that su rfaces as the best way to provide effective remedial/developmental instruction. Technology in remedial/developmental courses. McGrath & Spear (1992) suggest that the solution for remedial stude nts lies in using ap propriate educational technology. Cartwright identifies two primary types of software that reflect the many beliefs about how technology might best fit into remedial/developmental courses: those that improve generic basic sk ills and those that improve discipline-related skills. The generic basic skills approach is reported to be successful with moderately or highly motivated students (Cartwright, 1996, January/F ebruary). However, there are those Â“who argue that a basic skills a pproach cheats capable, if unde rprepared, students of the
36 opportunity to develop higher-o rder thinking skillsÂ” (Cartw right, 1996, January/February, 12). Due to this dichotomy of philosophies, there are software packages that present skills taught in remedial/developmental co urses in each way, providing choices in approach to institutions. The programs that present generic ba sic skills often use tutorials and exercises to strengthen a studentÂ’s skills The programs that are discipline-specific tend to be more interactive and allow more individualization based on student preferences (Cartwright, January/February 1996). One di fference between the basic skills approach and the discipline-specific approach to th e technology-assisted remedial/developmental courses is that the generic ba sic skills courses are most of ten housed in general computer labs, while the discipline-based courses are mo st often housed in a computer lab that is specific to the discipline. Discipline-based computer labs may be open to a more restrictive student population than are general computer labs, and therefore, the cost per student could be higher in a di scipline-based computer lab. Additionally, there are a gr owing number of programs th at utilize technology in multiple ways. Cartwright (1996, May/June) in troduces programs that allow students to utilize email and the Internet to do activ e writing, collaborating on assignments and posting assignments for peer review. Anothe r program at Indiana University-Purdue University at Indianapolis emphasizes technol ogy to stress active le arning and to get the faculty highly involved with the students. Us ing technology allows the faculty member to act as facilitator rather than instructor. Increas ed class sizes are feasible in this model.
37 Instructional Technology As new technologies increase on the edu cational landscape, institutions must explore benefits to students and financial im pacts of technology to survive. One dominant effect of the explosion of technology into e ducation relates to in structional delivery methods. Higher education is becoming more i ndividualized, to the ex tent that students will set their own educational agenda instead of conforming to the institutional agenda (Levine, 2000). Institutions are faced with the task of dete rmining the method and extent of technology in the educa tional opportunities offered. Instructional delivery methods may ha ve begun as rudimentary electronic worksheets, but current technology takes these de livery variations to new heights so that instructional delivery sometimes merges en tertainment into edu cation. MacDonald and Caverly (1999) cite an example in which an algebra software program is presented in a game format with animated video clips so th at the students become involved and forget to be nervous about the math or the t echnology. The boundary betw een education and entertainment has become somewhat blurred. Although there are other potential uses of technology in education, the media often considered when discussing technology in education is computer-based. Brothen (1998) suggests that technology must function at the level of the student in order to facilitate student independence, self-regula tion, and self confidence (Brothen, b, Goals, section). Brothen (1992) reports that computers can be of assistance with developmental students who may need more individual atte ntion than an instructor can provide. When expressing his prediction of the future of college mathematics, Maurer (1984) did not question at all the need for math in future college curricula. Instead, he
38 questioned the extent to which computers might replace math instructors. In the 2000 review of his earlier predictions, Maurer (2000) indicates that instead of replacing instructors, computers have provided an alternate mode of instruction often used to enhance the human instructor. Technology, if used very car efully, can be helpful to students in remedial/ developmental classes. Students must see many correct examples in order to develop a number and symbol sense. Technology allows students to see many more examples in the same amount of tim e. The question is do they pay attention to the answers? Examples done with tec hnology should be graded in difficulty of technology use or students will learn to hate buttons as much as they hate pencils. (Maurer, personal communication, May 22, 2003). Keup (1998) reports two positive factors th at surface in the use of technology in remedial/developmental education in comm unity colleges. The use of technology may change the role of instructor to that of facilitator, but technology does not replace the need for the instructor. Secondly, the use of technology in remedial/developmental education seems to increase the need for co llaborative learning. Since student-to-student communication may be integrated into the soft ware program, this need for collaborative learning may be met by the software program (Keup, 1998). Previous technological innovations of th e time were predicted to revolutionize education. For example, educators predicte d some 50 years ago that radio technology would cause tremendous changes in the clas sroom. However, the impact of radio on education never reached the level predicted. Subsequently, television came onto the scene with a similar prediction and result. Both th ese forms of technology are part of education
39 and have become integrated into classrooms as appropriate, rather than taking over the classrooms. Only time will show the extent to which current technology will impact the classroom. An example of high technology in the classroom can be found at California Polytechnic State University at San Luis Obispo (Cal Poly). Much of the remedial/ developmental math at Cal Poly is offere d through an interactive multi-media format. Even with as many as 50 students enrolled in the online mathematics courses, instructors are able to keep close tabs on each studentÂ’s individual progress by using the reporting functions built into the program. The coordi nator of the entry-level math and math placement exams at Cal Poly reports that student s learn and are able to move on to higher level math when beginning their college math track in an online format (Olsen, 2000). Teachers have a very different role in a course of this type: facilitati on, rather than direct instruction. In considering the expected affect of co mputers on education, what expectations are realistic? Hershfield ( 1980) identifies the individual faculty member as the most crucial facet in the acceptance of current technology into the classroom. (p. 402). Accepting the idea that it is cr ucial to have buy-in from the faculty member, perhaps the faculty member should be the one to select a delivery method. Widespread acceptance of any technological implementation into the classroom will depend on many people making individual choices for a particular fo rmat for their own classroom. Hershfield contends that both faculty a nd students must recognize the ad vantages to be gained from using technology in order to fully implement high technology in the classroom (p. 403). In considering the adoption of new tec hnologies, Johnson and J ohnson (1996) note that
40 the educational community is often slow to adopt and quick to discontinue the use of technology in classrooms. Contrary to the Hershfield idea that widespread acceptance will require many individual decisions, Kozma and Johnston ( 1991) believe that inst ructional innovations can be adopted collaboratively (p. 411). In reviewing more than 700 academic software packages, Kozma & Johnston have identifie d six ways in which the software and innovations are making positive diffe rences in higher education. 1) Rather than the student absorbing knowledge through a passive process, technology encourages active engageme nt on the part of the student. 2) Technology enables the institution to take the learning environment out of the brick-and-mortar classroom. 3) Technology allows for the use of multiple di mensions rather than simply relying on text to transmit knowledge. 4) Technology has the capacity to individualiz e the depth and breadth of drill on a particular skill to meet the individual student needs. 5) Technology has the ability through networking to conn ect individual students who may or may not be co-located. 6) Technology incorporates the ability to re produce conditions that are often costly or cumbersome in a physical classroom. For instance, chemistry experiments may be dangerous and expensive in th e classroom while interactive modeling allows the student to experiment without consuming costly chemicals or causing damage (pp. 409-410).
41 Kulik (1994) reports major implications fo r administrators in a meta-analysis of the effectiveness of compute r-based instruction. In summari zing the results of 97 studies, he reports that studen ts learn more and learn faster in courses which involve computerbased instruction. Additionally, students have more positive attitudes toward instruction and toward computers in courses which invo lve computer-based instruction. While these ideas seems to suggest that computer-based instruction has positive effects of student success, Kulik, however, also suggests that the re sults should be treate d as exploratory in nature. Technology has the capacity to present mate rials to students in a variety of ways. The effects of learning styles and abilitie s with computers are complex and varied. Regardless of the capacity to present materials in various ways, the instructor must ensure that the technology-assisted c ourse grows to its fullest pot ential rather than merely serving as a repository for electronic wo rksheets. There must be clearly defined objectives identified in order for the individua l instructor to maximize the positive effect of the technology. Â“Educators must take a stand against the mass introduction of online courses without clearly define d objectivesÂ” (Bothel, 2002). Mass introduction of online courses only increases the steep learning curve that some remedial/developmental students face, a fa ctor that has great po tential to affect the effectiveness of technology in remedial/devel opmental courses. Me hlenbacher (2002) reports Â“On-line learning environments are st ill very much in their infancy, and despite enthusiastic claims that such teaching and lear ning environments readily exist, instructors and students are still faced with a signific ant learning curveÂ” (p. 96). In presenting
42 courses in an online format, attention needs to be given to computer familiarity as well as the discipline-based skill set. Early math software simply presented electronic worksheets. MacDonald and Caverly (1999) reported that academic so ftware on the market has become more coordinated with learning styles of each student. An experiment called Project Synergy at Miami-Dade Community College produced re ports from the faculty that computerassisted instruction encouraged students to stay in college (Watkins, p. 2). However, if decisions are based primarily on the expectati on that student retenti on will increase while technology is used in classes, more information is needed. Using technology simply to increase student retention creates a nebulous hard to measure factor in the decision process (Watkins, 1991). Several concerns have been raised concerning effectiv eness and cost in choosing to present remedial/developmental courses through computer-assist ed instruction. The founder of one software company responded to concerns over the use of computerassisted instruction by insisting that the a dvantage of technology in a math classroom is not increasing enrollment to reduce the numbe r of faculty. Instead, the advantage comes in the form of increased student success, re ducing the need for repeats. Â“Greater learning productivity, more so than lower teaching co st, is the great promise of information technologyÂ” (Finkelstein & Sc holz, 2000, p. 23). Another co ncern over technology in the classroom beyond that of effectiveness in st udent success is simply who will pay for the technology costs. DeLoughry (1996) reports that the software needed to support technology in math classrooms may be paid for in different ways. The institution may
43 charge a course fee, similar to a lab fee, to cover the cost. The institution also has the option to pass the costs on to the student (p. 4). Another financial concern surfaces in th e implementation of academic software into remedial/developmental courses. The di rect cost of offering instruction with a technology component in remedial/developmenta l classes exceeds th e costs of offering the instruction to students in a classroom. The costs are greater because of fixed costs associated with the technology support: ha rdware and annual software licensing fees (Jewett, 2000, p.169). Although the decision to o ffer classes in a technology-based format is not purely a fiscal decision, the bu dgetary impact cannot be ignored. Relating literature on instru ctional technology to this study, the goal of effective instructional technology in remedial/developmen tal classes may be a matter of the right combination of controllable factors, one of which is the delivery mode chosen for a particular class. Pumerantz and Frances (2000) conclude that the deci sion is not whether to use the conventional mode of delivery or a technology-ba sed mode, but rather what is Â“the most effective combination of huma n and technological resourcesÂ” (p. 253)? Summary and Synthesis of Literature Review This study will build upon existing knowledge to investigate the effectiveness of the various formats of remedial/developmental math in community colleges in Florida. A review of the literature on curriculum reveal s that there is no co mmon general education curriculum which makes it even more difficult to find the most effective way to deliver remedial/developmental education to students w ho lack basic skills necessary to succeed in subsequent general education courses. A review of the literature on instructional
44 technology highlights the impact of technology on higher education as institutions now have the ability to offer instruction to st udents when, where, and how they want it. Instructional technology will have an impact on all aspects of higher education, including remedial/developmental education in comm unity colleges, and, as Newman (2000, p.7) points out Â“No institution, no matter how great its prestige in the traditional mode, will be able to escape the need to compete effec tively through the skilled use of technology to enhance learningÂ”. Although some of the existing literature suggests that students participating in remedial courses are very much like ot her community college students (Saxon & Boylan, 1999), some educators believe th at these students are not only under prepared in terms of basic skills, but ha ve had little or no access to technology and are intimidated and alienated by it. (McCabe, 103) A review of the literature on curriculum and instructi onal technology raises more questions that it answers. Do students enro lled in remedial/developmental courses in Florida community colleges r eadily accept technology? Shoul d the lack of familiarity with technology and the possible apprehensi on toward technology change the way that remedial/developmental courses are presented? The findings of this study, by addressing th ese questions, will provide a basis for colleges to make decisions for the directi ons and delivery formats of their remedial/ developmental math courses. If there is so significant difference found, institutions might re-examine spending limited funds on technolo gy. Conversely, if there is a significant difference found, institutions might seek out additional sources of funding to support technology in the remedial/d evelopmental math courses.
45 Chapter Three Method Introduction Remedial/developmental math formats a nd nomenclature vary across the state, with a single common element that exists in all 28 community colleges: the state exit exam. Among the 28 Florida community colle ges, the remedial/developmental math sequence may be offered in several ways, in cluding two 5-semester hour courses and two or three 3-semester hour courses. Regardle ss of the numbering of the course or the number of remedial/developmental math courses that are offered in a particular collegeÂ’s curriculum, all students must pass the state exit exam to be classified at college level, enabling those students to go into higher level math courses. The four research questions in this study addressed the overall search for the most e ffective delivery format for remedial/developmental math courses in the stateÂ’s community colleges. 1) What remedial/developmental math courses are offered in FloridaÂ’s 28 community colleges? Does the instructi onal delivery format of the remedial/ developmental courses offered in Flor idaÂ’s 28 community colleges vary by institutional size?
46 2) Is there a relationship between student success (defined on p. 16) and the technology-assisted delivery format of the gatekeeper remedial/developmental math classes in Florida community colleges? 3) Is there a relationship between student success and the technology-assisted delivery format of the gatekeeper remedi al/developmental math classes in Florida community colleges while controlling for initial placement test scores? 4) Is there a relationship between student success and the technology-assisted delivery format of the gatekeeper remedi al/developmental math classes in Florida community colleges while controlling for instructor influence? The first question was intended to captu re the scope of current remedial/ developmental math offerings in the state and to provide a foundation for investigating the other three questions. Info rmation on institutional size wa s noted in the event that a significant difference was found. The second ques tion was the primary focus of the study and addressed the question of effectiveness of the delivery of remedial/developmental math programs across the state. In other wo rds, do technology-assisted courses help students or not? The third and fourth questions controll ed for the intervening variables of initial student ability and agai n, instructor influence. Until the full coding process took place, it was not known if there would be cases of the same instructor teaching sections in more than one delivery format, the focus of the fourth question. The delivery format for gatekeeper reme dial/developmental math courses was the independent variable. The de pendent variable was student success. The researcher expected several different formats to be found in the Fall 2002 schedules of all
47 community colleges in the state during the codi ng process. A small pilot examination was conducted and 30 sections were coded by two outside veteran coders who worked on the Florida Fall 2000 curriculum study to ensure cl early defined parameters of definitions and consistency in the coding. The expected formats were traditional lecture, hybrid classes that included a tec hnology component, and totally co mputer-based formats. Any section that appeared with a specific meeting place and time without any additional information was coded as traditional. A computer-based section was listed in the schedule as one in which the students took th e course in a computer lab for the entire class period. A hybrid class was listed in the schedule as one in which the course contained both classroom and computer lab components. In any instance where there were identifiable instances of varyin g types of technology -synchronous or asynchronous, they were coded independently of each other. Until the full coding took place, it was not known how many of these or to what extent these formats would be found. Regarding question 1, the researcher expect ed to find no discernable pattern in the variety of remedial/developmental courses offe red in community colleges across the state when compared with institutional size. For questions 2,3, and 4, the researcher expected to find no evidence that delivery formats are a valid predictor of student success, even when the possible effects of e ither initial placement test scor es or instructor influence were removed.
48 Research design The overall structure of this research was a quantitative design. Question #1 was largely descriptive in nature while the other three questions were more analytical. There were several factors that might have been chos en to measure student success. Some of the other possibilities included mast ery of course content, enrollment in subsequent math courses, or successful completion of subseque nt math courses. However, with no clear prescription from the State of Florida of the remedial/developmental classes to provide a consistent framework, data to i nvestigate some of the factors that might have been seen to be effective measures of st udent success may not readily available. The only common thread in the remedial/developmental class o fferings in Florida we re the courses that served as gatekeeper and contained the ex it exam. The gatekeeper course numbers and titles were not consistent across the state, sin ce it exists with severa l different titles and several different course numbers. The degree of variation in the course offe rings focused attention on the gatekeeper course and exam to measure student success because so much leeway was given in the stateÂ’s loosely defined prescription for remedi ation. Because of the variety of ways in which the remedial/developmental courses were offered in Florida community colleges, it was important to simplify the questions into a consistent and measurable definition. The only consistent item measuring student succe ss in remediation was the state exit exam, so that became the variable used fo r measuring student success.
49 Population All credit-bearing sections of remedial/developmental math in the 28 community colleges in Florida provided the population for this study. Each section of remedial/ developmental math in the state was coded by its delivery format, sorting each section of the gatekeeper course in the remedial/developm ental track into the three delivery formats: traditional lecture, hybrid combination of l ecture and computer-assisted, and completely computer based. The delivery format was dete rmined by the entry in the printed course schedule. To verify the consistency and validate the coding of the researcher, two experienced coders coded a sampling of 30 sections of the schedules. The second research question used the full student populati on figures from the state. The researcher obtained data that included the studentsÂ’ en rollment by section, placement test scores, and final course grades from the Florida Division of Comm unity Colleges. The total population of students who were enrolled in a gatekeeper remedial/developmental math course in any Florida comm unity college in the Fall 2002 semester was examined for focused study. The researcher collected pretest scores and final grades in the gatekeeper math courses by section from the Florida Divi sion of Community Colleges and controlled statistically for the studentÂ’s initial placement test score to remove that potential impact on apparent effectiveness. A subsequent statisti cal test controlled for instructor variability isolating any case in which one instruct or taught in multiple delivery format. Instrumentation/measures In the first hypothesis, th e independent variable requi red information regarding institutional size from the Florid a Division of Community Colleges February 2002 Fact
50 Book. The size was measured by unduplicated headcount figures from Fall 2002. The different formats and the number of sections of each format found in each collegeÂ’s credit schedule were the dependent variables. The researcher gathered this information by coding and counting each section of all re medial/developmental math courses in the Florida community colleges. The researcher e xpected to find (1) trad itional lecture, (2) hybrid sections that include a technology co mponent, and (3) totally computer-based formats. The second hypothesis required additiona l information to measure student success. To maintain consistency, the research er ensured that the course used for this study was the one that includes th e stateÂ’s exit exam as the requirement before a student exits the remedial/developmental math sequence and is eligible to enroll in college level math courses, previously defined as the gate keeper course. The course selected for this study is often listed as MAT 0024 or MAT 0024C, College Preparatory Algebra. Some of the 28 Florida community colleges listed the gatekeeper course as MAT 0020, Basic Algebra II. Since MAT 0024(C) may not be the only course that cont ains the state exit exam, the course used for this research wa s the course(s) in each of the 28 community colleges that contained the exit exam as a re quirement to pass the course. The state exit exam was provided to community colleges to en sure consistent standards across the state. Data was gathered statewide regarding the passing rates of stude nts in the remedial/ developmental gatekeeper math course. The pretest used for the third hypotheses was the statewide college placement test (CPT). Controlling for initial st udent ability, as demonstrated in the placement test score, removed an additional confounding factor. In formation on faculty members assigned to
51 the remedial/developmental math classes to support the fourth hypothesis was obtained from the printed schedule, from the institutionÂ’s research office, or appropriate department chair. Procedures The first hypothesis was analyzed by size and proportion of sections that were traditional, hybrid, and totally computer-based. The variety was sorted by delivery format and course. For instance, curriculum planners would be interested to know if medium College A offers only its remedial/developm ental math courses in a hybrid delivery format and medium College B offers half its total math courses in a hybrid delivery format. This is particularly important if th e hybrid format (as defined in this study) is found to be the most successful delivery format. The second hypothesis tested was an an alysis of variance (ANOVA) using statewide data to examine any relationship that may exist between delivery formats of remedial/developmental math courses in the 28 community colleges in Florida and student success. Student success was measured against the delivery format by using the statewide exit exam. The third hypothesis was tested with an analysis of covariance (ANCOVA) to seek and identify interaction between student success in di fferent delivery formats of remedial/developmental math classes while co ntrolling for a studentÂ’s incoming score on the state placement test. The fourth hypothesis w ould have been tested with an analysis of covariance (ANCOVA) to seek and identify interaction between student success in different delivery formats of remedial/dev elopmental math classes while controlling for
52 instructor influences. The fourth hypothesis wa s not tested due to the limited occurrence of an individual faculty member teachi ng sections of the gatekeeper remedial/ developmental math course in multiple delivery formats. Focusing on those cases in which one instructor at a single institu tion taught multiple sections using multiple methods, the researcher again used the deliver y format as an independent variable and student success as th e dependent variable. The element of instructor influence was of interest because of the potential that students in class with Professor A would always perform better (and have a higher success rate as defined in this study) than the students in class with Professor B simply because Professor A was a more effective teacher. In isolating the cases in which the same instructor taught the gatekeeper class in two or more different formats, the element of teacher performance was removed. This que stion was to be addressed only if there were sufficient cases in which an instructor could be identified as teaching at least two sections in more than one delivery format. The researcher categorized each section of remedial/developmental math for the Fall 2002 semester and sorted the count by college size as reported in the Fall 2002 unduplicated headcount enrollment figures. The researcher collected data on the percentages of students who earne d the right to advance to college level. After identifying all sections of remedial/developmental ma th and coding them by delivery format, the researcher gathered faculty assignment information from the printed schedules, institutional research offices, or other appropriate office in each college to match those sections in which the same faculty member taught in more than one delivery format. There was not a large enough group to produ ce anything valuable The total of 1,121
53 sections of gatekeeper remedial/developmen tal math produced only 12 instances of an individual faculty member teaching in more than one delivery format. Although the researcher did not expect to find many inst ances in which the same faculty member taught in multiple delivery formats, the quest ion regarding instructor influence was an important one and would have been investigat ed if the frequency wa rranted investigation. The researcher identified formats for remedial/developmental math courses by examining the Fall 2002 credit course schedul es and college catalogs from each of the 28 community colleges in Florida. Once the formats were identified and sorted by college and format, the researcher gathered specific information for all students in each format to identify any relationships that existed. A positive relationship between pass rates and instruction delivered via technology might have illustrated a need fo r increased funding to smaller institutions or level statewide f unding for technology-delivered remediation. Data Analysis Descriptive statistics were computed for the first hypothesis to provide foundation for the remaining three hypotheses. Sectio ns of remedial/developmental math were counted and an analysis of variance on th e coding was conducted to test the second hypothesis. Two analyses of covariance were ru n to analyze the initial effects of initial placement test scores before comparing the between group variance and instructor difference.
54 Summary In summary, the effectiveness of the de livery method of remedial/developmental mathematics courses in the Fall 2002 semest er of FloridaÂ’s 28 community colleges was the focus of this study. The complete printed schedules were studied closely to identify relationships that might exist between a student Â’s pass rate and the delivery format of the section. The sections were coded by an exte nsion of the coding taxonomy developed by the Council for the Study of Community Colleges Sections were identified as traditional, hybrid, or computer-based delivery formats. After coding each section, the researcher compared the pass rates of students enrolled in each delivery. Again, the pass rates were compared to delivery format while controlli ng for the studentÂ’s incoming placement test score. The final research questi on would have controlled for in structor variability if there had been a sufficient number of cases in wh ich the same faculty member taught in more than one delivery format.
55 Chapter 4 Results The purpose of this research was to examine the effectiveness, as measured by student success, of technology-assisted in struction for remedia l/developmental math courses in Florida community colleges. This chapter presents results of the quantitative analysis used to investigate ea ch of the four research ques tions. Specifically, this chapter includes a summary of the data collection pro cess and the subsequent analyses as they relate to each question. Summary of the Data Collection The initial step necessary to complete a full assessment of the curriculum of remedial/developmental mathematics courses in all Florida community colleges was the collection of a complete set of college catal ogs and printed schedules applicable to the Fall 2002 semester for each of FloridaÂ’s 28 community colleges. The catalogs and schedules provided the foundation for the remainder of the research. Appendix A provides a clear description of the remedi al/developmental mathematics curriculum. Appendix B also provides a listing of all ma th courses in the stateÂ’s common course numbering system, highlighting the remedial/developmental courses. The second step, one that had to preced e the actual coding of the 28 printed community college schedules from the Fall 2002 semester, was a pilot coding completed
56 by two veteran coders from the 2000 Florid a curriculum study described in Chapter Two. The pilot coding of 30 sections was c onducted and highlighted the need to more clearly define the terms in order to ensure consistency in the full coding of all remedial/ developmental mathematics sections. The next step involved detailed definitions of the coding terms (shown in Appendix C). This wa s an important step in validating the consistency of the full schedule coding that follo wed. These criteria were used to code all remedial/developmental math sections in the entire printed schedules of the 28 community colleges in Florida. The third step involved examination of the remedial/developmental mathematics curriculum at each college as presented in th e college catalog. The vari ety of curricula in the 28 community colleges showed five different remedial/developmental math courses across the state, despite the fact that the mix of five courses varied quite a bit from one institution to the next. Alt hough the titles of the courses we re inconsistent, FloridaÂ’s common course numbering did provide a framew ork that produced some continuity since the numbering schemes were found to be consiste nt throughout the state. The course titles often included terms like College Prepar atory or Elementar y, Developmental or Introductory. The gatekeeper co urse titles were listed as Basic Algebra, Elementary Algebra, Fundamentals of Algebra, College Preparatory Algebr a, Introduction to Algebra, or Introductory Algebra, with similar variations in lab sect ion titles as well in the lecture portions of course titles. The fourth step in the data collection process involved compilation of the data provided from the Division of Community Co lleges. The state data selected for the detailed investigation incl uded all students enrolled in a gatekeeper remedial/
57 developmental math course in the 28 Flor ida community colleges during the Fall 2002 semester. There was no individually identifiabl e information included in the state data, only individual student records with a count er instead of a traceable identification number. To provide data and respond to que stion three, the incoming placement test score was included when available. All student records did not include a placement test score since there are other means of placi ng students into remedial/developmental courses, including prior scores on national college entrance exams or transfer from another institution. To support question four, the final step in the data collec tion process involved analysis of the delivery formats offered at each institution to identify the institutions that offered the gatekeeper course in multiple form ats. This step produced a list of 12 of the 28 community colleges that offered the gate keeper course in more than one delivery format. The remainder of the 28 institutions offered the gatekeeper course in only one format. Some of these 12 inst itutions provided faculty inform ation in the printed schedule so it was easy to determine the cases of faculty members teaching in multiple formats. The remaining institutions were contacted to request faculty information for each of the applicable sections. Again, no individual identifying information was collected. The information on faculty assigned to particular courses only answered the question: Â“Did the same faculty member teach the gatekeeper course in more than one delivery format?Â” Once the institutional remedial/developmental math curriculum was defined for each institution, all sections of remedial/d evelopmental math in the printed Fall 2002 schedules were coded according to an expa nsion of the coding taxonomy described in previous chapters that divides the liberal ar ts curriculum into six major disciplines. The
58 original coding taxonomy divided the liberal arts into six ma jor disciplines. This coding was specifically focused on the remedial/dev elopmental math portions of the printed schedules. The framework for the coding taxonomy was consistent with the taxonomy used in the CSCC coding taxonomy with the addition of coding all remedial/ developmental math sections by delivery format for this study. All remedial/ developmental math sections were coded in this manner to provide a clear method to identify those sections that were sections of gatekeeper courses. Prior to any coding, the researcher wrot e definitions to describe the delivery formats expected. With the assistance of th e veteran coders, and be fore beginning the full coding process, the definitions were discu ssed and points of vague ness were clarified. The reason that this step had to be completed before beginn ing the coding process using the printed schedules was to remove any tendenc y to write definitions to fit the schedule listings. The definitions needed to be cl ear enough that the veteran coders who participated in the pilot c oding would be able to code consistently and without questioning the coding decisions. With these cl ear definitions in ha nd, it was simple to code the printed schedules with confidence. The definitions that provided the foundation for the coding process were concluded with a consensus of the parameters of each delivery format definition and the coding of the sections selected for the pilot coding project with the veteran coders. The formats were traditiona l lecture, hybrid classes th at included a technology component, and totally computer-based form ats. Any section that appeared with a specific meeting place and time, without any additional information to specify a laboratory component, was coded as traditional. Sections that were coded as traditional
59 were listed in the printed schedule with a specific meeting place and time and with no indication of any use of technology during the delivery of the cour se. Additionally, the researcher conducted a validation check by comp aring the section listing in the printed schedule with the course listing in the colle ge catalog. There were cases of the course descriptions providing the only indication of the use of t echnology in the course. For instance, if a section was presented in the printed schedule with a specific meeting place and time and no mention of a computer lab, but the course listing in the college catalog indicated a co-requisite lab, the section was not coded as traditional. The only element that excluded the traditional coding for that section was the catalog description that showed the required lab to be take n with the lecture-based course. A hybrid class was listed in the schedule as one in which the course listing in the printed schedule contains both classroom and computer lab components. Sections that were coded as hybrid were those that clearl y contained elements of traditional lecturebased and technology. For instance, the co-requi site lab presented in the example above would provide justification to code those sect ions as hybrid rather than traditional. In order to be excluded from being coded as computer-based delivery, there must be an element of traditional delivery. This mi ght be shown through two different meeting places, one classroom and one computer lab. A computer-based section was listed in th e schedule as one in which the students took the course in a computer lab for the enti re class period. Sections that were coded as computer-based were those without any indica tion of lecture-based tr aditional classroom. These sections might be listed in the printe d schedules as online or distance learning. Other sections were coded as computer-based if the printed schedul e listing showed only
60 a computer lab as the meeting place or if there was a printed comment that the course was based on a specific software package as the primary focus. The researcher also separated fully comput er-based sections from online sections during the coding process as described in th e original method section of this study, but the total number of online sections was so sm all that those sections were combined with the computer-based sections for the analysis in this study. The state data was then sorted by institution to facilitate a careful cross-check of section numbers to validate the consistency of the coding and verify that all sections were counted. There were a total of 111 sections that appeared in the state data that were not in the printed schedules. This was not a surprise as institu tions often modify existing se ctions and create additional sections as needed to meet student demand. The printed schedules provided the full list of sections that was used in this study. Any section that was not in th e printed schedule and might ha ve been added later was not included in this study because of the unavailab ility of consistent information regarding delivery formats for those sections that might have been added later. To maintain the integrity of the research, any section that was included in the state data but was not reflected on the printed schedule was elim inated from the study. The researcher considered the idea of contacting each in stitution to ask for information on delivery format. However, the researcher decided against pursuing these additional sections because: a) Many of the Â“addedÂ” sections were likely not really additional sections but reworked presentations of sections that appeared to be cancelled sections. For instance, if there is some reason to ch ange the days that a class meets from
61 Monday/Wednesday to Tuesday/Thursday afte r the schedule has gone to print, the section might be cancelled and resubmitted in the system with only a change of days. One reason that it might be better to cancel an existing section and create a new section with only minor modification w ould be to ensure that the students enrolled in the course would have the co rrect schedule. Simply making the change in an existing section instead of cance ling it opens the possibility that some students register early en ough to see the incorrect schedule and build their schedule accordingly. This w ould appear to be one cancelled section and one added section, but it is actually a cosme tic modification of th e section with the only course offering information changed. b) Information on these added sections would have been obtained from an individual at each institution. That i ndividualÂ’s perception of the delivery format of the added sections might not have been consiste nt with this researcherÂ’s definition of each delivery format. If the definitions a nd perceptions are inconsistent with the sections already coded from the information available in the printed schedules, the institutional representativeÂ’s assessment of a hybrid se ction might not have been consistent with the researcherÂ’s assessme nt and had the potential to skew the data by reporting a section differently than it w ould have been coded from the entry in the printed schedule. Therefore, the elimination of these added s ections does not affect the results of the study, particularly in light of the small numbe r of added sections compared to the large number of sections that were presented in all sections of re medial/developmental math as shown in the printed schedules. Eliminating th ese sections removed less than 9% of the
62 sections reported by the state. The total number of sections added was less than 10% of the total number of sections in the printed schedules. The few sections in the printed schedules that were not reporte d in the state data accounted fo r less than 2% of the total number of sections in the printed schedules and were likely the sections that were cancelled after the schedule went to print. Data Analysis: Quantitative Design Research question 1. The first research question was: Â“What remedial/ developmental math courses are offered in FloridaÂ’s 28 community colleges? Does the instructional delivery format of the remedia l/developmental courses offered in FloridaÂ’s 28 community colleges vary by institutional size?Â” The catalog course descrip tions collectively provided the full scope of the remedial/developmental math courses across th e state. While the mixture of courses and the structure of the remedial/developmental ma th curricula were quite varied in the 28 institutions across the state, each of the 28 community colleges showed MAT 0020 and/ or MAT 0024 as the gatekeeper course(s) containing the state exit exam. The catalog course descriptions provided sufficient info rmation to identify th e sequence of courses that comprise the remedial/developmental math curriculum and clearly pinpoint the gatekeeper courses, that is those courses that contain the mandatory exit exam. A twocourse sequence comprised this remedial/dev elopmental math curriculum at 25 of the 28 community colleges. These courses were listed at zero to five seme ster hours of credit, with 82% of the institutions listing either three or four se mester hours per course in the college catalogs and in the remedial/developmen tal math portion of the printed schedules.
63 Only three community colleges offered 5-seme ster hour remedial/developmental courses and one offered 6-semester hour remedial/devel opmental courses. In the seven schedules offering both MAT 0020 and MAT 0024 as gatekeep er courses, these two courses were a combination of the entire remedial/developmental math sequence into one integrated course and were sometimes offered in diffe rent delivery formats, or showed other distinctions. The proportion of ga tekeeper sections offered in the various delivery formats was similar to the overall proportions of re medial/developmental math offered in hybrid and computer-based delivery formats. The researcher had originally expected to find sections presented in several delivery formats; including traditional, computer-based, hybrid, and online delivery formats. Once the printed schedules were re viewed, the remedial/developmental math sections were presented in each delivery fo rmat as expected with one exception. The researcher had expected to find more online sections in the remedial/developmental math portion of the schedules. Casual scanning of the remainder of the schedules showed that there seemed to be more online courses o ffered throughout the state in a variety of disciplines other than math. Additionally, ther e also appeared to be more online courses offered throughout the state in college leve l math than were found in the remedial/ developmental math portion of the schedules. Half of the 28 institutions offered the gatekeeper course in only one delivery fo rmat, although that single delivery format was not the same in each of these institutions acr oss the state. Additionally, 11 institutions offered students two choices of delivery format and only three of the 28 institutions offered remedial/developmental math to stude nts in all delivery format configurations.
64 The infrequent occurrence of fully online re medial/developmental math courses was the basis of the decision to include those into the computer-based numbers. Table 3 combines the information for each institutional size and indicates both the number of sections and percentages of all remedial/developmental math courses offered in each delivery format. The small institutions seem to favor the traditional delivery method as reflected in the 72.67% of the 150 total sections offered in that delivery format. Medium institutions offer similar pr oportions in traditiona l and hybrid delivery, both approximately 42%. The large institutions clearly favor the hybrid delivery format with almost two-thirds of the total 1,271 sections offered in that delivery format. It is interesting to note that no small instituti on offered a section of remedial/developmental math in the computer-based delivery format. The size of an institution does seem to be associated with the delivery format offered in gatekeeper remedial/developmental math courses. Table 3 Sections of all remedial/developmental math c ourses offered in each delivery format by institutional size Traditional Hybrid Computer based n % n % n % Small 109 72.67% 41 27.33% 0 0.00% Medium 228 42.93% 217 40.87% 86 16.20% Large 282 22.19% 831 65.38% 158 12.43%
65 Table 4 Distribution of delivery formats in a ll remedial/developmental math courses College Traditional Hybrid Computer based Small A 6 0 0 Small B 0 5 0 Small C 0 14 0 Small D 0 20 0 Small E 8 0 0 Small F 33 0 0 Small G 46 0 0 Small H 7 0 0 Small I 9 2 0 Medium A 73 0 22 Medium B 0 23 2 Medium C 0 52 1 Medium D 0 39 0 Medium E 0 43 4 Medium F 22 0 1 Medium G 65 0 0 Medium H 31 20 19 Medium I 3 40 0 Medium J 34 0 37 Large A 0 175 5 Large B 47 47 0 Large C 95 3 2 Large D 62 8 6 Large E 0 47 0 Large F 0 210 0 Large G 0 120 0 Large H 78 0 132 Large I 0 221 13 Totals 619 1089 244
66 The data in Table 4 represent the distribu tion of delivery formats of all levels of remedial/developmental math by institutional si ze. For the purposes of this study, small institutions are those with full-time enrollm ent of 3,000 or less. Medium institutions are those with full-time enrollment greater than 3,000 and smaller than 9,000. Large institutions are those with full-time enrollm ent greater than 9,000. All figures are taken from the Florida Community College 2002 F act Book. Table 4 also illustrates the combination of delivery formats that are offe red at each of the 28 institutions. It is interesting to note that only one medium institution and two large institutions offered sections in all three delivery formats. Table 5 Proportion of all remedial/developmental math sections by delivery format Delivery format # of sections % of all remedial/developmental math Traditional 619 31.7% Hybrid 1,089 55.8% Computer-based 244 12.5% Total 1,952 58.4% of all math courses According to the data in Table 5, the sect ions of all remedial/developmental math courses offered in a traditiona l delivery format account for almost one-third of the total number of sections. Hybrid sections comp rise more than half the total remedial/ developmental math sections in the 28 community colleges in the state. Only one-eighth
67 of all remedial/ developmental math sections in the state were offered in a wholly computer-based delivery format. The gatek eeper sections reflect almost 60% of all remedial/ developmental math s ections. Sections of all leve ls of remedial/developmental math taught in a traditional delivery form at account for 31.7% of the total remedial/ developmental math curriculum. The hybrid de livery sections are 55.8% of all levels of remedial/ developmental math. The computer-b ased sections account for 12.5% of all levels of remedial/developmental math in the state. Table 6 Distribution of all remedial/developmental ma th sections by delivery format and course Gatekeeper courses MAT 0001 MAT 0002 MAT 0012 MAT 0020 MAT 0024 Totals Traditional 0 153 115 10 341 619 Hybrid 2 135 293 203 456 1,089 Computerbased 0 38 67 4 112 221 Online 0 2 7 0 14 23 Totals 2 328 482 217 923 Table 6 represents the number of sections of all levels of remedial/developmental math courses in each delivery format, with pa rticular focus on the number of sections of gatekeeper courses. Once the MAT 0020 a nd MAT 0024 courses were identified as the
68 gatekeeper courses, clear parameters were es tablished to identify the 1,140 of the total sections that were sections of the two gatekeeper courses and therefore, included in the research analysis in this study. The 1,140 sect ions of the gatekeeper courses account for 58% of all remedial/developmental math courses in the state. The total number of sections of all levels of remedial/devel opmental math is 1,952. Although the 812 sections of non-gatekeeper remedial/dev elopmental math courses were not included in further research analysis, it is interesting to no te the proportions of gatekeeper and nongatekeeper sections across the state, part icularly when sorted by delivery format. Gatekeeper sections account for 58.4% of all remedial/developmental math sections in the state. The fully online sections were only 1% of the total 1,952 remedial/developmental math sections shown in the printed schedules When focusing on all courses of remedial/ developmental math in the state, only 23 sectio ns were identified as fully online sections. The fully online gatekeeper sections were onl y 14 of the 23 fully online sections at all levels and only 1% of the total number of ga tekeeper courses. For the purposes of this study, and since the incidence of the fully online sections of gatekeeper remedial/ developmental math was so small, these 14 sections were combined with the other computer-based sections for analysis. There was considerable inconsistency in the course descriptions provided to students regarding the remedial/developmental math track shown in the college catalogs throughout the state. Additional inconsistencie s exist in the ways that sections are presented in the printed schedules, details that may be confusing as students try to determine the delivery format of the section they chose. It is not alwa ys clear if a section
69 was offered in a traditional, hybrid, or co mputer-based delivery format. The catalog descriptions were sometimes so clear that a student selecting a c ourse would not have difficulty in knowing which of the courses to take and what options of delivery formats were available. However, in other cases, th e catalog descriptions and printed schedules were either contradictory or not very clear and left r oom for uncertainty regarding whether or not the course would be offered in traditional, hybrid, and/or computer-based delivery formats. In these instances, the stud ent might not have sufficient information to be able to make the most a ppropriate selection very easily. Individual sections in some printed schedules were very clearly identif ied as based on a speci fic software program, while others were less clearly identifiable in the printed schedules leaving the student with insufficient information to make the mo st informed decision about section selection. If the technology component was not clearly listed in the schedule, the student might have been surprised to find the first day of cl ass in a computer lab or a student who would really prefer the technology component might not register for that section since the technology element was not stated clearly. While many students may not be concerned about the delivery format of the section that they select, the delivery format might be an important factor for a student whose comput er literacy is limited. One schedule showed that all students who placed into remedial/developmental math were to be initially registered into the gatekeeper course and then would be placed downward into a lower level remedial/developmental class, de pending on the placement test score. One alternative that provides more opti ons for students found in the schedules of seven institutions is the comb ination of two courses that allows students the opportunity to complete all requirements for the full reme dial/developmental track in a single course.
70 The seven community colleges that offered an option to take one integrated course instead of multiple courses sometimes offered that course with a lower numbers of credit hours than the total of the tw o course sequence. For instan ce, if the two-step sequence was two 3-credit hour courses, the integrated course might have been one 5-semester hour course. There are several details that do no t appear in the either college catalogs or in the printed schedules. For instance, if th ere are additional criter ia that restrict a studentÂ’s eligibility to take these integrated sections, there is no explanation given in either the college catalog or in the printed schedule to pr ovide that information. Another detail that might be missing is any indication whether or not the student might have been restricted from registering for the integrated course without being placed directly into it by meeting specific criteria. For instance, th ere might be a restri ction that a student cannot register into the inte grated section without an au thorizing signature, a certain score on a diagnostic instrument given after th e initial placement test and/or an initial placement test score above a certain cut-off scor e. Four institutions created classes that were coded as the hybrid format by offering a separate lecture section with co-requisite lab. As defined earlier, the separate lab sect ions were not counted if required as corequisite with a lecture section. While the stat e definition of a course with a C suffix is a combination course, there was no indication that this was consistently enforced in the way that sections were offered and presen ted in the printed schedules. Other suffixes were used throughout the state without clear explanations of their meaning. These details are the types of information that the student might want to know prio r to registering for a particular section.
71 The data in Table 7 indicates the compar ison between the proportions of all levels of remedial/developmental math sections w ith particular focus on the sections of gatekeeper remedial/developmental math in all 28 institutions. This comparison indicates that the percentage of the ga tekeeper sections of remedia l/developmental math delivered in the traditional delivery format of course s is 1.7% less than th e percentage of the remedial/developmental math courses at all levels that are delivered in the traditional delivery format. The percentage of gatekeeper sections of remedial/developmental math delivered in the hybrid delivery format is 3% greater than the percen tage of the remedial/ developmental math courses at all levels that are delivered in the hybrid delivery format. The percentage of gatekeeper sections of remedial/developmental math delivered in the computer-based delivery format is 1.4% le ss than the percentage of the remedial/ developmental math courses at all levels that are delivered in the computer-based delivery format. Table 7 Proportion of gatekeeper courses compared to all remedial/developmental math courses Delivery format Portion of all remedial/ developmental math n=1,952 Portion of only gatekeeper sections n=1,121 Traditional 31.7% 30.0% Hybrid 55.8% 58.8% Computer-based 12.5% 11.1% Totals 100% 100%
72 Table 8 provides percentages to compare th e proportion of all le vels of remedial/ developmental math sections offered in each delivery format and by institutional size compared with only gatekeeper sections of re medial/developmental math courses in each delivery format and by institutional size. Th e proportion of gatekeeper sections of remedial/developmental courses offered in each delivery format does not mirror the proportion of all remedial/developmental math courses offered in each delivery format. In the small and medium institutions, the percentage of gatekeeper sections offered in the traditional delivery format is greater than the number of sections offered in the traditional delivery format in all levels of remedial/d evelopmental math courses. The number of sections offered in each delivery format at th e large institutions is just the opposite. Large institutions offered less of th eir gatekeeper sections of remedial/developmental math sections in a traditional delivery format than they offered in all levels of remedial/ developmental math courses. In the small and medium institutions, the percentage of gatekeeper sections offered in the hybrid delivery format is less than the number of sections offered in the traditional delivery fo rmat in all levels of remedial/developmental math courses. The number of computer-based sections of all levels of remedial/ developmental math is greater than found when focusing on only the gatekeeper sections in institutions across the state without regard to institutional size. In summation, the small and medium institutions offer a larger perc entage of traditional delivery gatekeeper sections and less in the hybrid delivery form at than the percentage of all traditional delivery sections. The percentage found in large institutions is just the opposite. The percentage of traditional delivery sections comparing all remedial/developmental math
73 sections with only the gatekeeper sections reveals a larger percentage in the hybrid delivery format and less in the traditional delivery format. Table 8 Percentages of all remedial/developmental math courses compared to gatekeeper remedial/developmental math courses by delivery format and institutional size Small < 3,000 FTE Medium 3,000-9,000 FTE Large >9,000 FTE All Gatekeeper All Gatekeeper All Gatekeeper Traditional 72.2% 78.2% 42.9%48.4% 22.2% 19.7% Hybrid 27.2% 21.8% 40.9%36.1% 65.4% 69.6% Computer-based 0.06% 0.0% 16.2%15.4% 12.4% 10.7% 100% 100% 100% Table 9 represents the number of gatek eeper sections offered in each format by institutional size and the per centage of sections of gate keeper remedial/developmental math by institutional size. It is not surprising to find that the majority of all remedial/ developmental math offered in the state is f ound in the larger institutions. No institution in the small category was found to offer a sect ion in the computer-based delivery format. As reported earlier, this matters a great deal if the delivery format is shown to affect student success. A summary of the remedia l/developmental math offered compared with the size of the institution revealed that all 12 of the institutions that offered the gatekeeper course in multiple delivery formats had fulltime enrollments of at least 3,000 and were
74 categorized as medium or large. For the pur poses of this study, small institutions are those with less than 3,000 full-time enrollm ents reported in the Florida Community College 2002 Fact Book. Medium institutions are institutions that reported full-time enrollments between 3,000 and 9,000. Large inst itutions reported more than 9,000 fulltime enrollments. No institution with full-time enrollment less than 3,000 offered its gatekeeper remedial/developmental math cour se in more than one delivery format. Table 9 Number of gatekeeper remedial/developmenta l math sections by institutional size Traditional n = 337 Hybrid n = 659 Computerbased n = 125 Percentage of all remedial/developmental math that are gatekeeper sections Small 67 18 0 56.7% Medium 124 96 42 49.3% Large 146 545 83 60.9% An unexpected item of note relates to the average class size in gatekeeper sections of remedial/developmental math. Since the non-gatekeeper sections were previously excluded from this study, it is unknown if the average cl ass sizes are similar in nongatekeeper remedial/developmental math. Figure 1 represents the range of class sizes of all gatekeeper sections of remedial/developmental math, from 5 to 60 students. Six sections with enrollments less than 5 were ex cluded from this study since the passing rate would be so easily influenced by the performa nce of a single student. The most frequent occurrence in class size was 29 students, w ith a definite clustering between 24 and 33
75 students and few sections with a larger than 36 average class size. The overall average class size in gatekeeper remedial/d evelopmental math sections was 25.811. 0 20 40 60 80 100 120 140 160 180 58121519222629333640434650535760Class SizeFrequency Figure 1 Average class size in gatekeeper remedial/developmental math classes Table 10 represents the average class by delivery format. The class sizes in gatekeeper remedial/developmental math classes showed a wide range. The average class size is sometimes presented in state data as 25 students in all remedial/developmental math classes. The average class size in all gate keeper sections in these data is consistent with the class size from the state. It is inte resting to note that the smaller average class size is found in computer-based sections. On e might expect that the computer-based sections could accommodate a larger number of students.
76 Table 10. Average class size of gatekeeper remedial/d evelopmental math sections by delivery format n Average class size Traditional 337 25.298 Hybrid 659 27.771 Computer-based 125 16.864 Research question 2. The second research questi on was Â“Is there a relationship between student success and the technology-assi sted delivery format of the gatekeeper remedial/developmental math sections (u sually MAT 0024C) in Florida community colleges?Â” The data in Table 11 indicate that th e passing rates do reflect a significant difference in student success between secti ons in the different delivery formats and provides the justification to support the sugge stion that the traditional delivery format might contribute to increased student success in remedial/developmental math. The initial analysis only shows that there is a diffe rence, but does not indicate which delivery method appears to be more successful than an other. A Tukey test of honestly significant difference (HSD) revealed that the student pass ra te for sections in th e traditional delivery method is significantly higher than are found in sections in the other two delivery methods at the alpha = 0.05 level. Recognizi ng that the mean passing rates of each group do differ, the researcher examined the pass rates of sections in each delivery method
77 more closely. This comparison supports the conclusion that the tr aditional delivery method appears to be associated with student success more than the other two delivery methods contribute to student success. The pass rate for sections of remedial/ developmental math in the traditional deli very format was 53.5%. The pass rate for sections of remedial/developmental math in the hybrid delivery format was 48.6%. The pass rate for sections of remedial/developmen tal math in the computer-based delivery format was 45.9%. The overall passing rate of all gatekeeper sections of remedial/ developmental math is 49.6%. Table 11 Analysis of passing rates in gatekeeper sections of remedi al/developmental math sections by delivery format Delivery method Total # of sections Passing rate Traditional 337 53.5% Hybrid 659 48.6% Computer-based 125 45.9% All 1,121 49.6% A three-level one-way analysis of varian ce presented in Table 12 demonstrates that the mean passing rates of the secti ons using the three delivery formats are significantly different from each other ( p = <0.0001). The F value and p value rejected
78 the null hypothesis indicating that differences do exist in the means among the three groups. The researcher conducted LeveneÂ’s test of homogeneity of variance to test the ANOVA assumption that the variance in each group is the same. Since the Levene statistic was not significant at the .05 level, the research er failed to reject the null hypothesis, concluding that th e groups are homogenous in variances. Although this analysis shows that there is a difference be tween delivery methods, further analysis is necessary to draw any conc lusions about which delivery method is more successful. Table 12 Analysis of variance summary table Student success and delivery fo rmat in gatekeeper remedial/developmenta l math sections Source df Sum of Squares Mean Square F value Pr > F Between groups 2 0.7630 0.3815 15.24 <.0001 Within groups 1117 27.9709 0.0250 Total 1119 27.7339 Research question 3. Is there a relationship between student success and the technology-assisted delivery format of the gatekeeper remedial/developmental math sections (usually MAT 0024C) in Florida community colleges while controlling for initial placement test scores?
79 The results of the analysis of covarian ce listed in Table 13 indicate that the interaction between the placement test scor e and the delivery format variables is significant. Furthermore, the statistically signi ficant F value (alpha =.05) for the covariate indicates that the analysis of covariance is not the most a ppropriate test to assess the relationship between delivery format and outcomes. Table 13 Analysis of covariance summary table deli very format while controlling for CPT score in gatekeeper remedial/developmental math sections Source DF SS Mean Square F value Pr > F CPT score (C) 1 0.0067 0.0067 0.27 0.6013 Delivery format (D) 2 0.1816 0.0909 3.67 0.0258 C x D interaction 2 0.3057 0.1528 6.18 0.0022 Residual 1092 27.0208 0.0247 Following the inconclusive results of the analysis of covariance, the researcher pursued another avenue to assess the inte ractions between the CPT score and delivery method with an investigation of possible co rrelations between the CPT placement test score and pass rate compared to each deliv ery method. Regression supports a comparison between the possible interact ions between CPT score and delivery formats and the relationships between the pass rates and delivery formats.
80 Table 14 Mean CPT scores of gatekeeper remedial /developmental math by delivery method n Mean SD Traditional 337 46.242 8.9058 Hybrid 659 48.093 5.0998 Computer-based 125 44.501 6.6600 Table 14 lists the mean CPT scores and st andard deviations for students enrolled in sections offered in each delivery format. The sections that are offered in a hybrid delivery format list a higher average section me an and a lower standard deviation than do the other two delivery formats. These data show that traditional delivery sections have the greatest variety in CPT scores. The effect size for traditional delivery is small for both combinations involving the tradit ional delivery sections. CohenÂ’s d for traditional and hybrid is -0.255 and 0.221 for traditional a nd computer-based. Th e effect size in comparing the means of the hybrid and comput er-based delivery formats is medium with CohenÂ’s d 0.605. The interactions between pa ss rates and delivery formats are presented in Figures 2 and 3 in two different layouts. Figure 2 represents the scatter plots and lines of regression of each delivery method while Figure 3 removes the scatter to focus on the lines of regression. The scatter points are impor tant because they show that there is huge variety in the test scores for all delivery methods. Figure 2 reveals the clustering around the middle of both axes with a considerable amount of scatter. The first glance at this
81 scatter plot and regression lines might l eave the general impression that there is no significant difference in the relationshi p between CPT score and pass rate. Figure 2 Comparison between CPT scor e and pass rate by delivery method Upon closer examination of each delivery format viewed in Figure 3 with the scatter points removed, however, differences do emerge. The data seem to suggest that the student with higher CPT scores may have a greater likelihood of success in a traditional delivery course than in sections e ither the hybrid or computer-based delivery
82 methods. This is consistent with the finding in the second research question but delves deeper into the interaction between the placement test score and pass rate for a student enrolled in a section delivered in the traditional delivery format. In the traditional delivery sections, a stude nt with a CPT score of 20, at the lower end of the 60-point range, might expect a 45 % chance of success in the course while the student whose CPT score is near 80, at the upper end of the range might expect a 65% chance of success in the course. Conversely, the range of expected success for the hybrid delivery sections decreases from 54% to 41% as the studentÂ’s CPT score increases. In the computer-based sections, the range of expect ed success is relatively stable, with a 45% chance of success at the lower end of the CP T score range and 46% chance of success at the upper end of the range. A studentÂ’s CPT score seems to increase the expectation of passing the course as the CPT score increases when the student is enrolled in a traditional delivery format and decrease the expectati on of passing the course as the CPT score increases when the student is enrolled in a section offered in the hybrid delivery format. A studentÂ’s CPT score does not seem to increa se or decrease the expectation of passing the course for computer-based delivery format. Figure 2 highlights the apparent interaction between CPT score and pa ss rate for traditional delivery. Removing the scatter points that were pr esented in Figure 2, Figure 3 illustrates the interaction between CPT score and passing rate when focusing on the regression lines while allowing comparison between lines of regression by delivery format. This view indicates that the pass rate for sections offere d in the traditional deli very format increases as the average CPT scores in those secti on increases. Conversely, the pass rate for sections offered in the hybrid delivery form at decreases as the average CPT scores in
83 0% 20% 40% 60% 80% 100% 20304050607080 CPT scorePass rate Traditional Hybrid Computer-basedthose section increases. This seems to cont radict the findings from question 2 and calls for further investigation befo re any conclusions are drawn. Figure 3. CPT score and pass rates by delivery fo rmat for all gatekeeper remedial/ developmental math sections To provide the foundational comparison for examining each delivery format individually, Table 15 presents the mean plac ement test scores for each delivery format. Sections presented in the traditional delivery fo rmat reflect the lowest mean and sections presented in the hybrid delivery reflect the highest mean in hybrid delivery format.
84 Table 15 Mean placement test scores for each delivery format Delivery format Mean Traditional 46.242 Hybrid 48.093 Computer-based 44.501 To expand this line of thinking further, it is relevant to compare the proportions in each delivery format compared to the means reported in Table 15. Figure 4 represents the mean placement test scores for each delivery format ranged from a low mean CPT score of 44.501 in the computer-based delivery sections to a high mean CPT score of 48.093. The mean CPT score for sections in th e traditional delivery format was 46.242. 0 10 20 30 40 50 60 1020304050607080CPT scores % of Section s Traditional Hybrid Computer-Based Figure 4. Distribution of mean placement test scores in three delivery formats
85 Figure 4 represents a proportional distribution of placement test scores by delivery format while controlling for CPT score. This view of the same data represents a visual comparison between the passing rates while co ntrolling for the incoming placement test score Â– particularly showing the relative size of each group and the centering of each delivery format mean. n = 337 mean SD Pass rate 0.5357 0.1529 CPT score 46.2422 8.9058 Figure 5. Correlation between CPT score and pa ss rate for traditional delivery sections of all gatekeeper remedial/developmental math
86 Focusing on the regression lines of each delivery format, it is easier to identify patterns in each delivery format. Figure 5 presents the s catter plot with 95% confidence intervals for sections in traditional deliver y. With an increase of 20% in expected student success from the low end to the high end of the CPT range, the data suggest that there is a positive relationship between CPT score and stude nt success in tr aditional delivery. n = 659 mean SD Pass rate 0.4817 0.1521 CPT score 48.0926 5.0998 Figure 6. Correlation between CPT score and pass rate for hybrid deliv ery sections of all gatekeeper remedial/developmental math
87 The scatter plot with 95% confidence intervals for s ections with hybrid delivery format is presented in Figure 6. A decrease of 13% in the rate of success from the low end of the CPT range to the upper end sugge sts that there is a slightly negative relationship between CPT score and student success in the hybrid delivery format. n = 125 mean SD Pass rate 0.4597 0.1978 CPT score 44.5005 6.6600 Figure 7. Correlation between CPT score and pass rate for computer-based delivery sections of all gatekeeper remedial/developmental math
88 As shown in Figure 7, the line of regressi on and scatter plot for sections with computer-based delivery format seems to be truly scattered without any apparent clustering. With a relatively stable pass rate, le ss than 1% variation from the low end to the upper end of the range, th e data suggest that there is no relationship between CPT score and student success in the computer-based delivery. Research Question 4 Is there a relationship between student success and the technology-assisted delivery format of remedial/developmental ma th classes in community colleges in Florida while controlling for instructor influence? The occurrence of an individual faculty member teaching in multiple formats was not found to be sufficient to research this question with confidence. Of the 28 community colleges in the state, only 12 were found to offer the gatekeeper remedial/developmental math course in multiple delivery formats. Furthermore, of the institutions that did offer the gatekeeper remedial/developmental math course in multiple delivery formats, the faculty assignments were most often limited to one delivery format or another. Of the 12 potential institutions that do offer the gatek eeper remedial/developmental math course in multiple delivery formats, only five institutions of those institutions actually reported a single faculty member teaching the gatekeeper remedial/developmental math course in more than one delivery format. As shown in Table 16, there were a total of 41 sections taught by 15 different faculty members. No i ndividual faculty member taught in all three delivery formats.
89 Table 16 Pass rates in sections when faculty memb ers taught in multiple delivery formats Traditional Hybrid Computer-based 46.7% 33.3%1 Faculty A 42.3% Faculty B 45.3% 45.4% 78.3% 34.8% Faculty C 61.9% 58.1% 37.0% Faculty D 37.5% 22.2% 62.5% 65.5% Faculty E 55.2% Faculty F 63.0% 17.4% Faculty G 72.0% 36.0% Faculty H 69.2% 62.5% 80.8% 52.2% Faculty I 80.0% Faculty J 52.0% 33.3% Faculty K 43.3% 31.0% 34.6% 57.1% Faculty L 76.0% 55.6% Faculty M 86.7% 66.7% 48.1% 36.4% Faculty N 46.2% 68.2% 65.0% Faculty O 54.5% Average 57.8% 61.03% 44.79%
90 Eight different faculty members taught a combination of traditional and computerbased delivery formats and seven faculty me mbers taught in hybrid and computer-based delivery. There was no combination of a singl e faculty member teaching in traditional and hybrid delivery. Although the numbers of in stances in which a single faculty member taught in multiple formats is limited, it is intere sting to note that the passing rates seem to be higher in traditional or hybrid delivery sections compared to the computer-based sections. Summary The purpose of this research was to examine the effectiveness, as measured by student success, of technology-assisted in struction for remedia l/developmental math courses in Florida community colleges. For question 1, this study shows that 55.8% of all remedial/developmental math courses in Fl orida community colleges are offered in a hybrid delivery format -that is, with at least some tec hnology component. Gatekeeper sections Â– those that contain the state ex it exam -comprise 58% of all remedial/ developmental math sections in Florida community colleges. Half of the Florida community colleges offer their remedial/devel opmental math in only one delivery format. Ninety-six percent of the 1,089 to tal sections of the gatekeeper course that were offered in the hybrid delivery format were offered in either medium or large community colleges. All of the 244 total sections that were offere d in the computer-based delivery format were offered in medium and large community colleges. There is little consistency in the ways that remedial/developmental math is offered in the 28 community colleges in Florida. More than half the remedial/
91 developmental math in Florida is offered in a hybrid delivery format. Results of this study suggest that sections of remedial/developmental math offered in the traditional delivery format might contribute to student success more often than in comparable sections offered in either hybrid or computer-based delivery. For question 2, there is a difference in the passing rates by delivery format in Florida community colleges. The mean passi ng rates for each delivery format suggest that there is an increased lik elihood that a student will be successful in a traditional classroom setting for the gatekeeper remedi al/developmental math course in a Florida community college. Additionally, question 3 re veals that a studentÂ’s likelihood of being successful in the gatekeeper remedial/dev elopmental math course increases as the studentÂ’s corresponding CPT score increases in a traditional delivery format and decreases as the studentÂ’s co rresponding CPT score increases in a hybrid delivery format. Results also suggest that as a studentÂ’s pl acement test score increases, the incidence of student success in gatekeeper remedial/d evelopmental math increases only in the traditional delivery format. In the hybrid de livery format, a studentÂ’s likelihood actually decreases as the placement test score increa ses. There is no change in the studentÂ’s likelihood of success when enrolled in a computer-based delivery format section of gatekeeper remedial/developmental math. Question 4 reveals that there is little incidence of a single faculty member teaching remedial/developmental math in more than one delivery format. This phenomenon might suggest that a single cour se offered in different delivery formats would require additional work for the faculty member.
92 This chapter presented the resulting da ta analysis following the procedures described in Chapter 3. The findings show that there is much variety in the remedial/ developmental math in the Florida community colleges. The data suggest that there is a significant difference in the pass rates of th e gatekeeper courses in Florida community college in different delivery formats. Furtherm ore, the data suggest that the traditional delivery format might contribute to student success in remedial/developmental math courses in Florida community colleges.
93 Chapter Five Summary of Findings, Conclusions, and Im plications for Practice and Research The purpose of this study was to inves tigate the effectiveness, as measured by student success, of technology-assisted in struction for remedia l/developmental math courses in Florida community colleges. Furthe rmore, this study isolated two variables that might have been relevant as predictors of student success in th ese courses: placement test score and faculty variance. For the purposes of this study, student success was defined as completion of the remedial/developmental math sequence and pass ing the statewide exit exam. The sections of remedial/developmental courses identified as gatekeeper sections were sorted in traditional hybrid and computer based Traditional sections are those in which a specific meeting time and place are identified and the instructor provides most of the instruction without a signi ficant computer segment. Computer-based sections are those that take place in a computer lab and ar e completely based on computer software packages. Hybrid sections are those that have clearl y identifiable components of lecture and computer support. Hybrid sections are a combination of the other two formats. For the purposes of this study, only the gatek eeper courses were analyzed. Gatekeeper courses are those that contain th e mandatory statewide exit exam.
94 Method Summary To isolate the gatekeeper sections of the remedial/developmental math courses offered in the 28 Florida community colle ges, the 2002 catalogs and Fall 2002 printed schedules of each institution were analyzed to provide a concise lis t of the applicable courses. Each section of remedial/dev elopmental math was coded by a taxonomy developed by the Center for the Study of Community Colleges and used in seven previous national curriculum studies. The c oding revealed 1,121 sections of gatekeeper remedial/developmental courses in the Fa ll 2002 semester, a sufficient number of sections to analyze for statistical purposes. Summary of Findings Using quantitative analysis techniques, this study explored four research questions, each of which is presented below with a summary of the findings for each question. 1. What remedial/developmental math courses are offered in FloridaÂ’s 28 community colleges? Does the instructi onal delivery format of the remedial/ developmental courses offered in Flor idaÂ’s 28 community colleges vary by institutional size? There were a total of 1,952 sections of all remedial/developmental math courses in the 28 community colleges in Florida in the Fall 2002 semester. More than half of these sections (1,140 of 1,952) were gatekeep er courses, that is the courses that
95 contained the single common measure of st udent success -passing the statewide exit exam. The gatekeeper sections comprised 58.4% of all remedia l/developmental math courses. Half of the 28 institutions offered their gatekeeper remedial/developmental math course in only one delivery format. Two c hoices of delivery format for sections of remedial/developmental math courses were offe red at eleven instit utions and only three of the 28 institutions offered the remedial/developmental math courses all three delivery formats. All of the institutions that offere d a choice of delivery format in remedial/ developmental math courses to students were institutions with at least 3,000 FTE as reported in the 2002 Fact Book of the Florida Community College System The sections offered in the traditional instructor-based lecture delivery format were 31.7% of all remedial/developmental math sections. Hybrid delivery format sections (those that include clearly identifiable segm ents in a traditional and computer-based laboratory format) made up 55.8% of all remedi al/developmental math sections. Sections of remedial/developmental math courses that were wholly computer-based sections were only 12.5% of all remedial/developmental math sections. Of the 28 community colleges in the state, 12 institutions offered reme dial/developmental math in more than one delivery format. The hybrid gatekeeper remedial/developmental courses comprised 59.3% of all remedial/developmental sections. In summary, there is a considerable vari ety in the choices offered to students in remedial/developmental math classes in Flor ida community colleges. More variety in delivery format is offered to students in the medium and large community colleges than is offered to students in small community colleg es. Students in institutions with less than 3,000 full-time enrollments are not offered any op tion in the delivery format of remedial/
96 developmental math courses. More than ha lf of all remedial/developmental math in Florida community colleges is offe red in a hybrid delivery format. 2. Is there a relationship between student success and the delivery format of the gatekeeper remedial/developmental ma th sections (usually MAT 0024C) in Florida community colleges? The initial hypothesis stated earlier that the resear cher expected to find a significant difference at the .05 level in the st udent success rate relative to the variety of formats of remedial/developmental math. An analysis of varian ce supports the initial hypothesis and shows that there is a significant difference ( p =.05) in the passing rates of students who were enrolled in a traditional delivery format of the gatekeeper remedial/ developmental math course. The overall pass ing rate of all gate keeper sections of remedial/developmental math is 49.6%. Isolating traditional delivery format sections of gatekeeper remedial/developmental math pr oduces 53.5% passing rate in the sections offered in a traditional delivery format, a 3.7% increase in the passing over all gatekeeper sections. In comparison, the passing rate for gatekeeper sec tions of remedial/ developmental math in the hybrid delivery format is 48.6% and 45.9% for computerbased delivery format gatekeeper sections of remedial/developmental math. Both the hybrid and computer-based delivery format s ections reflect lower pass rates than the overall pass rate of all gatekeeper remedial/developmental math sections. While it appears that the traditional delivery format is more successful than the other two delivery formats for remedial/developm ental math courses, further research is
97 needed to make a categorical st atement to that effect. Items that should be considered in further research include a stude ntÂ’s registration and success in subsequent math courses. Student satisfaction and faculty satisfaction are other elements to consider with delivery format and class size. Further research is al so needed before this statement could be expanded to include other remedial/developmen tal areas, such as reading and writing. In summary, there is a significant increase in student success in sections of gatekeeper remedial/developmental math offered in tradit ional delivery formats, particularly as compared to the success rates in hybrid and computer-based delivery formats of gatekeeper remedial/developmental math. 3. Is there a relationship between stud ent success and the technology-assisted delivery format of the gatekeeper remedi al/developmental math classes in Florida community colleges while controlling for initial placement test scores? The hypothesis stated earlier indicated that the resear cher expected to find a significant difference at the .05 level in the st udent success rate relative to the variety of formats of remedial/developmental math while controlling for initial placement test scores. Conventional wisdom suggests that a technology component in remedial/ developmental courses will improve student success rates. KulikÂ’s (1994) meta-analysis that reviewed the use of computers in inst ruction reports that st udents learn more and faster in computer-based courses. Perhaps th e reason for the apparent contradiction that surfaces in this study relates to the role of the instructor in computer-based instruction.
98 Also, the literature reported earlier points to differences in the students who are enrolled in remedial/developmental courses as co mpared to the whole student population. The analysis of covariance reveals no di scernable pattern of student success in gatekeeper sections of remedial/developmenta l math when controlling for placement test scores. However, when isolating the lines of regression and confidence intervals at the 95% level, there is a significant interacti on between placement test score and student success in the traditional delivery format. This finding is consistent with the finding from the second research question. There is not a similar interaction fo r the hybrid or the computer-based delivery format. Contrary to the finding related to traditiona l delivery format sections of remedial/ developmental math, the hybrid and compute r-based delivery formats do not mirror the interaction of the traditional delivery format sections. The impact of this finding suggests that students who have higher placement test scores have an in creased incidence of success in the gatekeeper remedial/developm ental math classes in Florida community college in a section offered in a traditional delivery format than in either hybrid or computer-based delivery formats. The sections of gatekeeper remedial/developmental math offered in a hybrid delivery format reflect a decrease in the ra te of student success as their placement test scores increases. In the sections of gatekeeper remedial/ developmental math offered in a computer-bas ed delivery format, there is no interaction between placement test scores and student su ccess. These data only partially support the initial hypothesis as the analys is of covariance was not conc lusive justification of the initial hypothesis. Upon clos er scrutiny, the initial hypot hesis actually has differing results for the three delivery methods: traditional, hybrid, and computer-based.
99 4. Is there a relationship between studen t success and the delivery format of remedial/developmental math classes in community colleges in Florida while controlling for instructor influence? The remedial/developmental math in Flor ida community colleges is most often offered in a single delivery format. In the institutions that do offer the gatekeeper remedial/developmental math course in multiple delivery formats, it is most often with an individual instructor being a ssigned to sections of a single delivery format. Even in the institutions that do offer gatekeeper remedial/developmental math in multiple delivery formats, the instructor assignments are usuall y linked to only one of the delivery formats. There were only 12 occurrences of the same in structor teaching sect ions of gatekeeper remedial/developmental math in Florida community colleges in more than one delivery format in the Fall 2002 semester out of the 1,121 gatekeeper sections in this study. These data reject the null hypothesis since ther e is insufficient evidence to validate the relationship as described in the initial hypothesis. Conclusions The findings of this study support the conc lusion that gatekeeper sections of remedial/developmental math seem to be more successful in a traditional delivery format than in hybrid or computer-based delivery formats. Furthermore, controlling for the variable of incoming placement test scores, th e data support the conclusion that students in traditional delivery format sections with higher CPT average scores have an increased likelihood of success. This study seems to show that technology assistance in remedial/
100 developmental math courses does not provide the help that a teacher in a traditional classroom delivery provides. Limitations This study has several limitations. The first and most obvious limitation is the lack of consistency throughout the state with regard to the placement test scores that place a student into remedial/developmental math courses. There is lack of reliability and validity data surrounding the ma ndated statewide exit exam and exact specifications as to how it will be offered and interpreted. Additiona lly, there is the possibi lity that remedial/ developmental math might be offered in a non-credit schedule or by a third-party vendor. The non-credit sections offered at Florid a community colleges and the remedial/ developmental math offered by third-party vendors were not included in this study because of the initial parameters of the st udy and lack of accessibility to corresponding data on the non-credit portion of the cu rricula or from third-party vendors. Implications for Practice The results of this study lead to seve ral implications for decision-making about remedial/developmental math in Florida community colleges. The results of this study provide several notes of encouragement for ins titutions that may not be able to offer as much variety in the delivery of remedial/dev elopmental math courses as other institutions offer. There is also encouraging news in the findings for community colleges that do elect to offer remedial/developmental math in an online or wholly computer-based delivery
101 format. These implications and reco mmendations include implications and recommendations at both the state leve l and at the institutional level. State level implications. At the state level, policy implications include a call for consistency across in the state in the cr iteria that place students into remedial/ developmental math courses and definition of the avenues for students to exit the remedial/developmental math program. Change s at the state level should begin with reliability and validity norming for the stat ewide mandated placement test score. Texas faced this issue and chose to test their plac ement test for reliability and validity rather than abandon their placement test. Increased standardization throughout the state would provide more consistent data that would enhance in-depth statewide assessment and analyses of best practices. Also at the statewide level, there are ad ministrative implications. Two particular inconsistencies in the ways that remedial/dev elopmental math is administered across the state contribute to a disparate implementati on across the legislative assignment to the community colleges. (1) A statewide standard score for the placement test that places a student into remedial/developmental math in Florida community colleges would provide the consistency needed to accurately assess th e implementation of the legislative mandate that the community colleges are responsible for remediation. (2) Additionally, a statewide standard for the criteria that allow a student to take the exit exam as well as a statewide standard for the score that is required to pa ss the exit exam before proceeding into college level math courses would only strengthen th e program. Similarly, a consistent standard
102 that applies in all community colleges in th e state to determine how student are placed into remedial/developmental math classe s would provide a le vel playing ground. Institutional implications. At the institutional level, there are identifiable bright spots in the findings of this study. The first good news is a suggestion that each delivery method may be successful, but in different ways. One item will be of interest for those institutions that may face fiscal constrai nts that might inhib it the purchase and the continued expense needed to support offering remedial/developmental math courses in a computer-based delivery format. These data suggest that the institution that offers remedial/developmental math in only one de livery format may not be limiting student success. The reasons for offering only one de livery format in remedial/developmental math may include limited funding, but may also be tied to a myriad of other reasons. While the possibility of fiscal constraints exists in all institutions, the problem may particularly acute at the sma ll community colleges. The findings of this study suggest that the institutions that do not offer remedial /developmental math courses in multiple delivery formats may not rest rict students by providi ng only one delivery format, particularly since the least expensive delivery fo rmat is the traditional delivery format. In fact, the pass rate seems to increase for stude nts enrolled in a traditional delivery format. This may be good news from the financial perspective because the traditional delivery format is likely the most cost-effective deliv ery method, cost effec tive because the only per term cost for the instituti on is compensation for an instru ctor. This may also be good news for the student who is looking at th e cost per course si nce the textbook in a traditional delivery format can often be reused from one term to the next and therefore,
103 may be available at a used book price. This study also suggests that an institution that may encounter difficulty in securing fundi ng to support the more expensive delivery formats may not be limiting student success by not offering more options of delivery formats. The bottom line is that the data sugge st that traditional ch alk-and-talk approach in which an instructor teaches in a lecture-based format may be as at least as successful as the other varieties of delivery formats, if not more successful than other delivery formats. The results of this study provide a bright spot for instituti ons that might have invested funds into technology to support re medial/developmental labs or courses or may have faculty members who especially want to teach in the hybrid delivery format. While there are a multitude of factors that contribute to student suc cess, the data suggest that sections delivery in a hybrid delivery form at may contribute to student success. Any institution that chooses to o ffer these courses in several delivery formats may certainly want to provide an option for hybrid delivery. The data suggest that the hybrid delivery format may be particularly su ccessful with students whose placement test scores are at the lower end of the range of placement test scores. Also at the institutional level, there is encouraging news for the institutions that have reason to offer remedial/developmental math through fully computer-based and/or online delivery formats. This may also apply to the students who have a need to find a section of remedial/developmental math cour se at a time or location other than the traditional class allows. The finding is simply that the pass rate seems to be about the same for students in the fully computer-bas ed and online sections regardless of the studentÂ’s placement test score. While there ma y be concerns about st udent retention in an online section, the data sugge st that any student who does complete the remedial/
104 developmental math course in an online de livery format will likely be as successful without regard to placement test score. Inconsistencies in the presentation of remedial/developmental math courses in the college catalogs and printed sc hedules could very well lead to confusion and negative reinforcement. One institution identified two levels of remedial/developmental math in the college catalog but only one level was listed in the schedule There was a schedule note that students should enroll in the gatek eeper level of remedial /developmental math as was listed in the printed schedule. Student s would subsequently be placed into an appropriate level of math base d on a cut-off score. If this is a way to allow students the opportunity to test out of the remedial/devel opmental math into college level math and bypass remedial/developmental mat h, the wording should be cleare r. However, if this is a way to administratively place students into the lower level remedial/developmental math course, this student will likel y perceive this as backward placement. This backward placement will surely foster a negative attit ude toward remedial/developmental math and could have a negative correlati on with student retention. Several community colleges specify the le cture and lab components of the class separately but require them as co-requisites while other institutions show the courses as integrated without specifying the lab component Some course descriptions make it very clear that there is an integrated lab component. There shoul d be clear descriptions so that the student reading the printed schedule with s ection descriptions would be able to clearly identify the delivery format prior to the firs t day of class. While delivery format may not be a top priority in the mind of some indivi dual students, the sugge stion that there is a
105 difference in the likelihood of student success indicates that it may actually matter which delivery format the student chooses. The decision-makers in each institution may want to consider the pass rates for the different delivery formats as they choose the delivery format for remedial/ developmental math sections. One considera tion in making these decisions might be the expense involved in each delivery format. The expenses considered might include the impact on the financial resources of (a) th e institution and (b) each student who enrolls for the semester. (a) The impact on financial resources for th e institutions is largely centered on the cost of the initial hardware for a com puter lab and then the ongoing expense of maintaining the hardware and personnel to staff the computer lab. Additionally, the software to support the remedial/developmental math classes might be charged as an annual license that must be constantly upgraded or calculated on a per student basis. Either way, the softwa re costs are most likely not a one-time expenditure. If the software is purcha sed without the limitation of an annual license, the institution still faces the f act the newer and improved software will constantly be promoted. (b) A student who enrolls in a remedial /developmental math course will not necessarily think about any cost diffe rential between the different delivery formats available since the tuition charge will be cal culated by the credit hours associated with the course. The student may not even realize that a cost differential might exist in the course requi rements for sections offered in different delivery formats. A student who selects a section offered in a traditional delivery
106 format may likely have the opportunity to purchase a book that might be available as a used book at a lower cost than pu rchasing a new book. In c ontrast, the student in a computer-based section will not understand why there is no used textbook available. The computer-based delivery sec tion may utilize a text that is actually a license that the student must purchase for a semester with a book that supports the software. In this case, the book is not one th at the student will be able to sell back as a used book. The student may beco me confused about the book that is purchased with the software license for the semester and may not understand why it cannot be sold back to the bookstore. The book used in hybrid delivery format sections may be a combination of the other delivery formats or only a textbook. Either way, the selection of delivery format for each section should include consideration of the financial impact on each student with regard to the textbook requirement. Implications for Research The results of this study suggest several areas for future research: 1. Expand this study to include remedial/developmental reading and writing. This study only scratches the surface in provi ding needed information to decision-makers who select delivery formats for remedial/dev elopmental math courses. These findings may apply to other remedial/developmental disciplines but cannot be expanded to other areas without appropriate resear ch to explore their applicab ility to other areas. Further research should be done to investigate these same questions in other remedial/ developmental areas, specifically remedi al/developmental reading and remedial/
107 developmental writing. Similarly, further study is needed to inve stigate these same questions using the individual student as the unit of analys is rather than the section. 2. Compare student success in the integrated remedial/developmental course with the two or three course sequence of re medial/developmental math courses. Since the integrated remedial/developmental math cour se (often MAT 0020) is not offered at all community colleges in Florida, further resear ch is needed to analyze any difference in student success in the integrat ed course. If there is a signi ficant difference in student success in the integrated course, more institutio ns might want to include this course in their curriculum perhaps in addition to the tw o-step sequence. The institutions that offer the two-course sequence in addition to an inte grated course seem to offer more sections of the two-course sequence than of the inte grated courses. Since this option does offer choices to the student, furthe r research might investigate and compare the student success rates in both formats. 3. Compare student success in computer -based remedial/developmental math courses with computer-based college level math courses. Further research is needed to analyze some of the other fact ors that affect the success rate of remedial/developmental math students in computer-based classes as compared to students who are enrolled in college level math courses in a computer-bas ed delivery format. There is research to indicate that technology in th e classroom enhances the lear ning process. However, there are suggestions in the literature that the very factors that have led to studentsÂ’ placement in remedial/developmental math classes such as inadequate preparation for college level math or lack of the self-discipline needed for college success suggest that technology is not necessarily the most successful format for that student population. The focus of this
108 study did not concentrate on cl ass size, age, or gender. One observer suggested that perhaps the student who chooses to enroll in a computer-based sect ion feels comfortable doing so because of an increased computer literacy that is mo re common with younger students. On campus, an increase in computer-b ased classes might relate to a desire to maintain cutting edge technology in the classroom. Summary In summary, the implications for practi ce provide suggestions at the state level and at the institutional level. The first requirement might be the development of consistent standards to be applied to all remedial/developmental math courses across the state. The community collegeÂ’s responsibil ity for remedial/developmental math might include statewide tests that have been nor med and validated, including both a placement test and an exit exam. Secondly, at the institu tional level, decision-makers might consider the pass rates for students in al l remedial/developmental math courses, particularly in the gatekeeper courses when selecting a delivery format for the course. Implications for research should begin w ith similar studies in reading and writing. Further research should be done to investigate the success rate of the integrated remedial/ developmental math course as compared to the two or three course sequence. Additionally, further research should to compare the success rates of students in remedial/developmental math courses and stude nts in college level math courses. The area of remedial/developmental courses is rich with other possibilities for further study.
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118 Appendix A: Configuration of Remedial/D evelopmental Math Sequence Community College 001 002 012 020 024 Small A MAT 002 MAT 024 Small B MAT 002 MAT 024 Small C MAT 002 MAT 024 Small D MAT 012 MAT 024 Small E MAT 002 MAT 024 Small F MAT 012 MAT 024 Small G MAT 012 MAT 024 Small H MAT 012 MAT 024 Small I MAT 001 MAT 002 MAT 024 Medium A MAT 012 MAT 020 MAT 024 Medium B MAT 012 MAT 024 Medium C MAT 002 MAT 012 MAT 020 MAT 024 Medium D MAT 002 MAT 024 Medium E MAT 012 MAT 024 Medium F MAT 002 MAT 024 Medium G MAT 002 MAT 024 Medium H MAT 002 MAT 020 MAT 024 Medium I MAT 012 MAT 020 MAT 024 Medium J MAT 002 MAT 024 Large A MAT 012 MAT 020 MAT 024 Large B MAT 002 MAT 024 Large C MAT 002 MAT 024 Large D MAT 002 MAT 024 Large E MAT 012 MAT 020 MAT 024 Large F MAT 002 MAT 020 MAT 024 Large G MAT 012 MAT 020 Large H MAT 012 MAT 024 Large I MAT 012 MAT 020 MAT 024
119 Appendix B: Mathematics courses offered in Fall 2002 in Florida community colleges Course number Course title MAC 1105 College Algebra MAC 1114 College Trigonometry MAC 1140 Pre-calculus Algebra MAC 1147 Pre-calculus Algebra/Trigonometry MAC 1154 Analytic Geometry MAC 1233 Essentials of Calculus MAC 1930 Special Topics in Calculus MAC 1932 Special Topics in Mathematics MAC 2233 Business Calculus MAC 2234 Applied Calculus II MAC 2253 Calculus for Engineering Technology MAC 2311 Calculus and Analytic Geometry I MAC 2312 Calculus and Analytic Geometry III MAC 2313 Calculus and Analytic Geometry III MAD 2104 Discrete Mathematics MAE 2801 Elementary School Mathematics MAP 2302 Differential Equations MAS 2103 Linear Algebra MAT 0002 Basic Mathematics MAT 0012 Basic Algebra MAT 0020 Integrated Arithmetic and Algebra MAT 0024 College Preparatory Algebra MAT 1033 Intermediate Algebra MAT 1325 Engineering Technology Math I MAT 1326 Engineering Technology Math II MGF 1106 Math for Liberal Arts I MGF 1107 Math for Liberal Arts II MGF 1112 Logic MTB 1101 Business Math MTB 1103 Business Mathematics
120 Appendix B (continued) Course number Course title MTB 1310 Applied Mathematics MTB 1321 Technical Algebra and Trigonometry I MTB 1322 Technical Algebra and Trigonometry II MTB 1327 Math for Electronics I MTB 1328 Math for Electronics II MTB 1348 Technical Mathematics MTB 1370 Math Topics for Health Professionals MTG 2204 Geometry for Teachers MTG 2206 College Geometry QMB 1001 College Business Mathematics QMB 2100 Business and Economics Statistics indicates remedial/developmental mathematics course
121 Appendix C Coding Decision Rules Delivery format Decision rules Traditional delivery Any section that app eared with a specific meeting place and time, without any additional info rmation to specify a laboratory component, was coded as traditiona l. Sections that were coded as traditional were listed in the printed schedule with a specific meeting place and time and with no indication of any use of technology during the delivery of the course. The section listing in the printed schedule wa s compared with the course listing in the college catalog. There were cases of the course descriptions providing the onl y indication of the use of technology in the course. For instance, if a section was presented in the printed schedule with a specific meeting place and time and no mention of a co mputer lab, but the course listing in the college catalog indi cated a co-requisite lab, the section was not coded as traditional. Hybrid delivery A hybrid class was listed in the schedule as one in which the course listing in the printed sc hedule contains both classroom and computer lab components. Hybr id sections were those that clearly contained elements of traditional lecture-based and technology. For instance, if the co -requisite lab was indicated in the college catalog, the co-r equisite lab would provide justification to code those s ections as hybrid rather than traditional. In order to be excluded from being coded as computer-based delivery, there must be an element of traditional delivery in addition to the computer lab element of the course listing. This might be shown through two different meeting places, one classroom and one computer lab. Computer-based delivery A computer-based section was liste d in the schedule as one in which the students took the course in a computer lab for the entire class period. Sections that were coded as computer-based were those without any indicati on of lecture-based traditional classroom. These sections might be listed in the printed schedules as online or distance learning. Other sections were coded as computer-based if th e printed schedule listing showed only a computer lab as the meeting place or if there was a printed comment that the course was based on a specific software package as the primary focus.
122 About the Author Mary M. Bendickson received a Bachelor of Arts degree in Mathematics and Education in 1972 from Tift College, Forsyth, Georgia and a Master of Education degree in Counselor Education in 1975 from the Univer sity of Georgia, Athens, Georgia. More than thirty years of teaching and counseling experience in numerous educational settings involves 12 different locations including five states a nd two overseas locations. Her teaching assignments include Trident Techni cal College in Charleston, South Carolina; Virginia Beach City Public Schools in Virginia Beach, Virginia; Harrison Central High School in Gulfport, Mississippi; and a Depart ment of Defense Dependent School (George Cannon School) on Midway Islands. She served as guidance counselor and e ducation specialist for military education programs at two different military bases, becoming uniquely conversant on the particulars of all branches of military service. She has served as an administrator at Hillsborough Community College in Tampa, Florida for five years