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THE EFFECT OF MATH ANXIETY ON THE ACADEMIC SUCCESS OF DEVELOPMENTAL MATHEMATICS STUDENTS AT A TEXAS COMMUNITY COLLEGE A Dissertation by KRISTEN D. FANNINCARROLL Submitted to the Office of Graduate Studies Texas A&M UniversityCommerce in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION May 2014 THE EFFECT OF MATH ANXIETY ON THE ACADEMIC SUCCESS OF DEVELOPMENTAL MATHEMATICS STUDENTS AT A TEXAS COMMUNITY COLLEGE A Dissertation by KRISTEN D. FANNINCARROLL Approved by: Advisor: Madeline Justice Committee: Joyce Miller Joyce A. Scott Head of Department: Glenda Holland Dean of College: Gail Johnson Dean of Graduate Studies: Arlene Horneiii Copyright © 2014 Kristen D. FanninCarroll iv ABSTRACT THE EFFECT OF MATH ANXIETY ON THE ACADEMIC SUCCESS OF DEVELOPMENTAL MATHEMATICS STUDENTS AT A TEXAS COMMUNITY COLLEGE Kristen D. FanninCarroll, EdD Texas A&M UniversityCommerce, 2014 Advisor: Madeline Justice, EdD The purpose of this study was to examine the relationship between math anxiety and academic success of developmental mathematics students at a Texas community college based on age, gender, and level of developmental mathematics program. A quantitative, casualcomparative design was used to determine relationships. A total of 185 developmental mathematics students were surveyed using the Revised Mathematics Anxiety Scale and a demographic questionnaire. Of the 185 survey packets returned, fully completed, and analyzed, 61.6% (N = 114) of the participants were female, 44.3% (N= 82) of the participants were between the ages of 18 and 22 years old, 24.9% (N = 46) of the participants were enrolled in the fourth level of developmental mathematics (DMAT 0098), and 28.6% (N = 53) of the participants earned a C for their final course grade. Of the 185 participants, 41.1% (N = 76) were v enrolled in a low difficulty level developmental course (DMAT 0066 or DMAT 0090), and 58.9% (N = 109) were enrolled in a high difficulty level developmental mathematics course (DMAT 0097, DMAT 0098, or DMAT 0099) (see Table 5). Of all the participants, 70.3% (N = 132) successfully completed their developmental mathematics course with a letter grade of A, B, or C, indicated academic success. A total of 57.3% (N = 106) of the participants scored a 71 or lower on the RMARS, which indicated a low level of math anxiety. A total of 42.7% (N = 79) of the participants scored a 72 or higher on the RMARS, which indicated a high level of math anxiety. A statistical difference existed between level of math anxiety based on developmental mathematics courses with low and highlevel difficulty, but there was no statistical difference between level of math anxiety based on age or gender. vi ACKNOWLEDGEMENTS First, I give all my praise and glory to my Lord and Savior Jesus Christ for He has truly blessed me during this doctoral process. This journey has been long and difficult, but by His grace and mercy, I accomplished this professional and personal goal. Now that this journey has concluded, I look forward to seeing what He has in store for me. “And whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks to God the Father through Him” (Colossian 3:17). To my husband, Eric, words cannot express how grateful I am for your patience, understanding, motivation, and encouragement. You supported me throughout this journey and allowed me to cry, sing, scream, and rejoice. Thank you for your words of inspiration and being one of my biggest cheerleaders. I am truly blessed to have you not only as my partner, but also as my best friend. I love you with all my heart and soul. To my parents, Bruce and Barbara, I could not have done this without you. You have been by my side and pushed me to succeed and meet every challenge and obstacle with persistence and focus. Your continued prayers lifted me when I was down and kept me going when I wanted to give up. I thank God for giving me parents who have always been there and love me unconditionally. This is for you. To my siblings, Randall (Rachella) and Cres, thank you for being supportive and showing me what it takes to be successful in spite of any obstacle. To my nieces and nephews, know that you can do anything you desire with hard work and determination. I love you all. To the rest of my family (Fannins, Askews and Fraziers), thank you for believing in me and encouraging me. Even if you do not know what you said or did to help, your words did not go unnoticed and were vii greatly appreciated. Your prayers, jokes, hugs, and phone calls boosted my confidence and determination to complete this degree. Thank you all for supporting me as I achieved this dream. To my friends, fellow doctoral buddies, and work family, thank you for all of your prayers and words of encouragement. To Dr. Rosalyn Walker, thank you for taking me under your wing when I first began the doctoral program back in 2009. Meeting you was truly a blessing. To Rayna Matthews, it has been a pleasure experiencing this educational journey together; you mean more to me than just a colleague, I consider you my friend and my sister. A special thank you to Anastasia Lankford and my friends at the writing center for taking my mind off things when I needed to lighten up. Thank you to my church families, New Life Baptist Church (Quitman, Texas) and North Dallas Community Bible Fellowship (Plano, Texas). Thank you to my sisters in Alpha Kappa Alpha Sorority, Incorporated, specifically to my line sisters, E.S.O.E, Fall 2003. To the faculty and staff at Texas A&M UniversityCommerce, I would like to thank you all for your guidance and support. To my committee, Dr. Madeline Justice, Dr. Joyce A. Scott, and Dr. Joyce Miller, I thank you for your support, wisdom, and supervision. Each of you continuously pushed me to be better and raise my expectations. Your support has truly been unconditional. A special thank you goes to Dr. Katy Denson for her time and assistance. To Dr. Rodger Pool, you are the reason I started this journey. You saw greatness in me when I did not see it myself, and you gave me the confidence to do more with my education and my career. I will forever be grateful to all who have assisted me in realizing this dream. “But thanks be to God, who gives us the victory through our Lord Jesus Christ” (1 Corinthians 15:57) viii TABLE OF CONTENTS LIST OF TABLES ....................................................................................................................... xi LIST OF FIGURES .................................................................................................................... xii CHAPTER 1. INTRODUCTION ........................................................................................................ 1 Statement of the Problem ....................................................................................... 4 Purpose of the Study .............................................................................................. 5 Research Questions ................................................................................................ 5 Research Hypotheses ............................................................................................. 6 Significance of the Study ....................................................................................... 6 Method of Procedure............................................................................................ 12 General Procedures .................................................................................. 12 Design of Study........................................................................................ 13 Selection of Location Site ........................................................................ 13 Preliminary Procedures ............................................................................ 14 Selection of Sample Population ............................................................... 14 Selection of Participant Criterion............................................................. 16 Description of Instruments ....................................................................... 16 Collection of Data .................................................................................... 17 Treatment of the Data .............................................................................. 19 Definitions of Terms ............................................................................................ 21 Limitations ........................................................................................................... 22 Delimitations ........................................................................................................ 23 ix CHAPTER Assumptions ......................................................................................................... 23 Organization of Dissertation Chapters ................................................................. 23 2. REVIEW OF LITERATURE ..................................................................................... 25 Developmental Education .................................................................................... 25 Issues in Developmental Education ......................................................... 25 Initiatives and Alternatives in Developmental Education ....................... 30 Developmental Mathematics ............................................................................... 34 Issues in Developmental Mathematics..................................................... 36 Initiatives in Developmental Mathematics .............................................. 38 Math Anxiety ....................................................................................................... 42 Attitudes toward Mathematics ................................................................. 42 Studies of Math Anxiety in Preservice Teachers ..................................... 45 Studies of Math Anxiety in Students ....................................................... 49 Summary .............................................................................................................. 50 3. METHOD OF PROCEDURE..................................................................................... 52 Design of Study.................................................................................................... 52 Description of Sample Population ........................................................... 52 Description of Participant Criterion ......................................................... 53 Description of Instruments ....................................................................... 54 Collection of Data .................................................................................... 55 Treatment of Data .................................................................................... 57 Summary .............................................................................................................. 58 x CHAPTER 4. PRESENTATION OF FINDINGS ............................................................................. 60 Descriptive Analysis ............................................................................................ 60 Description of Participants ....................................................................... 60 Statistical Analysis of the Research Questions and Hypotheses ......................... 63 Research Question 1 ................................................................................ 64 Research Question 2 ................................................................................ 67 Research Question 3 ................................................................................ 69 Research Question 4 ................................................................................ 71 Summary ........................................................................................................... 74 5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH ..... 75 Summary of the Findings ..................................................................................... 76 Conclusions .......................................................................................................... 78 Implications.......................................................................................................... 79 Recommendations for Further Research .............................................................. 80 Summary .............................................................................................................. 81 REFERENCES ............................................................................................................................ 83 APPENDICES ............................................................................................................................. 91 Appendix A. Instrument Permission Letter and Response ........................................................ 92 B. Recruitment Letters .............................................................................................. 95 C. Participant Survey Packet .................................................................................... 98 VITA……………. ..................................................................................................................... 106 xi LIST OF TABLES TABLE 1. Number of Sections by Course Name .................................................................. 15 2. Level of Difficulty by Course Name ................................................................... 20 3. NCES Remedial Math Statistics: 2009 ................................................................ 35 4. Returned Survey Packets Breakdown .................................................................. 56 5. Descriptive Statistics for Variables ...................................................................... 61 6. Mean and Standard Deviation of RMARS Anxiety Score by Course Difficulty Level .................................................................................................... 66 7. ANOVA Statistics for RMARS Anxiety Score by Course Difficulty Level ....... 66 8. Mean and Standard Deviation of RMARS Anxiety Score by Age Group .......... 68 9. ANOVA Statistics for RMARS Anxiety Score by Age Group ........................... 69 10. Mean and Standard Deviation of RMARS Anxiety Score by Gender................. 70 11. ANOVA Statistics for RMARS Anxiety Score by Gender ................................. 71 12. Correlation Results of RMARS Anxiety Score and Final Course Grade ............ 73 13. Regression Statistics for RMARS Anxiety Score and Final Course Grade ......... 73 xii LIST OF FIGURES FIGURES 1. RMARS total score .............................................................................................. 62 2. RMARS anxiety level by course difficulty level ................................................. 65 3. RMARS anxiety level by age group .................................................................... 67 4. RMARS anxiety level by gender ......................................................................... 70 5. RMARS anxiety level by final course grade ....................................................... 72 1 Chapter 1 INTRODUCTION Understanding mathematics has become more challenging for many high school and college students compared to any other subject. Research shows that many students do not have basic mathematics skills when they enter college (Achieve, 2011; ACT, 2010c; Haycock, 2010). As students transition into institutions of higher education, their academic skills and comprehensive knowledge are questioned and tested, and many students realize their lack of skills needed to succeed at the college level. As the demand for higher education and the need to address the inadequacy of mathematics skills has increased, community colleges have begun to help students transition from high school to college. According to Cohen and Brawer (2003), The percentage of those graduating from high school grew from 30 percent in 1924 to 75 percent by 1960, and 60 percent of the high school graduates entered college in the latter year. Put another way, 45 percent of eighteenyearolds entered college in 1960, up from 5 percent in 1910. (p. 6) The creation of community colleges began as an idea to lessen the burden of teaching general education courses to younger students. The first junior or community colleges were proposed in 1851 by the President of the University of Michigan, Henry Tappan, in 1859 by a University of Georgia trustee, William Mitchell, and in 1869 by the President of the University of Minnesota, William Folwell (Cohen & Brawer, 2003; Jurgens, 2010). These educational leaders noted that providing general education skills to high school graduates presented a challenging responsibility to universities and required more research. In the late 19th Century, William Rainey Harper of the University of Chicago, Edmund J. James of the University of Illinois, and David Starr Jordan of Stanford 2 promoted the idea of creating institutions that were extensions of secondary schools. In 1901, these ideas and the passion of William Rainey Harper led to the founding of the first junior college, Joliet Junior College, located in Chicago (Cohen & Brawer, 2003). The growth of community colleges continued as the United States realized that the rapid increase in high school graduates and the need for a more skilled workforce called for more communitybased institutions to fulfill the demand (American Association of Community Colleges [AACC], 2008; Cohen & Brawer, 2003). As community colleges became more popular, state legislators and policymakers placed more responsibility upon these schools. Community colleges were designed to provide appropriate curricular functions including “academic transfer preparation, vocationaltechnical education, continuing education, developmental education and community service” (Cohen & Brawer, 2003, p. 20). The roles and responsibilities of community colleges continued to expand, and the education of their students was top priority. As the United States continued to seek methods to increase the quality of education of high school graduates who were transitioning to postsecondary education, community colleges were faced with the challenge of meeting the needs of students who lacked basic reading, writing, and mathematics skills. At local community colleges, many students found themselves in developmental education programs. As such, developmental education, sometimes called remedial education, had become the driving force behind the mission of most community colleges. According to Bailey (2009), Community colleges are charged with teaching students collegelevel material, yet a majority of their students arrive with academic skills in at least one subject area that are judged to be too weak to allow them to engage successfully in collegelevel work. Thus, 3 a majority of community college students arrive unprepared to engage effectively in the core function of the college. (p. 11) Community colleges strive to provide a quality education to all students, and structure developmental programs to ensure that additional instruction in basic skills is available to and adequate for these students. Courses that are designed to assist underprepared college students with basic skills and college aspirations are considered part of developmental education (Boylan, 2002). According to Boylan (1999a), “almost every community college campus in the country offers some combination of remedial and developmental courses, learning labs, and tutoring programs” (p. 5). Boylan also identified a spectrum of developmental education interventions including “tutoring programs, special academic advising and counseling programs, learning laboratories, and comprehensive learning centers [and] developmental courses” (p. 2). From 2000 to 2010, nearly 100% of public 2year institutions offered remedial services or developmental education courses (National Center for Educational Statistics [NCES], 2011). Boylan and Saxon (1998) evaluated developmental education in Texas public colleges and universities. The following findings pertain to the 44 community colleges that participated: 1. 37.7% of students surveyed were placed in developmental reading. 2. 40.4% of students were placed in developmental writing. 3. 61.8% of students were placed in developmental mathematics. 4. 70.7% of firsttime students who failed at least one section of the Texas Academic Skills Program (TASP) test took at least one developmental course. (pp. 23) As enrollment numbers in community colleges nationwide have steadily risen over last 10 years, these colleges have also experienced drastic increases in the number of students requiring 4 developmental courses (NCES, 2010). Across the nation, 19.1% of all firstyear undergraduate students took a remedial course from 20032008. By the 20072008 academic year, this rate had increased to 20.2% (NCES, 2010). The NCES (2004) found that, nationally, fewer than 30% of entering freshmen had registered for at least one remedial (developmental) course. The report also indicated that more students were enrolling in developmental mathematics courses than in developmental writing and reading courses nationwide (NCES, 2004). Among students enrolled in developmental mathematics courses, the fear of not succeeding is omnipresent. Researchers have found that the negative perception of mathematics is a contributing factor to the failure of mathematics students (Mji & Mwambakana, 2008; Suinn & Edwards, 1982). Some developmental mathematics students are faced with the task of completing several remedial mathematics courses prior to beginning collegelevel mathematics courses. Therefore, the anxiety to succeed looms over the heads of these students. Research has also found that math anxiety, coupled with poor mathematics skills, is interlinked as a possible causal relationship (Bai, Wang, Pan, & Frey, 2009; Brady & Bowd, 2005; Cates & Rhymer, 2003; Chinn, 2009; Lavasani & Khandan, 2011; Mji & Mwambakana, 2008; Prevatt, Welles, Li & Proctor, 2010). However, developmental mathematics students continue to struggle, as they are required to take a variety of noncredit courses before enrolling in college algebra. Statement of the Problem Various researchers have conducted studies to determine the influence of math anxiety on students (Bai et al., 2009; Boylan, Bonham & White, 1999; Chinn, 2009; Meece, Wigfield, & Eccles, 1990). Research has shown that the level of a student’s math discomfort and anxiety directly affects his or her achievement and progress (Brady & Bowd, 2005; Bull, 2009; Cates & Rhymer, 2003). As negative reactions and attitudes toward mathematics increase, student 5 successes and understanding of mathematics concepts decrease (Lavasani & Khandan, 2011; Mji & Mwambakana, 2008; Prevatt et al., 2010). Research has also found that students who were enrolled in developmental courses are faced with a greater challenge of academic success and have a higher risk of developing math anxiety than do students who were not enrolled in developmental courses (Asera, 2011; Brothen & Wambach, 2004; Fike & Fike, 2012; Kolajo, 2004; Phipps, 1998). The problem of this study was to examine the level of math anxiety in developmental mathematics students at community colleges and its effect on academic success. Purpose of the Study The purpose of this study was to examine the relationship between math anxiety and academic achievement among developmental mathematics students to determine the following: 1. The level of math anxiety in developmental mathematics students at a Texas community college based on age, gender, and developmental program level. 2. The effect of high and low levels of math anxiety on academic success in developmental mathematics courses. Research Questions The following research questions guided this study: 1. Does a difference exist in math anxiety among developmental mathematics students who take lower levels or higher levels of developmental mathematics courses? 2. Does a difference exist in math anxiety of developmental mathematics students between age groups (i.e., 1822, 2327, 2832, 3337, 38 and older)? 3. Does a difference exist in math anxiety among developmental mathematics students by gender? 6 4. Does a difference exist between math anxiety of developmental mathematics students and final course grades? Research Hypotheses The following null hypotheses guided this study, and were tested at the 0.05 level of significance: 1. No significant differences exist in the level of math anxiety of students who take higher difficulty levels of developmental mathematics courses compared to those who take lower difficulty levels of developmental mathematics courses. 2. No significant differences exist in the level of math anxiety of developmental mathematics students based on age. 3. No significant differences exist in the level of math anxiety of developmental mathematics students based on gender. 4. No significant relationship exists in overall developmental mathematics final course grades and level of math anxiety of developmental mathematics students. Significance of the Study Researchers have examined the increased need for programs that promote academic preparation and success among students, including those in community college (Conley, 2008; Phipps, 1998; Southern Regional Education Board [SREB], 2001). College readiness has become a global issue for high school students, parents, high school principals, high school counselors, admissions counselors, and college professors. Conley (2008) defined college readiness “as a level of preparation a student needs in order to enroll and succeed, without remediation, in a creditbearing general education course at a postsecondary institution” (p. 4). Students who are deemed collegeready must possess a strong foundation in reading, writing, 7 mathematics, science, and history. They must also have adequate critical thinking skills and a strong work ethic (ACT, 2010a; SREB, 2001). Therefore, a strong academic curriculum in high school must include courses that challenge and motivate students. Further, alignment of high school graduation requirements and college readiness standards is needed to ensure the sufficient preparation of high school graduates (ACT, 2010c). Conley (2008) identified the following four components necessary for a student to be collegeready: Key cognitive strategies Academic knowledge and skills Academic behaviors Contextual skills and awareness Key cognitive strategies consist of problemsolving skills, research capabilities, reasoning, interpretation of literature, and precision of tasks. Collegeready students must “encompass behaviors that reflect greater student selfawareness, selfmonitoring, and selfcontrol of processes and actions” (Conley, 2008, p. 9). Conley also noted that, for a student to possess adequate academic knowledge and skills, he or she must develop comprehensive skills in all core subjects. Several academic concerns have elicited questions surrounding the academic preparedness of many students who enroll in college as the United States continues to fall behind other countries in science and mathematics. Lack of adequate preparation to complete collegelevel coursework has become a focal point of many K12 systems and higher education institutions in the United States. The Alliance for Excellent Education (AEE, 2006) reported that students who complete the more strenuous track of 4 years of advanced English and at least 3 years of advanced mathematics, science, and social sciences are more prepared for collegelevel 8 curriculum than those that do not take advanced and honors courses in high school. Several policymaking entities have conducted research that suggest college readiness requires global attention (Achieve, 2011; ACT, 2010d, SREB, 2001), and have convened conferences, initiatives, and summits to work on aligning high school curricula and expectations with the standards of postsecondary education (Achieve, 2008; ACT, 2010b, Haycock, 2010). President Barak Obama asked for a new Elementary and Secondary Education Act (ESEA) to “require states to set college and careerready standards” (Haycock, 2010, p. 19). The nation’s mission is to align the curriculum and expectations of high schools with the expectations and needs of postsecondary institutions and employers. The United States has become aware of the significant influence that college readiness has on producing stability in the economy and understands that the students of the future will lead the way. Whether students are heading to college or entering the workforce, their levels of education influence all aspects of their lives. Graduating from high school is an important milestone, and educators, policy makers, and legislators must strengthen the educational foundation of the United States. The educational spotlight is on adequate student preparation for college and career, and the debate as to who is to blame for deficiencies has become more intense. College readiness is more than just how much a student knows; rather, it also involves understanding basic skills and possessing a higher work ethic to shift successfully to postsecondary education. With the federal government advocating K16 alignment of core curriculum standards, institutions of higher education work with high schools to develop partnerships to ensure student success in higher education and the workforce. According to Achieve, Inc. (2011), 47 states and the District of Columbia have developed and implemented 9 alignment of high school standards and postsecondary expectations; 20 states and the District of Columbia have raised the bar on graduation requirements; and 14 of the 50 states administered assessments that produced adequate readiness data. In addition, 22 states have created P20 data systems that connect K12 data with postsecondary systems (Achieve, 2011). Concerning the accountability systems standard, only one state, Texas, met the four indicators; however, Achieve reported optimism that more states would follow in providing data that show improvement in college readiness criteria. Various studies have provided insight into the enrollment and retention rates of developmental students (Boylan et al., 1999; Umoh, Eddy & Spaulding, 1994). Findings suggest that students who successfully pass their first developmental courses are more likely (66.4%) to stay enrolled at the institution the following year (Boylan & Saxon, 1998). Retention has become a focal point for many higher education institutions, and community colleges are no different. The NCES (2004) reported the following enrollment pattern in developmental courses: The proportion of freshman enrolling in at least one remedial reading, writing, or mathematics course was higher at public 2year colleges than it was for all other types of institutions; 42 percent of freshman at public 2year colleges compared with 12 to 24 percent of freshmen at other types of institutions enrolled in such courses. (p. 32) Research has also shown that students in remedial courses are less likely to complete their degrees (AEE, 2006). The National Conference of State Legislatures (NCSL, 2011) stated, “less than 25 percent of remedial students at community colleges earn a certificate or degree within eight years” (p. 2). Rather, many students drop out of community college because of the cost of remedial education and the time required. 10 Developmental mathematics has been placed under a microscope as academic preparedness and developmental education continue to be focal points of higher education. The academic success of developmental mathematics students is at the forefront of many institutional leaders’ and department chairs’ concerns. Of specific concern in the current study is that findings suggest that poor academic performance among developmental mathematics students may be linked to math anxiety (Brady & Bowd, 2005). Many researchers have discussed math anxiety and its influence on various programs and groups such as nursing, finance, teaching, middle school students, and secondary students (Abidin, Alwi & Jaafar, 2010; Brady & Bowd, 2005; Bull, 2009; Chinn, 2009; Wigfield & Meece, 1988). Studies have also reported a variety of findings on the effects of gender and math anxiety. Additionally, several math anxiety assessments and scales have been created, modified, or adapted to identify the indicators and effects of math anxiety (Bai et al., 2009; Baloğlu, 2005; Deniz & Üldaş, 2008; Hopko, 2003; Miller & Mitchell, 1994; Richardson & Suinn, 1972; Suinn & Edwards, 1982). Continuous research has been conducted to test the validity and reliability of these scales (Baloğlu, 2005; Deniz & Üldaş, 2008; Hopko, 2003). Cates and Rhymer (2003) administered the FennemaSherman Mathematics Anxiety Scale (FSMAS) to identify the level of math anxiety and its effect on the fluency and accuracy of college students. The researchers found that participants with higher math anxiety had lower fluency and accuracy than did those with lower levels of math anxiety. Deniz and Üldaş (2008) developed a 39item scale, the Mathematics Anxiety Scale toward Teachers (MAST), to measure math anxiety in teachers and prospective teachers. Bai et al. (2009) used a 14item Mathematics Anxiety ScaleRevised (MASR) to determine the reliability and validity of the bidimensional affective scale, and found that this tool was an authentic measure of math anxiety. 11 Chinn (2009) examined secondary students in England using a 20item questionnaire with a variety of items that focused on different activities and situations in mathematics that may correspond with math anxiety. He found that formal and informal assessments in mathematics increased math anxiety among participants. Abidin et al. (2010) used an adapted version of Richardson and Suinn’s (1972) Mathematics Anxiety Rating Scale (MARS) and found that males in a mathematics of finance course experienced lower levels of anxiety than did female students. The researchers also reported that students’ anxiety levels increased as final examination time arose. Brady and Bowd (2005) examined the level of math anxiety in preservice teachers by combining Richardson and Suinn’s (1972) MARS and a demographic questionnaire. The researchers found that female teachers had higher levels of math anxiety than did male teachers. The findings also indicated, “Mathematics anxiety correlated negatively with confidence to teach mathematics” (Brady & Bowd, 2005, p. 42). Gresham (2007) administered the Richardson and Suinn’s MARS in fall of 2003 and then again in the fall of 2005 to 246 early childhood and elementary teachers. Findings indicated that math anxiety decreased over the course of 2 years. Few researchers have focused solely on the effects of math anxiety on the academic success of developmental mathematics students. A single study was conducted that examined the effects of math anxiety on developmental mathematics students at the community college level. Johnson and Kuennen (2004) applied a mixed methods design and administered a 10question math anxiety test, developed by Ellen Freedman, as a pre and posttest to determine whether math anxiety could be reduced following an intervention. The researchers found a significant difference between the treatment and control groups; however, no statistically 12 significant difference in math anxiety was found between developmental mathematics students and college algebra students. The current study attempted to determine the effect of math anxiety in community college developmental mathematics students. The focus was to understand the effect of math anxiety on the academic success of developmental mathematics students, which has received little attention in recent years. Waycaster (2001) found that 40% of students who transitioned directly to a community college from high school needed some remediation in mathematics. The need to understand more about math anxiety and its effects on developmental mathematics students’ academic achievement was the focus of this study. Method of Procedure To investigate the effect of math anxiety on the academic achievement of developmental mathematics students at various levels of a program, the researcher applied a variety of quantitative research methods and procedures. The methodology of this study is presented in sections dedicated to (a) General Procedures, (b) Design of the Study, (c) Selection of Location Site, (d) Preliminary Procedures, (e) Selection of the Participants, (f) Selection of the Instruments, (g) Collection of the Data, and (h) Treatment of Data. General Procedures Written permission to conduct the study was obtained from the Texas A&M UniversityCommerce (TAMUC) Internal Review Board (IRB) for the Protection of Human Subjects. Following IRB approval, permission to use and reproduce the Revised Mathematics Anxiety Rating Scale (RMARS) was obtained from the author (Appendix A). Permission was acquired from the administrators and developmental mathematics instructors at the selected Texas 13 community college to collect data from students enrolled in the colleges’ developmental mathematics program during the spring 2013 semester. Design of Study This study sought to explain the effects of math anxiety on the academic achievement of developmental mathematics students. The study design was quantitative and used a causalcomparative method. According to Gall, Gall, and Borg (2007), causalcomparative research is a quantitative investigation “in which researchers seek to identify causeandeffect relationships" (p. 306). Within this quantitative study design, four null hypotheses were formulated and tested for statistical significance. A null hypothesis is “a prediction that no relationship between two measured variables will be found, or that no difference between groups on a measured variable will be found” (Gall et al., 2007, p. 646). The criterion to measure math anxiety was the RMARS. The criterion to measure academic achievement was the final developmental course grade during the spring 2013 semester. Selection of Location Site To gain access to developmental mathematics students at a Texas community college within driving distance of Dallas County, inquiries were made at seven 2year community college campuses to generate an accessible population of participants. An accessible population is defined as a population in which “all members of a set of people, events, or objects [that] feasibly can be included in the researcher’s sample” (Gall et al., 2007). The application of accessible population resulted in the selection of a single community college as the research site. The selected college is a large, public 2year institution in a multicampus community college district. Using the Carnegie Classification of Institutions of Higher Education (CCIHE) system from the Carnegie Foundation for the Advancement of Teaching (CFAT) to ensure 14 population validity, the selected community college met the classification parameters of being an associate’s degreegranting institution that served a public, urban community in Texas. The researcher sent the selected institution’s dean of College Readiness and Mathematics and the appropriate department chairperson a letter that detailed the study and requested participation. The researcher completed all requirements for institutional approval, including submitting TAMUC IRB forms. Preliminary Procedures Following permission from the selected institution and college instructors, the researcher sent a letter to each developmental mathematics instructor during the spring 2013 semester (Appendix B). The letter described the purpose of the study and sought consent from instructors to allow their classes to participate. All developmental mathematics instructors were required to have at least 18 graduate hours of mathematics and have been a faculty member at the institution for at least 2 years. The researcher was available to visit the institution’s mathematics department during the spring 2013 semester, and answered all questions and concerns prior to beginning the study. Selection of Sample Population Participants included students enrolled in a developmental mathematics course at the selected Texas community college. All students were enrolled in various courses and levels of the developmental mathematics program during a traditional semester (16 weeks) and remained enrolled for the duration of the study. The selected institution had five courses and levels that were identified as developmental mathematics courses. The courses included (1) Concepts in Basic Mathematics, (2) PreAlgebra Mathematics, (3) Algebra Fundamentals I, (4) Algebra 15 Fundamentals II, and (5) Algebra Fundamentals III. The course catalog was used to identify and categorize the course names into levels of difficulty (low and high). The target population included 224 sections of developmental mathematics offered during the spring 2013 semester. Five sections of each of the five developmental mathematics courses were selected. Stratified random sampling was used to ensure that adequate representation of each level of developmental mathematics was selected and represented in the sample. The sample was chosen from 16week, lecturebased sections in which students received direct instruction and could only complete one level of developmental mathematics per semester. Sections listed as Computerized Modular Math (CMM), Personalized System of Instruction (PSI), and online were excluded from the sample because students were able to complete more than one level of developmental mathematics in these courses, and they did not receive direct instruction in the case of the online sections. The selected institution had 76 courses that met the criteria set by the researcher for the sample population. A goal of 25 total developmental mathematics sections was desired (see Table 1). Table 1 Number of Sections by Course Name Course Name Sections Offered: Spring 2010 16Week Lecture Sections (N) DMAT 0066: Concepts in Basic Mathematics 23 13 DMAT 0090: PreAlgebra Mathematics 36 16 DMAT 0097: Algebra Fundamentals I 57 18 DMAT 0098: Algebra Fundamentals II 55 15 DMAT 0099: Algebra Fundamentals III 53 14 16 Selection of Participant Criterion Twentyfive sections of developmental mathematics courses were chosen with 2025 students enrolled in each class, which yielded a sample size of 500625 students. The researcher applied the following participant criteria: 1. At least 18 years old. 2. Currently enrolled in a 16week, lecture developmental mathematics course. 3. Has never taken the RMARS test. 4. Willing to participate in the study. If a student did not meet all of the criteria, he or she was not included in the study. Instructors read participants a letter of recruitment prior to the data collection window (Appendix B). Description of Instruments Instructors of the randomly selected course sections were given an approximate number of survey packets for enrolled students. The survey packets contained study directions, an informed consent letter, a demographic questionnaire, the RMARS, and an optional puzzle activity in a sealable envelope (Appendix C). The informed consent letter briefly described the study and the criteria to participate. The letter also described the potential risks and benefits of participating in the research. The letter informed students that their spring 2013 final developmental mathematics course grade would be obtained from the institution at the conclusion of the semester. Students who chose to participate signed with their initials and campus identification number as a verification of voluntary participation. A brief demographic questionnaire was included for students to complete prior to beginning the RMARS. Participants were asked to write their campus identification number at the top of the questionnaire and to complete the remaining information by circling the 17 appropriate response. The questionnaire asked participants to indicate their age group (1822, 2327, 2832, 3337, 38 and older), gender (male or female), and the level of developmental mathematics enrolled in during the spring 2013 semester (course name). Only the researcher had access to the information on the demographic questionnaire, and all information remained confidential. The RMARS, developed by Plake and Parker (1982), was used to collect data pertaining to level of math anxiety. The RMARS was adapted from Richardson and Suinn (1972) MARS and is a 24item scale that consists of items concerning anxiety about the process of mathematics learning and testing situations. Responses are answered on a 5point Likerttype scale that ranges from 1 (not at all) to 5 (very much) (Hopko, 2003). According to Plake and Parker (1982), the RMARS, “which yielded a coefficient alpha reliability estimated at .98, was correlated at .97 with a full scale MARS” (p. 551); therefore, the revised scale generated a more adequate score of the level of math anxiety. The puzzle activity was a word search that was optional for all students to complete. Students who chose not to participate had the option of completing only the puzzle activity. Students who chose to participate could also complete the puzzle activity if time permitted. Collection of Data At the beginning of the spring 2013 semester, the researcher randomly selected five sections from each developmental mathematics course (25 sections in total) to participate in the study. The researcher spoke with the department chairperson and determined that no chosen section had more than 25 students enrolled. The researcher combined approximately 25 survey packets for each instructor, rubber banded and labeled them by course section number, and placed the survey packets in the College Readiness and Mathematics office for pick up. The 18 survey packets were available to instructors on the first day of the study distribution window set by the researcher. The instructor handed out the survey packets to the enrolled students during a single class period at their convenience during the 2week study distribution window. On the day chosen by the instructor for study distribution, each student was given a survey packet. Students were instructed to remove the items from the sealable envelope and read directions as the instructor read them aloud. The instructor allowed students 30 minutes to complete the survey packet materials. All students then read the informed consent letter for further explanation of the study and decided if they wanted to participate. Students who chose to participate (from this point referred to as participants) signed the informed consent letter with their initials, campus identification number, and the date. After signing the informed consent letter, participants completed the demographic questionnaire, the RMARS, and the optional puzzle activity if they so desired. Students were assured that their responses to the demographic questionnaire and the RMARS would be confidential and have no effect on their course grades. Only participants’ campus identification numbers were used to keep responses and final course grades confidential. Students who chose not to participate had the option to complete the puzzle activity during the 30 minutes allotted for participants to complete the forms. All students sealed their survey packets at the conclusion of the data collection period and then returned the packets to the instructor. When all survey packets were returned, the instructors returned the exact number of survey packets distributed to the institution’s division office. The researcher gathered all survey packets at the conclusion of the 2week distribution window. Data for the investigation were collected from the brief demographic questionnaire and the RMARS, which was administered by the instructor during the data collection window. The questionnaire was used to categorize the responses by gender, age, and developmental 19 mathematics course level. The puzzle activity was not used as a form of data collection; rather it was used as an optional activity. At the end of the spring 2013 semester, the participants’ final developmental mathematics course grades were obtained from the institution’s Decision Support department using participants’ campus identification numbers to ensure confidentiality. Treatment of the Data The researcher accessed and analyzed data collected from the brief demographic questionnaire, RMARS, and the final course grades using the computer package software Statistical Package for the Social Sciences (SPSS) version 16.0. The researcher generated a total math anxiety score by obtaining the sum of the items on the RMARS instrument from each participant; higher totals indicated higher levels of math anxiety (Baloğlu, 2005, Richardson & Suinn, 1972). The researcher coded each participant’s total score as lowlevel or highlevel math anxiety. The RMARS median score was 72, meaning that participants with a score below 72 had low math anxiety and those with 72 or above had high math anxiety. The researcher formed various comparison groups based on the level of developmental mathematics program in which each student was enrolled by gender and age group. Descriptive statistics were obtained using frequencies and the explore procedure to test the assumption for the categorical and continuous variables. The researcher obtained descriptive statistics output for all variables. The group mean, standard deviation, range of scores, skewness and kurtosis were calculated for each comparison group. Each developmental mathematics course was categorized as low or highlevel of difficulty using the course descriptions from the institution’s course catalog (see Table 2). 20 Table 2 Level of Difficulty by Course Name Course Name Level of Difficulty DMAT 0066: Concepts in Basic Mathematics Low DMAT 0090: PreAlgebra Mathematics Low DMAT 0097: Algebra Fundamentals I High DMAT 0098: Algebra Fundamentals II High DMAT 0099: Algebra Fundamentals III High The researcher conducted a oneway Analysis of Variance (ANOVA) to find differences within and between comparison groups among the RMARS scores as the dependent variable and age, gender, and developmental mathematics level of difficulty as the independent variables. The researcher conducted an ANOVA to address Research Questions 13 and test Hypotheses 13. Differences were reported at a confidence level of 95% (p < 0.05) to generate a wide range of practical significance and decrease the risk of Type I and Type II errors. The Levene’s Test for Equality of Variance and effect sizes were also calculated. The researcher used a simple linear regression to determine the correlation between academic achievement and the presence of high levels of math anxiety among developmental mathematics students. Research Question 4 and Hypothesis 4 were analyzed using linear regression. The correlation coefficient (R) and the coefficient of determination (R2) were calculated to establish the relationship between academic success (participants’ final course grades) and level of math anxiety. The F statistic was also calculated during the regression test. 21 Definitions of Terms The following terms are defined for clarification as used in this study: Academic success. For the purpose of this study, academic success refers to the completion of a course by earning a letter grade of C or better (ACT, 2010c). College readiness. College readiness is “a level of preparation a student needs in order to enroll and succeed, without remediation, in a creditbearing general education course at a postsecondary institution” (Conley, 2008, p.4). Developmental education. According to the National Association of Developmental Education [NADE] (2011), “Developmental education is a field of practice and research within higher education with a theoretical foundation in developmental psychology and learning theory” (para. 2). High difficulty level developmental mathematics course. For the purpose of this study, courses listed as Algebra Fundamental I, Algebra Fundamentals II, and Algebra Fundamentals III in the institution’s course catalog indicated a highlevel of developmental mathematics courses. Highlevel math anxiety. For the purpose of this study, a total score of 72 or higher on the RMARS indicated a highlevel of math anxiety (Plake & Parker, 1982). Low difficulty level developmental mathematics course. For the purpose of this study, courses listed as Concepts in Basic Mathematics and PreAlgebra Mathematics in institution’s course catalog indicated lowlevel developmental mathematics courses. Lowlevel math anxiety. For the purpose of this study, a total score of 71 or lower (below 72) on the RMARS indicated a lowlevel of math anxiety (Plake & Parker, 1982). 22 Math anxiety. Math anxiety includes “feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (Richardson & Suinn, 1972, p. 551). Mathematics Anxiety Rating Scale (MARS). The MARS is a 98item, Likertstyle assessment that was “constructed to provide a measure of anxiety associated with the single area of the manipulation of numbers and the use of mathematical concepts” (Richardson & Suinn, 1972, p. 551). Revised Mathematics Anxiety Rating Scale (RMARS). Plake and Parker (1982) developed the RMARS, which “a 24item version of the Mathematics Anxiety Rating Scale” (Mji & Mwambakana, 2008, p. 24). Remedial. In this study, remedial is synonymous with developmental (NADE, 2011). Traditional developmental mathematics course. For the purpose of this study, developmental mathematics courses refer to full 16week semester courses with direct instruction and lecture as the modality of instruction in the institution’s course catalog. Limitations The following limitations were applied to this study: 1. The researcher was an employee at the selected Texas community college used in this study. 2. Instructors did not use any strategy to decrease math anxiety during the study. 3. Students may or may not have responded to the study instruments with candor and seriousness. 4. The researcher did not control for the experience or expertise of the developmental mathematics instructors used in this study. 23 Delimitations The following delimitations were applied to this study: 1. Only one public community college in Dallas County, Texas was selected using the Carnegie Classification of (a) medium public urbanserving multicampus or (b) large public urbanserving multicampus. 2. Only community college students enrolled in a developmental mathematics course during the selected Spring 2013 semester were invited to participate in the study. 3. Only traditional 16week semester developmental mathematics courses using a lecturebased mode of instruction were included in the sample population. 4. Academic success was determined by the successful completion of a developmental mathematics course with a letter grade of C or better. Assumptions This study was based on the following assumptions: 1. The Revised Mathematics Anxiety Rating Scale instrument accurately measured the level of anxiety of each participant. 2. Participants responded to the items on the Revised Mathematics Anxiety Rating Scale thoroughly. 3. Participants understood each item of the Revised Mathematics Anxiety Rating Scale. Organization of Dissertation Chapters This study investigated the influence of math anxiety on the educational achievement of developmental mathematics students at a Texas community college. A review of the literature is presented in Chapter 2 and addresses the research pertaining to the topics of developmental education, developmental mathematics, math anxiety, and the effect of math anxiety on students 24 and teachers. The methodology used in this study is described in detail in Chapter 3. Chapter 3 also includes the selection of participants, collection of data, and the treatment of data. An analysis of the data is provided in Chapter 4, in which the research questions and hypotheses are addressed. Chapter 5 includes a summary of the study, a report of the findings, and the researcher’s conclusions concerning possible implications for practice and recommendations for further research. 25 Chapter 2 LITERATURE REVIEW Developmental mathematics programs at community colleges are scrutinized, revised, and restructured continuously in an effort to create the most effective sequence of learning mathematics for students who do not possess these basic skills. According to Bonham and Boylan (2011), “developmental mathematics as a barrier to educational opportunity represents a serious concern for the students as well as higher education policy makers” (p. 2). Remediation in mathematics is also a source of frustration for community college leaders and students (Bonham & Boylan, 2011). The current developmental mathematics programs have become a target for criticism and attack from all fronts (Boylan, 1999b; College Complete America [CCA], 2012). Developmental Education Community colleges across the United States are charged with the task of building the skills of underprepared high school students who enter college. According to Kolajo (2004), “Nearly all community colleges nationwide offer developmental education to underprepared students as a prerequisite for collegelevel courses” (p. 365). Developmental education has continued to be essential to community colleges (Kolajo, 2004). However, because the cost of remedial education is a burden on community colleges, they tirelessly debate whether keeping these programs is worthwhile. Issues in Developmental Education In addressing the problems surrounding developmental education, Phipps (1998) indicated that structural questions exist about earlier education and students’ academic backgrounds, which may affect the amount of remediation needed. One major finding was that 26 developmental education is a common part of postsecondary education (Phipps, 1998); in fact, it has been an essential component of higher education since the early 17th Century (Phipps, 1998; Kolajo, 2004). Phipps also noted the following: A 1995 survey by the National Center for Education Statistics (NCES) found that 78 percent of higher education institutions that enrolled freshman offered at least one remedial reading, writing, or mathematics course. One hundred percent of public twoyear institutions and 94 percent of institutions with high minority enrollments offered remedial courses. Twentynine percent of firsttime freshmen enrolled in at least one of these courses in the fall of 1995. Freshmen were more likely to enroll in a remedial mathematics course than in a remedial reading or writing course, irrespective of the institution they attended. (p. vvi) This conclusion indicated that remediation or developmental programs would continue to be cornerstones of colleges and universities. Phipps (1998) also found the costs of remediation are typically equal to the costs of other academic programs. The researcher stated that, on a national level, remediation programs cost “approximately $1 billion annually in a public higher education budget of $115 billion—less than 1 percent of expenditures” (p. vii). This national cost estimate includes costs for students, regardless of age or demographics; however, it does not include costs incurred in private or corporate sectors because of a lack of education and preparedness of potential employees (Phipps, 1998). Phipps suggested that the national cost estimation “could be twice as high as previously reported or closer to $2 billion” (p. 13), meaning that it is still a low amount to spend on such an important program. Phipps (1998) also reported that consistent standards do not exist for collegelevel work, the investment in remediation benefits all stakeholders, and not providing 27 remedial education results in social and economic repercussions. Phipps provided several strategies to improve the effectiveness of remediation and ultimately to reduce the need for these courses such as promoting collaboration between colleges and universities within states, redesigning remedial programs to include more than tutoring, and increasing the use of technology in the courses. Brothen and Wambach (2004) attempted to redefine the core elements and components of developmental education to address structural concerns. With pressure to reduce remediation programs, researchers have questioned whether these efforts are effective in preparing students for collegelevel work and degree completion. Brothen and Wambach noted the increase in enrollment at 4year institutions because of openadmission policies in the 1960s and 1970s. These openenrollment policies have caused many schools to develop courses that focus primarily on remediation and developmental education. Another concern the researchers addressed is whether these courses adequately serve developmental education students (Brothen & Wambach, 2004). Finally, they addressed research on the effect of having underprepared students in collegelevel courses, and cited that having underprepared students in their courses has resulted in teachers adapting and modifying their teaching styles as preemptive responses. This finding suggests that teachers have lowered their expectations of student achievement and may cover less material in an effort to maintain high retention and success rates (Brothen & Wambach, 2004). Brothen and Wambach (2004) offered the following seven concepts to improve developmental education: 1. Continue and refine literary skill development courses. 2. Vary course placement requirements based on student goals and program of study. 28 3. Develop a range of placement testing procedures. 4. Integrate alternative teaching/learning approaches. 5. Use theory to inform practice. 6. Integrate underprepared students into mainstream curriculum. 7. Adjust program delivery according to institutional type. (p. 1822) The implementation of these critical concepts and approaches would assist in creating a more successful future for developmental education. The researchers suggested a continuation of supplemental instruction that incorporates study skills, developing consistency in cut scores for placement assessments, and infusing the curriculum with theory and quality instruction that meets the needs of all students. A reconfiguration of developmental education would promote motivation and progression of students and encourage teachers to be openminded about applying methods and strategies to aid in the academic success of all students (Brothen & Wambach, 2004). Smith (2012) discussed student readiness in Texas and stated that less than 50% of students met the required standardized assessment scores necessary to be considered collegeready. Smith also reported that identifying college readiness skills is easy, but it is the actual measurement of these skills that presents incomplete evidence. A debate over who is to blame for the low performance and lack of student preparedness for postsecondary education has resulted in finger pointing and blaming (Smith, 2012). Smith (2012) reported that experts believe some students are placed in remediation courses because of scores that may have been affected by the lack of preparation or focus during the admission exam, rather than low skill level. He questioned whether state standardized or 29 college admissions exams provide accurate data about college preparedness. In fact, Smith reported the following: Studies support the theory that high school grades, not placement or admissions exams, give a better picture of whether students are ready for college, said Pamela Burdman, an education policy analyst who recently wrote a report on the role of placement exams in assessing college readiness for Jobs for the Future, a Bostonbased nonprofit. And the best measures, she said, use some combination of high school gradepoint averages and standardized test scores. (p. 2) Smith (2012) suggested steps that the state is taking to develop more efficient and effective evaluation measures including creating an assessment that provides a more detailed account of what students are missing in their high school curriculum. Smith (2012) discussed a contract between Texas and the College Board “to develop a statewide placement assessment, which all institutions would be required to administer to incoming students who did not meet the benchmark scores on state standardized exams or college admissions tests” (p. 2). The purpose of this new assessment is to ensure uniformity and a better view of student deficiencies. He also provided examples of community colleges and school districts in Texas that are tackling the challenge head on. For example, El Paso Community College collaborated with their local high schools to allow students to take the college placement exam during their junior years of high school (Smith, 2012). In doing so, students are able to work with counselors to develop a plan for their senior year coursework. Another example included school districts that work in collaboration with community colleges by allowing students to take more dualcredit courses and leave high school with an associate’s degree (Smith, 2012). 30 Texas transitioned to the new standardized assessments, the State of Texas Assessments of Academic Readiness (STAAR) exams in the spring of 2012, which addressed a few of the issues with students not entering college adequately prepared for collegelevel courses. Because the STAAR exams align sufficiently with college readiness standards, school districts and colleges are obtaining a better view of entering students (Smith, 2012). However, if students choose to take dualcredit courses, they must take both the standardized STAAR exam and a college final, which often deters student from wanting to take that path and enroll in those types of courses (Smith, 2012). Initiatives and Alternatives in Developmental Education Boylan (1999b) embarked upon finding solutions to the complaints of the time and cost of remedial courses, which hinder students’ academic progress in college. The researcher noted, “Traditionally, developmental education has included such activities as remedial/developmental courses, tutoring, learning laboratories, and various forms of individualized instruction” (Boylan, 1999b, p. 2). Boylan (1999b) provided alternative approaches to current programs including a freshmen orientation, supplemental instruction (SI), paired courses, collaborative learning communities, and critical thinking courses and programs, many of which have been around since the late 1970s. The researcher supported traditional approaches because these interventions have proven effective, especially among students who may not have persisted without such instructional support (Boylan, 1999b). Freshmen seminars or orientations typically last a day or two at universities and even less time at community colleges. The alternative approach increases the time span and orientation lasts the entire academic semester. Boylan (1999b) stated the following: 31 Instead of concentrating on rules and traditions, the freshmen seminar actually explores issues in college life, the purposes of higher education, and the requirements and expectations of college attendance through the vehicle of a regular, creditbearing, college course conceived as an integral part of the firstyear experience. (p. 3) Freshmen orientation has generated opportunities for all students, including developmental students, to learn more about the campus culture and expectations. Supplemental Instruction was developed in the early 1970s at the University of MissouriKansas City to help students progress through difficult courses. Specifically, SI consists of small groups of students with one group leader who took the course during a previous semester. The group leader serves as a peer mentor to help the students develop strategies for success such as testing and notetaking skills. Using this approach in developmental education programs may result in more students being placed in remedial courses to be successful in regular college courses eventually. Since its development, SI has been incorporated into various academic programs, including developmental education (Boylan, 1999b). Another alternative is including learning communities and collaborative learning in a developmental education program. Boylan (1999b) noted, “[A] learning community is arranged by having students enroll together as a cohort in several courses linked together by a common theme” (p. 3). Course instructors also work as a team to link content so that students can make connections while working with others to study and complete assignments (Boylan, 1999b). Paired courses are another alternative that is related closely to collaborative learning. Like collaborative learning, paired courses include a cohort of students that enrolls in two courses together, a main course and a supplement to the main course (Boylan, 1999b). In the paired course approach, instructors work together to provide connections and support between the two 32 courses (Boylan, 1999b). Using paired courses in developmental education can reduce the amount of time students spend in developmental education courses and allow them to earn course credit in collegelevel courses (Boylan, 1999b). Boylan (1999b) suggested that lack of critical thinking skills is a primary cause of failure among developmental students; therefore, he suggested an alternative approach that addresses increasing these skills. Developmental educators can address the lack of critical thinking skills by providing students with single courses or workshops that focus on these skills or by integrating critical thinking into the curriculum. Boylan (1999b) concluded by stating that implementing strategies for interventions and alternatives to remedial education requires organization, training, and collaboration of advisors and faculty, as well as consistency in availability and resources. Kozeracki and Brooks (2006) evaluated the effectiveness of the developmental education program at Davidson County Community College (DCCC) in North Carolina as it prepared for its 2002 accreditation. Specifically, the college engaged in a selfassessment of developmental education strategies applied on each campuses. The college chose developmental education as the selfassessment focus for the following reasons: 1. There had been a dramatic increase in the number of underprepared students enrolling at the college in recent years. 2. There was also a concern that the developmental courses did not create a sound foundation for success in collegelevel courses and programs. 3. Faculty and staff were aware that a disproportionate amount of time and resources were being dedicated to the placement and advising of underprepared students. 33 4. A number of projects conducted by the college in the mid1990s had helped familiarize faculty with how to teach to students’—especially developmental students’—learning styles. (Kozeracki & Brooks, 2006, pp. 6869) The committee in charge of conducting the selfassessment hired an outside consultant experienced in developmental education who recommended, “Subcommittees explore the following areas: advisement, assessment, coordination and learning support, communication, evaluation, and curriculum and development” (Kozeracki & Brooks, 2006, p. 69). The advisement subcommittee found that students need immediate advising following their first assessment, and advisors need continuous training to communicate the requirements of the developmental education program effectively (Kozeracki & Brooks, 2006). The assessment subcommittee found that benchmark scores should be consistent and compatible with aiding students in proper placement and skills intervention (Kozeracki & Brooks, 2006). The coordination and learning support subcommittee reviewed the organizational structure and alignment between developmental education and the mission of the institution (Kozeracki & Brooks, 2006). This subcommittee found that the preparatory (developmental) education mission statement and that of the college were aligned, and the program was essential to the mission of the college (Kozeracki & Brooks, 2006). The college decided that “A hybrid organization model, in which developmental courses are housed in their own disciplines but support services and other activities are centrally coordinated, would be most appropriate” (Kozeracki & Brooks, 2006, pp. 6970). The curriculum and development subcommittee discovered that no explicit expectations existed for students in the developmental courses and many courses were inconsistent because faculty added activities or requirements (Kozeracki & Brooks, 2006). Therefore, 34 recommendations included standard student expectations related to student behavior, class and homework, grading policies, and academic integrity. The evaluation subcommittee discovered that onethird of the 389 students who graduated in 19992000 had taken at least one developmental course; however, some students graduated from the college without taking the recommended developmental education courses (Kozeracki & Brooks, 2006). The communications subcommittee discovered that faculty who taught the same developmental education courses had no consistency in syllabi formatting, which caused difficulties for students in understanding the expectations and goals of the courses (Kozeracki & Brooks, 2006). Additionally, this subcommittee revealed that faculty exuded a negative tone and attitude toward the program in the language they used when speaking of developmental education programs (Kozeracki & Brooks, 2006). Kozeracki and Brooks (2006) urged community colleges to address the needs of underprepared students and to evaluate their developmental education programs. The realization that underprepared students can be in any class meant that faculty in every division and department should be prepared to address and meet students’ needs to achieve success (Kozeracki & Brooks, 2006). Full institutional support, from the administration to the faculty and students, is necessary for the growth and success of developmental education programs (Kozeracki & Brooks, 2006). Developmental Mathematics Radford and Horn (2012) reported on NCES data that listed precollege credits; remedial education participation; withdrawals and repeated courses; and credits earned in science, technology, engineering, and mathematics (STEM) from 20032004 for firsttime postsecondary students who were followed for 6 years. Table 3 offers an abbreviated version of the data from 35 the NCES on percentages of students that took a remedial mathematics course and the average number of remedial mathematics courses taken and passed (Radford, & Horn, 2012). Over the course of the 6year period, nearly 17,000 students participated in the survey and 42.2% took at least one remedial mathematics course at a postsecondary institution, The average was two mathematics courses taken during the 6year period and students passed an average of 1.3 mathematics courses (Radford & Horn, 2012, p. 15). Most participants who took a remedial mathematics course were female (44.0%), Black (51.6%), and 2023 years of age when first enrolled in 2003 (Radford & Horn, 2012, p. 15) (see Table 3). Table 3 NCES Remedial Math Statistics: 2009 Took remedial math course (%) Remedial math courses taken (M) Remedial math passed (M) Total 42.2 2.0 1.3 Sex Male 39.8 2.0 1.2 Female 44.0 2.0 1.3 Race/ethnicity White 39.4 1.9 1.3 Black 51.6 2.2 1.3 Hispanic 49.5 2.3 1.4 Asian 31.2 2.0 1.3 Other or Two or more 40.6 2.1 1.2 Age when enrolled in 20032004 18 or younger 38.2 2.0 1.3 19 42.0 2.0 1.3 2023 50.3 2.1 1.3 24 or older 46.3 2.0 1.4 36 Issues in Developmental Mathematics In an interview with Dr. Paul Nolting, Boylan (2011) posed several questions on improving developmental mathematics programs. Nolting stated that the levels of developmental mathematics may vary by state or university, and some universities had as many as four or even five levels of developmental mathematics, which increases the likelihood that students will enroll in developmental mathematics (Boylan, 2011). Nolting also noted several possible reasons why so many incoming students are placed in developmental mathematics courses. First, placement cut scores, which determine whether a student is required to enroll in a developmental mathematics course, vary by institution, which implies that benchmark scores to enter collegelevel mathematics courses may be harder to reach than those for reading and English (Boylan, 2011). Nolting also suggested that the time between mathematics courses, the inability to use calculators on placement tests, students entering college on a General Equivalency Diploma (GED), and test anxiety are factors that may result in students being placed in developmental mathematics courses (Boylan, 2011). Nolting also discussed the low prevalence of passing collegelevel algebra among students who take lower level developmental mathematics. Reasons for this low pass rate in collegelevel mathematics includes the length of developmental courses, high failure rates, inability to develop the necessary skills for college math, deficiencies in abstract reasoning and math anxiety. These factors result in students who avoid math and develop poor study habits. Nolting also suggested that failing mathematics is socially acceptable among the college student population, and “students with personal problems usually withdraw from math first, and repeating students usually get the same type of instruction that originally led to their failure” (Boylan, 2011, p. 21). Nolting also commented on the linear nature of developmental 37 mathematics, the notion of math phobia, and student procrastination as factors that may exist more among developmental mathematics students than other students (Boylan, 2011). Nolting proposed initiating an open conference to address the issues and concerns of developmental mathematics programs where administrators, faculty, and students could discuss factors that plague the program (Boylan, 2011). Nolting also provided two options for students who fail a developmental mathematics course, “retaking the placement test to score out of the developmental math course or retaking the final exam” (Boylan, 2011, p. 21). However, these choices pose more questions than they offer solutions to the problem, including whether the score on college placement assessments better shows students’ skills and knowledge than the final grade in previous mathematics courses (Boylan, 2011). Finally, Nolting discussed the role that math and test anxiety play in developmental mathematics students. He believed that math anxiety over the tests and content materials affect how students perform in class, on homework and on assessments (Boylan, 2011). To address these issues, Nolting suggested that universal placement assessments, resources for developmental mathematics, adequate preparation for the workforce, and effective teaching for developmental students are appropriate approaches that colleges should consider (Boylan, 2011). Fike and Fike (2012) surveyed 3,476 firsttime college students to compare those who enrolled in developmental mathematics during their first semester compared to those who delayed enrollment at an urban, private Hispanicserving university in the Southwest United States. The researchers suggested that delayed enrollment in developmental mathematics courses may have a negative effect on academic success. The researchers also suggested a more indepth look at the placement policies and examinations to determine their influence on 38 academic success. Of firsttime students, “884 (25%) were college ready in mathematics at initial enrollment, 1,139 (33%) enrolled in developmental mathematics during their first semester, and 1,453 (42%) deferred enrollment in developmental mathematics during their first semester” (Fike & Fike, 2012, p. 3). Findings revealed that students who were college ready in mathematics were more academically prepared than were students who either deferred enrollment or were enrolled in developmental mathematics (Fike & Fike, 2012). Additionally, 71% of students enrolled in developmental mathematics successfully completed with a grade of A, B, or C (Fike & Fike, 2012). These findings suggested that students in developmental mathematics were as successful as were those in college mathematics, which supports the need for developmental mathematics courses in college (Fike & Fike, 2012). Additional findings showed that final grade point averages (GPA) of students who passed developmental mathematics courses were higher than were those of students who deferred their developmental mathematics courses or failed their developmental mathematics courses (Fike & Fike, 2012). This finding implies that developmental mathematics students reach the same level of achievement as do collegeready students (Fike & Fike, 2012). Additionally, universities should not allow students to postpone enrollment into developmental mathematics courses. Fike and Fike (2012) concluded that requiring all students who are not prepared for collegelevel courses to take a developmental mathematics course within their first year might be the best solution. Initiatives in Developmental Mathematics Mireles, Offer, Ward, and Dochen (2011) examined study strategies among students in developmental mathematics and college algebra programs. Specifically, the researchers 39 addressed the problem of developmental mathematics as a barrier that results in many students repeating these courses. The researchers applied a mixed methods design to assess 47 students who participated in a rigorous summer hybrid program of developmental mathematics and college algebra. The program integrated mathematics and science, and used “peerled team learning and computer theme modules that link content” (Mireles et al., 2011, p. 12). Mireles et al. (2011) measured students using the Learning and Study Strategies Inventory (LASSI; 2nd edition), LASSI PrePost Achievement Measure, and the Mathematics Information Survey. The program length was 5.5 weeks with the developmental mathematics course for 2 hours in the early morning and the college algebra course for 2 hours in the late afternoon. The program integrated study strategies into the developmental mathematics course curriculum and reinforced those study strategies during the college algebra course. Mireles et al. (2011) found that incorporating study skills, supplemental instruction, and learning strategies improved program success. Specifically, the findings showed that students were more aware of their anxiety, attitudes, and motivation levels, and were able to monitor their concentration levels (Mireles et al., 2011). This finding implies that over the duration of the summer program, students decreased their math anxiety and increased their level of motivation (Mireles et al., 2011). Additionally, the program design aided students’ overall feelings of success and achievement (Mireles et al., 2011). Students were also aware of the resources available to them. They learned study strategies and continued to use those strategies in other classes (Mireles et al., 2011). Mireles et al. (2011) suggested that additional research investigate the effect of introducing study skills at an earlier stage in the developmental mathematics program. Additionally, the researchers noted that the study “highlighted positive impact on the strategies utilized by developmental 40 mathematics students through study strategy incorporation in both a developmental mathematics and college algebra class” (pp. 4041). Asera (2011) explored interventions for a developmental mathematics program at 11 California community colleges. The project Strengthening PreCollegiate Education in Community Colleges (SPECC) was designed in 2005 to allow colleges to redesign and improve their developmental education programs and focus on the program effects on student learning and achievement (Asera, 2011). According to Asera (2011), The SPECC campuses offered the range of the intervention programs that are common across community colleges: different configurations of learning communities; firstyear experiences; various uses of technology in both math and English classrooms; as well as use of tutors and instructional aides in the classroom, in scheduled study sessions, and in labs. Many of these interventions were small programs, nurtured by the faculty and staff responsible for them. (p. 28) The SPECC program had some limitations including the realization that a high number of mathematics students failed developmental mathematics courses regardless of strategies and interventions (Asera, 2011). Other findings discussed the use of technology in the classroom. While the researcher found technology had a moderate effect, it was helpful as a means of tutoring. Additionally, redesigning course materials and examinations to be the same in similar courses created a more consistent developmental mathematics program but did not seem to affect students’ results (Asera, 2011). At the conclusion of the SPECC program, the Carnegie Foundation shifted its focus to developmental mathematics with the induction of the new president, Tony Bryk (Asera, 2011). Along with other organizations, educational reform initiatives begun including Achieving the 41 Dream Developmental Education Initiative (ADDEI), National Center for Academic Transformation (NCAT), Changing the Equation (CtE), the California State Basic Skills Initiative (CTBSI), and Global Skills for College Completion (GSCC). Many of these initiatives focused on the sequence of developmental mathematics programs and challenges to completion. One study from the Community College Research Center (CCRC) revealed the following: The studies pointed out the low percentage of students who complete the sequence (overall 31% of students who start anywhere in developmental mathematics) and the somewhat counterintuitive finding that more students are lost before initial enrollment and between courses than from courses. The very length of the sequence is problematic because the longer the sequence, the more chances there are—in every course and between courses—for students to leave. (Asera, 2011, p. 29) To address the sequencing issue, the Carnegie Foundation and others created new sequencing pathways to align course materials with academic and professional goals (Asera, 2011). Asera (2011) stated that minimal changes to the system would not be adequate and that major course and program reform would be needed. The Carnegie Foundation began by forming two initial pathways, the Mathway and the Statway. The Mathway started “with a onesemester experience of integrated problem solving and critical thinking called Mathematical Literacy for College Students (MLCS)” (Asera, 2011, p. 29). The Statway was “an integrated pathway from developmental mathematics (starting with students who place into elementary algebra) through collegelevel statistics in 1 year” (Asera, 2011, p. 29). The program design aimed to avoid the possibility of a limited pathway by a higher level of rigor in mathematics, to connect both pathways, and to gather data and evidence to support findings (Asera, 2011). Asera (2011) concluded that it would not be easy redesigning 42 and restructuring the current model of developmental mathematics courses into specific pathways that focused on student learning and achievement. She also noted that neither design would meet the needs of all developmental students, but either program design may work for the right set of students. Math Anxiety Various studies have been conducted to discover the possible effect of math anxiety on mathematics performance. Richardson and Suinn (1972) characterized math anxiety as “feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (p. 551). Gresham (2007) defined math anxiety as “a feeling of helplessness, tension, or panic when asked to perform mathematics operations or problems” (p. 182). Furner and GonzalesDeHass (2011) stated the following: Mathematics anxiety can be defined as feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations. Some students tend to be more anxious about the testing process and can often freeze up (math test anxiety), others just cringe when they are confronted with any form of computational exercise (number anxiety), and others dread taking math classes which can occur in the elementary school, middle school, high school, or college levels (math course anxiety). (p. 228) Attitudes toward Mathematics Geist (2010) examined the root causes of math anxiety in the classroom and the negative attitudes toward mathematics. The researcher stated that many children develop math anxiety early in life, especially if their parents are from low socioeconomic backgrounds and have math 43 anxiety (Geist, 2010). Additionally, the role that gender plays on math anxiety suggests that more female students have math anxiety because of their negative attitudes toward testing compared to male students (Geist, 2010). Considering the gender gap in academic achievement, it is possible that gender is influential and math anxiety or negative attitudes toward mathematics are more influential in this gap (Geist, 2010). Geist (2010) offered the following: Studies have shown that at this time in children’s learning of mathematics, textbooks take over the process of teaching and the focus on shifts from construction of concepts using children’s own mathematical thinking to teacher imposed methods of getting the correct answer (Geist, 2000). Teachers begin to focus on repetition and speed or “timed tests” as important tools for improving mathematical prowess and skill which can undermine the child’s natural thinking process and lead to a negative attitude toward mathematics (Popham, 2008; Scarpello, 2007; Thilmany, 2004; Tsui & Mazzocco, 2007). (pp. 2425) As children develop and enter formal schooling, math anxiety is a serious obstacle at all levels and for all groups, which produces an achievement gap in mathematics (Geist, 2010). Geist (2010) examined gender differences in negative attitudes toward mathematics, and found that female students develop negative attitudes because of the timed and highstakes testing, which results in higher levels of math anxiety. Gender differences increase because of the assumption that one teaching method or style meets all students’ learning needs and abilities (Geist, 2010). Geist (2010) also examined teacher’s beliefs and instructional approaches as factors that influence students’ attitude toward mathematics. The researcher revealed the belief that mathematics achievement among females is because of hard work, while that among males is because of natural talent. Thus, children may adopt their teachers’ attitudes and the confidence level of female students pertaining to their performance may decrease as selfdoubt increases 44 (Geist, 2010). According to Geist (2010), anxiety develops in individuals when the focus is on the correct answers, speed, and repetition instead of ensuring that students can critically think through and process the answers and concepts. Students may inherit their teachers’ negative attitudes about areas of mathematics, which develop from teachers’ own levels of math anxiety and inadequacies (Geist, 2010). Geist (2010) also expressed the need to examine how mathematics is taught because of the global necessity of mathematics. Geist (2010) traced the cause of negative attitudes toward mathematics to poverty and family. He noted that a low household income and low level of education in parents are risk factors for low achievement in mathematics (Geist, 2010). Concerning attitudes toward mathematics and parental education, Geist noted the following: This data shows that the father’s education level seems to have a greater effect in almost all groups. Yet studies have shown that a mother’s attitude and encouragement toward mathematics was a significantly more important factor to children having a positive attitude toward mathematics (Scarpello, 2007) (p. 27). The parents may have less knowledge of mathematical concepts, lower comfort level with mathematics and a negative attitude toward mathematics leading to math anxiety and an aversion to mathematics. (p. 28) Geist (2010) expressed concern for developing students who shy away from higher levels of mathematics, which leads to avoidance of postsecondary education. He concluded by stating that educators must remember their experiences in mathematics so as not to repeat the same mistakes (Geist, 2010). Amirali (2010) examined attitudes and perceptions toward mathematics of eighthgrade private school students in Pakistan. Overall, the researcher found that a dislike of mathematics 45 was universal. She also stated that most secondary students believed mathematics is difficult and not very interesting. Convenience sampling and accessibility strategies were used to locate the research site and sample population. Amirali noted she used eighthgrade students as the sample population because eighthgrade mathematics represents the middle point of attainment in skill level for secondary mathematics. Eightytwo students from an Englishspeaking school participated in the study and were mostly between the ages of 13 and 15. To examine attitudes toward mathematics in Pakistan, Amirali (2010) used four foci, “usefulness of mathematics, the nature of mathematics, attitude towards the subject as well as mathematics anxiety” (p. 29). The researcher developed an instrument consisting of 35 items that were rated on a 5point Likert scale to address the four areas (Amirali, 2010). Amirali (2010) found little difference between male and female responses. Findings suggested that most students had a positive outlook and felt confident about their mathematics skills and ease in learning the content. Additionally, more female students had positive attitudes toward mathematics compared to male students, which produced lower levels of math anxiety among female students. Amirali implied that further research needed to be conducted regarding students learning mathematics because most students considered mathematics as highly important. The researcher also suggested research address the issue of engaging students in learning problemsolving skills that are relevant to their lives. Studies of Math Anxiety in Preservice Teachers Sloan (2010) conducted a mixed methods study of math anxiety with future teachers to examine the prevalence of teachers with math anxiety passing it along to students. The researcher cited additional research that included the following ideas: 46 Mathanxious teachers actually teach differently than teachers who are less anxious about mathematics, teachers who do not enjoy mathematics spend 50 percent less time teaching this subject than teachers who feel comfortable with this subject, and teachers with negative attitudes toward mathematics frequently rely on teaching algorithms while neglecting cognitive thought processes and mathematical reasoning. (Sloan, 2010, p. 243). Sloan (2010) also stated that a number of future teachers had math anxiety and negative attitudes and perceptions towards mathematics. To examine these claims and to add to the literature, Sloan (2010) examined “72 preservice teachers from three sections of an undergraduate mathematics methods course” (Sloan, 2010, p. 243). Participants ranged in age from 18 to 27, and the sample included 66 females and 6 males. Among participants, 61 had taken high school algebra, 45 had taken high school geometry, 72 had taken high school trigonometry, 41 had taken college algebra, four had taken college calculus, and five had taken college precalculus. The intervention was a mandatory course to aid future elementary teachers in the preparation for and evaluation of mathematics teaching (Sloan, 2010). This course incorporated a variety of topics including “basic mathematics content for preschool through third grade; an examination of learning principles; an exploration of various instructional strategies, techniques, and materials; and other issues related to teaching mathematics to children in the primary grades” (p. 244). Course requirements included presenting instruction to peers, working with mathematics manipulatives, using technology in the classroom, and field experience (Sloan, 2010). The researcher used the Mathematics Anxiety Rating Scale (MARS) to measure the levels of math anxiety before and after the methods course to determine the effectiveness of the 47 15week course (Sloan, 2010). The researcher also interviewed 12 participants who yielded the greatest differences on the MARS pre and posttest (Sloan, 2010). The researcher found statistically significant differences between pre and post course math anxiety among all participants, and attributed these differences to participation in the methods course (Sloan, 2010). Findings revealed, “At the completion of the standardsbased mathematics course, mathematics anxiety levels of preservice elementary teachers were significantly reduced from their initial levels at the beginning of the course” (Sloan, 2010, p. 246). Specific intervention methods, such as required time in the field and overall course atmosphere, helped reduce math anxiety levels, while intervention, such as course examinations, increased math anxiety levels (Sloan, 2010). Sloan (2010) exposed the emergence of the following nine categories of antecedents of math anxiety: (a) parental influences, (b) negative school experiences, (c) methodology of former mathematics teachers, (d) low mathematics achievement, (e) test anxiety, (f) lack of confidence, (g) negative attitudes, (h) mathematics avoidance, and (i) mathematics background (p. 250). Sloan (2010) offered several implications and recommendations for further study. 1. A required mathematics methodology course for all future teachers. 2. Developing a positive and encouraging learning environment. 3. Continued research using the same participants at the end of their course work and field experience to reassess math anxiety levels. Isiksal (2010) studied “the relationship among Turkish preservice elementary teachers’ mathematics teaching efficacy beliefs, mathematics anxiety, and mathematical selfconcept” (p. 501). In this study, “data were collected from 276 Turkish preservice elementary teachers enrolled in teacher education programs of two universities in the Southwest part of Turkey” (p. 48 504). The study used the Mathematics Teaching Efficacy Belief Instrument (MTEBI), the Abbreviated Mathematics Anxiety Scale (AMAS), and the Experience with Mathematics Questionnaire (EMQ) to examine the variables (Isiksal, 2010). The MTEBI is a 21item scale used to measure teaching efficacy beliefs and perceptions of teaching abilities. The AMAS is a 9item scale used to measure anxiety in certain mathematical situations, including learning process and mathematics test anxiety. The EMQ is a 27item questionnaire used to measure perceived mathematics learning ability. The researcher found the following: 1. Preservice teachers who had higher beliefs in their ability in learning new topics in mathematics and in translating teachers’ action into student learning also had higher beliefs in their own ability to teach mathematics effectively. (Isiksal, 2010, p. 508) 2. Preservice teachers’ higher beliefs in their own ability to teach mathematics and higher anxiety during testing situations were associated with higher beliefs in translating teachers’ action into student learning. (Isiksal, 2010, p. 508) 3. Higher anxiety about process of learning mathematics affected test anxiety positively and increased preservice teachers’ mathematics evaluation anxiety. (Isiksal, 2010, p. 508) 4. Preservice teachers with higher anxiety had lower beliefs in their ability to learn and perform task in mathematics. (Isiksal, 2010, pp. 508509) Isiksal (2010) stated that courses for teacher preparation have been structured successfully to implement new curriculum changes, strategies, and requirements effectively. The researcher further concluded that preservice teachers should be allowed to practice and experience the mathematics curriculum, and the teacher preparation curriculum should be aligned with the school curriculum to lower math anxiety and increase confidence levels (Isiksal, 2010). 49 Studies of Math Anxiety in Students Zakaria and Nordin (2008) “investigated the effects of mathematics anxiety on matriculation students as related to motivation and achievement” (p. 27). The researcher aimed to determine whether study relationships existed between math anxiety and motivation, and math anxiety and achievement (Zakaria & Nordin, 2008). The researchers administered the Mathematics Anxiety Scale (MAS), Effectance Motivation Scale (EMS) and the Mathematics Achievement Test (MAT) to 73 female students and 15 male students (Zakaria & Nordin, 2008). Participants were divided into three groups based on their math anxiety scores: (1) low math anxiety group (lower 33%), (2) moderate anxiety group (between 33% and 67%), and (3) high math anxiety group (33%) (Zakaria & Nordin, 2008). The results revealed a significant difference in achievement between the low and high anxiety groups, but no significant difference between the low and moderate and between the moderate and high anxiety groups (Zakaria & Nordin, 2008). The results showed that students with high math anxiety had low achievement scores (Zakaria & Nordin, 2008). The results also revealed significant differences for motivation between the low and moderate, low and high, and moderate and high anxiety groups. This finding indicates that the level of math anxiety affects student motivation in such a way that the higher the level of math anxiety, the less motivation to complete any mathematicsrelated tasks (Zakaria & Nordin, 2008). In other words, the relationship between math anxiety and achievement indicates that as math anxiety scores increase, achievement scores decrease (Zakaria & Nordin, 2008). The researchers implied that teachers should be mindful that student academic success is tied to their levels of anxiety, and teachers should vary their teaching methods and strategies to meet all student needs (Zakaria & Nordin, 2008). 50 Kesici and Erdogan (2010) sought to determine whether social comparison affected student motivation and anxiety levels by studying students in Turkey. Participants included 156 eighthgrade students (86 males and 70 females). The instruments included the MARS, Achievement Motivation Scale (AMS), and Social Comparison Scale (SCS) (Kesici & Erdogan, 2010). The MARS consists of 98 items aimed to determine the level of math anxiety (Kesici & Erdogan, 2010). The AMS measures consist of 14 items aimed to determine the level of motivation to achieve (Kesici & Erdogan, 2010). The SCS consists of 18 selfevaluation items to determine the perception of abilities and skills compared to peers (Kesici & Erdogan, 2010). The results revealed a significant difference in math anxiety and achievement motivation between students classified as high achievement motivation and those classified as low achievement motivation (Kesici & Erdogan, 2010). Results showed that students with high achievement motivation scores had a higher level of math anxiety than did those with low achievement motivation (Kesici & Erdogan, 2010). Concerning math anxiety and social comparison, the results revealed that math anxiety was higher among students with negative selfesteem compared to those with positive selfesteem (Kesici & Erdogan, 2010). Kesici and Erdogan (2010) concluded that math anxiety among students varies depending on their motivation to succeed and their perceptions of their capabilities within their peer group. The researchers suggested that students set goals and develop motivation based on personal expectation, not peer achievements and scores (Kesici & Erdogan, 2010). Summary Extensive research has been conducted on developmental education, developmental mathematics, and math anxiety among teachers and students. This literature review outlined the body of knowledge available that addresses the developmental education world, specifically, 51 developmental mathematics programs. In regard to the developmental education system, the CCA (2012) stated, “While more students must be adequately prepared for college, this current remediation system is broken. The very structure of remediation is engineered for failure” (p. 2). According to Furner and GonzalesDeHass (2011), increased advertisement of STEM fields is generating more interest in those areas, which is causing universities and community colleges to focus on adequate preparation in those areas. Bonham and Boylan (2011) concluded, “It is unfortunate that developmental courses, once envisioned as a gateway to educational opportunity, have become barriers to that opportunity for many students” (p. 8). As the sequencing of the developmental mathematics program continues to present challenges for students, the likelihood that more students will feel the effect of math anxiety increases (Bai et al., 2009; Boylan et al., 1999; Chinn, 2009; Meece et al., 1990). 52 Chapter 3 METHOD OF PROCEDURE The purpose of this study was to examine the relationship between the achievement of developmental mathematics students and math anxiety. This study sought to determine whether a significant difference exists in levels of math anxiety based on age, gender, and developmental mathematics program level. Additionally, this study strived to establish a connection between the effects of high and low levels of math anxiety and academic success. Design of Study This quantitative, casualcomparative study focused on the effect of math anxiety on the academic achievement of developmental mathematics students at a Texas community college. The researcher formulated four null hypotheses and then tested for statistical significance to determine whether each null hypothesis could be rejected. The researcher administered the Revised Mathematics Anxiety Rating Scale (RMARS) to students enrolled in various levels of developmental mathematics programs during the spring 2013 semester to measure the level of math anxiety. The researcher also collected students’ final spring 2013 semester developmental mathematics course grades from the institution to explore the effect of math anxiety on academic achievement. Description of Sample Population The researcher sent letters to the dean of mathematics and the mathematics department chairperson at the selected Texas community college and obtained IRB approval to conduct this study. Following approval, the researcher reviewed the spring 2013 course listing for developmental mathematics and found 224 sections of developmental mathematics. A letter detailing the study and the amount of participation by the instructor was placed in each 53 developmental mathematics instructors’ campus mailbox and sent via email. The researcher narrowed the target population by selecting only traditional, 16week, lecturebased sections, which resulted in 76 sections. The selected college had five levels of mathematics in the developmental program, which included two lowlevel difficulty courses (DMAT 0066: Concepts in Basic Mathematics and DMAT 0090: PreAlgebra Mathematics), and three highlevel difficulty courses (DMAT 0097: Algebra Fundamentals I; DMAT 0098: Algebra Fundamentals II; and DMAT 0099: Algebra Fundamentals III). The researcher selected five sections of each level of developmental mathematics using stratified random sampling. Three of the 28 developmental mathematics instructors declined participation following an email about the study and an informal meeting to answer questions and concerns. Description of Participant Criterion Twentyfive sections of developmental mathematics were chosen to participate in the study, and the instructors were notified via email. The researcher gave participating instructors a letter of recruitment (Appendix B) and asked them to read the letter to the selected section 1 week prior to the distribution of the survey packets. The scripted letter detailed the study and the criteria to participate. The student participation criteria included the following: 1. At least 18 years old. 2. Currently enrolled in a 16week, lecture developmental mathematics course. 3. Have never taken the RMARS test. 4. Willing to participate in the study. Each section had no more than 25 students enrolled; therefore, a sample size of 625 potential participants was generated. 54 Description of Instruments The survey packets contained five items, study directions, informed consent letter, demographic questionnaire, the RMARS, and an optional puzzle activity (Appendix C). The researcher created color duplicates of each instrument and copied, collated, folded, and placed them into 6x9 inch sealable brown envelopes. The study directions were included in the survey packet and given to the instructor to read aloud to students on the day of data collection. A onepage summary included the research process and length of time allotted to complete the packet. The informed consent letter briefly explained the study, criteria for participation, and any foreseeable risks and benefits. The letter also explained that the researcher could obtain students’ final spring 2013 developmental mathematics course grades from the institution. Also included in the letter were the confidentiality procedures to ensure security of all information provided. Students who chose to participate signed and dated the consent form with their initials and campus identification number. Students were also given the opportunity to receive the results of their RMARS by listing their personal email addresses. The researcher designed the demographic questionnaire to obtain certain descriptive data about each participant. Participants were asked to write their campus identification number at the top and then circle the appropriate response to questions about their age, gender, and developmental course level. The age groups were categorized as follows: 1822, 2327, 2832, 3337, and 38 and older. The developmental course levels were listed with full course name and corresponding course number. The RMARS was duplicated with permission from the creator. The instrument includes a 24item scale for level of math anxiety that uses 5point Likerttype scale (1 = not at all, 2 = a little, 3 = moderate, 4 = much, and 5= very much) to depict the level of fear or apprehension. 55 Statements include, “Walking into a math class,” “Watching a teacher work an algebraic equation on the blackboard,” “Thinking about an upcoming math test on the day before,” and “Taking an examination (final) in a math class.” The researcher created the optional puzzle activity using an online word search puzzle making system. Fortyfive words were selected from basic Texas eighthgrade Algebra vocabulary. The puzzle activity was designed to provide students something to work on while waiting for others to complete the survey packets. The puzzle activity was optional and no data were obtained. Collection of Data At the beginning of February 2013, during the spring 2013 semester, the developmental mathematics instructors of the selected 25 sections were notified via email that the survey packets were available in the mathematics division office for pickup. The survey packet materials were placed in empty copier paper boxes, separated by course number (i.e., DMAT 0066, DMAT 0090, DMAT 0097, DMAT 0098, and DMAT 0099), and color coded by course number as indicated on the study directions sheet (i.e., DMAT 0066red, DMAT 0090light green, DMAT 0097turquoise, DMAT 0098purple, and DMAT 0099yellow). Each DMAT instructor’s name and selected section course number were placed on the study directions sheet along with 25 survey packets and were rubberbanded together. A total of 625 survey packets were prepared for distribution. From February 18 to March 1, DMAT instructors distributed survey packets to the appropriate class section and return them to the same copier paper box. The researcher sent emails to remind DMAT instructors of the surveys, dates of the 2week data collection window, and the deadline to return all materials. The researcher returned to the division office to retrieve 56 the copier paper boxes with all the survey materials during the first week of March. At that time, the researcher sent an email to instructors indicating that the data collection window had closed and that all survey materials should have been returned. The researcher left one copier paper box in the office for an additional week to ensure that all materials had been returned. Of the 625 survey packets distributed, 542 survey packets were returned to the researcher, resulting in 86.72% return rate. Of the 542 survey packets returned, 283 were sealed but partially incomplete and discarded, and 259 were unsealed and blank and discarded (see Table 4). Table 4 Returned Survey Packets Breakdown Type Total Completed 185 Consented and Completed 93 Consented, Email Response, and Completed 92 Partially Incomplete 98 No Campus ID Number Provided 66 Demographic Questionnaire Incomplete 8 RMARS Incomplete 24 Blank 259 Total Returned 542 The consented and completed category indicates that the participant signed the consent form appropriately and completed the demographic questionnaire and the RMARS in their entirety. The consented, email response, and completed category type indicated that the participant signed the consent form appropriately, requested his or her RMARS scores be sent to him or her individually, and completed the demographic questionnaire and the RMARS in their 57 entireties. The partially incomplete category type indicates that the participant did not complete the consent form, demographic questionnaire, or RMARS adequately for the researcher to obtain all data needed. The blank category type indicated that no information within the survey packet was completed and the envelope was unsealed. The researcher first scored the RMARS documents for each participant by calculating the sum of the responses provided. Each participant’s total score was coded as lowlevel or highlevel math anxiety. The RMARS median score was 72, meaning that participants with a score below 72 were categorized as having lowlevel math anxiety and those with 72 or above were categorized as having highlevel math anxiety. The researcher then organized the data and created an Excel spreadsheet to compile the necessary information from the consent forms, demographic questionnaires, and RMARS. To obtain the final developmental mathematics course grades of all participants, the researcher created and compiled a separate Excel spreadsheet and listed only participants’ campus identification numbers and their enrolled developmental mathematics course numbers. The spreadsheet was emailed to the institution’s decision support department 2 weeks after the conclusion of the spring 2013 semester. The decision support department returned the spreadsheet with the final course grades inputted to the researcher via a file transfer. Both Excel spreadsheets were merged to show all data. Treatment of Data The data collected from the brief demographic questionnaire, RMARS, and the final course grades were accessed and analyzed using the computer software, Statistical Package for the Social Sciences (SPSS) version 16.0. Various comparison groups were formed based on the level of the developmental mathematics program in which each student was enrolled by gender and age group. Descriptive statistics were obtained using frequencies and explore procedures to 58 test the assumption for the categorical and continuous variables. The descriptive statistics output answered all four research questions. The researcher calculated group means, standard deviation, range of scores, skewness, and kurtosis for each comparison group, and categorized each developmental mathematics course as low or high difficulty level. A oneway Analysis of Variance (ANOVA) was performed to determine whether significant differences existed within and between comparison groups with RMARS scores as the dependent variable and age, gender, and developmental mathematics level of difficulty as the independent variables. The researcher formulated four null hypotheses and tested them for statistical significance to determine whether each null hypothesis could be rejected. The ANOVA tested Hypotheses 13. Differences were reported at a confidence level of 95% (p < 0.05) to generate a range of practical significance and decrease the risk of Type I and II errors. The researcher also calculated the Levene’s Test for Equality of Variance and effect sizes. The researcher used a simple linear regression to determine the correlation between academic achievement and the presence of high levels of math anxiety among developmental mathematics students. Hypothesis 4 was analyzed using linear regression. The correlation coefficient (r) and the coefficient of determination (r2) were calculated to establish the relationship between academic success (final course grades) and level of math anxiety. The F statistic was also calculated during the regression test. Summary This study used a quantitative approach to explore the effects of math anxiety on the academic success of developmental mathematics students at a Texas community college. Participants included students who were enrolled in traditional 16week, facetoface developmental mathematics courses during the spring 2013 semester. The developmental 59 mathematics department provided the researcher access to survey their students and the institution’s decision support department provided access to the final course grades for participating students. The researcher analyzed the gender, age, and difficulty level of developmental course (spring 2013) data using ANOVA and linear regression tests. 60 Chapter 4 PRESENTATION OF FINDINGS The purpose of this study was to investigate the relationship between math anxiety and student achievement among developmental mathematics students. Participants in this study were enrolled in a developmental mathematics course at a Texas community college during the spring 2013 semester. Data collection included a demographic questionnaire, a math anxiety rating scale, and participants’ final course grades to determine the effect of math anxiety on the academic success of developmental mathematics students based on age, gender, and course difficulty level. Specifically this study attempted to determine the following: 1. The level of math anxiety in developmental mathematics students at a Texas community college based on age, gender, and developmental program level. 2. The effect of high and low levels of math anxiety on academic success in developmental mathematics courses. Descriptive Analysis The researcher used an Excel spreadsheet to compile the data by students’ campus identification numbers, gender, age group, developmental mathematics (DMAT) course, Revised Mathematics Anxiety Rating Scale (RMARS) score, and final course grades. The researcher used the Statistical Package for the Social Sciences (SPSS) version 16.0 to analyze all data. Descriptive data from the instruments describe the participant characteristics. Description of Participants Of the 185 survey packets returned, fully completed, and analyzed, 61.6% (N = 114) of the participants were female, 44.3% (N = 82) of the participants were between the ages of 18 and 22 years old, 24.9% (N = 46) of the participants were enrolled in the fourth level of 61 developmental mathematics (DMAT 0098), and 28.6% (N = 53) of the participants earned a C for their final course grade. Of the 185 participants, 41.1% (N = 76) were enrolled in a low difficulty level developmental course (DMAT 0066 or DMAT 0090), and 58.9% (N = 109) were enrolled in a high difficulty level developmental mathematics course (DMAT 0097, DMAT 0098, or DMAT 0099). Of all the participants, 70.3% (N = 132) successfully completed their developmental mathematics course with a letter grade of A, B, or C, indicated academic success (see Table 5). Table 5 Descriptive Statistics for Variables Variable Frequency Percent Gender Male 71 38.4 Female 114 61.6 Age Group 1822 82 44.3 2327 31 16.8 2832 28 15.1 3337 14 7.6 38+ 30 16.2 DMAT Course 0066 45 24.3 0090 31 16.8 0097 38 20.5 0098 46 24.9 0099 25 13.5 Final Course Grade A 38 20.5 B 41 22.2 C 53 28.6 D 7 3.8 F 32 17.3 W 14 7.6 Total 185 100.0 62 Plake and Parker (1982) developed the RMARS and indicated a median score of 72, meaning that participants with a score lower than 72 are categorized as having low math anxiety and those with a score of 72 or higher were categorized as having high math anxiety. These scoring criteria were also used in the current study. A total of 57.3% (N = 106) of students scored a 71 or lower on the RMARS, which indicated a low level of math anxiety. A total of 42.7% (N = 79) of students scored a 72 or higher on the RMARS, which indicated a high level of math anxiety. The mean score was 67.82 and standard deviation was 19.318; therefore, the RMARS scores were considered normally distributed (see Figure 1). Figure 1. RMARS total score. 63 Statistical Analysis of the Research Questions and Research Hypotheses Descriptive data were generated prior to conducting the oneway analysis of variance (ANOVA) tests in which the percentages, group mean, standard deviation, and 95% confidence interval were calculated for each comparison group and math anxiety level. Regression procedures were used to analyze data regarding the association between math anxiety and final course grade in a developmental mathematics course. This output allowed the researcher to answer the following research questions: 1. Does a difference exist in math anxiety among developmental mathematics students who take lower levels or higher levels of developmental mathematics courses? 2. Does a difference exist in math anxiety of developmental mathematics students between age groups (i.e., 1822, 2327, 2832, 3337, 38 and older)? 3. Does a difference exist in math anxiety among developmental mathematics students by gender? 4. Does a difference exist between math anxiety of developmental mathematics students and final course grades? Oneway ANOVA tests were conducted to determine the overall significance of each comparison group and math anxiety level. Regression procedures were used to analyze data regarding the association between math anxiety and final course grade in a developmental math course. This output allowed the researcher to test the following research hypotheses: 1. No significant differences exist in math anxiety of students who take higher difficulty levels of developmental mathematics courses compared to those who take lower difficulty levels of developmental mathematics courses. 64 2. No significant differences exist in the level of math anxiety of developmental mathematics students based on age. 3. No significant differences exist in the level of math anxiety of developmental mathematics students based on gender. 4. No significant relationship exists in overall developmental mathematics final course grades and level of math anxiety of developmental mathematics students. Research Question 1 Most participants were enrolled in a high difficulty developmental mathematics course (DMAT 0097, DMAT 0098, or DMAT 0099) and had low math anxiety. Of the 76 participants in a low difficulty level developmental mathematics course (DMAT 0066 or DMAT 0090), 52.7% (N = 40) had low levels of math anxiety and 47.3% (N = 36) in a low difficulty level developmental mathematics course had high levels of math anxiety. Of the 109 participants in a high difficulty level developmental mathematics course, 60.5% (N = 66) had low levels of math anxiety and 39.4% (N = 43) had high levels of math anxiety (see Figure 2). 65 Figure 2. RMARS anxiety level by course difficulty level. Dotted line indicates separation between low difficulty level and high difficulty level. Participants in low difficulty level courses had a mean of 71.87 and a standard deviation of 20.139 on the RMARS, and participants in high difficulty level courses had a mean of 65.00 and a standard deviation of 18.292 on the RMARS. Participants in developmental mathematics courses with a lower difficulty level had a higher mean RMARS anxiety score than did those in higher difficulty level developmental mathematics courses. Confidence intervals revealed the true mean for level of math anxiety for participants in low level difficulty developmental mathematics courses was between 67.27and 76.47. The true mean for level of math anxiety among participants in high difficulty developmental mathematics courses was between 61.53 and 68.47 (see Table 6). 31.6% 21.1% 22.0% 21.1% 17.4% 27.6% 19.7% 12.8% 21.1% 5.5% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% DMAT 0066 DMAT 0090 DMAT 0097 DMAT 0098 DMAT 0099 Percentage DMAT Course Anxiety by Course Low Anxiety High Anxiety66 Table 6 Mean and Standard Deviation of RMARS Anxiety Score by Course Difficulty Level Course Difficulty N M SD Low Difficulty 76 71.87 20.139 High Difficulty 109 65.00 18.292 Total 185 67.82 19.318 In analyzing the level of math anxiety among participants in developmental mathematics courses with low and high levels of difficulty, the Levene’s Test indicated homogeneity of variance between the two groups. The overall F statistic was significant, which signifies that a significant difference existed between the level of course difficulty [F(1,183) = 5.808, p = .017, η2 = .03]. The very small effect size shows that 3% of the variance in the RMARS anxiety scores could be explained by the difficulty level of the developmental mathematics course. Post hoc tests were not performed because there were fewer than th
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Title  The Effect of Math Anxiety on the Academic Success of Developmental Mathematics Students at a Texas Community College 
Author  FanninCarroll, Kristen D'Ann 
Subject  Community college education; Mathematics education 
Abstract  THE EFFECT OF MATH ANXIETY ON THE ACADEMIC SUCCESS OF DEVELOPMENTAL MATHEMATICS STUDENTS AT A TEXAS COMMUNITY COLLEGE A Dissertation by KRISTEN D. FANNINCARROLL Submitted to the Office of Graduate Studies Texas A&M UniversityCommerce in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION May 2014 THE EFFECT OF MATH ANXIETY ON THE ACADEMIC SUCCESS OF DEVELOPMENTAL MATHEMATICS STUDENTS AT A TEXAS COMMUNITY COLLEGE A Dissertation by KRISTEN D. FANNINCARROLL Approved by: Advisor: Madeline Justice Committee: Joyce Miller Joyce A. Scott Head of Department: Glenda Holland Dean of College: Gail Johnson Dean of Graduate Studies: Arlene Horneiii Copyright © 2014 Kristen D. FanninCarroll iv ABSTRACT THE EFFECT OF MATH ANXIETY ON THE ACADEMIC SUCCESS OF DEVELOPMENTAL MATHEMATICS STUDENTS AT A TEXAS COMMUNITY COLLEGE Kristen D. FanninCarroll, EdD Texas A&M UniversityCommerce, 2014 Advisor: Madeline Justice, EdD The purpose of this study was to examine the relationship between math anxiety and academic success of developmental mathematics students at a Texas community college based on age, gender, and level of developmental mathematics program. A quantitative, casualcomparative design was used to determine relationships. A total of 185 developmental mathematics students were surveyed using the Revised Mathematics Anxiety Scale and a demographic questionnaire. Of the 185 survey packets returned, fully completed, and analyzed, 61.6% (N = 114) of the participants were female, 44.3% (N= 82) of the participants were between the ages of 18 and 22 years old, 24.9% (N = 46) of the participants were enrolled in the fourth level of developmental mathematics (DMAT 0098), and 28.6% (N = 53) of the participants earned a C for their final course grade. Of the 185 participants, 41.1% (N = 76) were v enrolled in a low difficulty level developmental course (DMAT 0066 or DMAT 0090), and 58.9% (N = 109) were enrolled in a high difficulty level developmental mathematics course (DMAT 0097, DMAT 0098, or DMAT 0099) (see Table 5). Of all the participants, 70.3% (N = 132) successfully completed their developmental mathematics course with a letter grade of A, B, or C, indicated academic success. A total of 57.3% (N = 106) of the participants scored a 71 or lower on the RMARS, which indicated a low level of math anxiety. A total of 42.7% (N = 79) of the participants scored a 72 or higher on the RMARS, which indicated a high level of math anxiety. A statistical difference existed between level of math anxiety based on developmental mathematics courses with low and highlevel difficulty, but there was no statistical difference between level of math anxiety based on age or gender. vi ACKNOWLEDGEMENTS First, I give all my praise and glory to my Lord and Savior Jesus Christ for He has truly blessed me during this doctoral process. This journey has been long and difficult, but by His grace and mercy, I accomplished this professional and personal goal. Now that this journey has concluded, I look forward to seeing what He has in store for me. “And whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks to God the Father through Him” (Colossian 3:17). To my husband, Eric, words cannot express how grateful I am for your patience, understanding, motivation, and encouragement. You supported me throughout this journey and allowed me to cry, sing, scream, and rejoice. Thank you for your words of inspiration and being one of my biggest cheerleaders. I am truly blessed to have you not only as my partner, but also as my best friend. I love you with all my heart and soul. To my parents, Bruce and Barbara, I could not have done this without you. You have been by my side and pushed me to succeed and meet every challenge and obstacle with persistence and focus. Your continued prayers lifted me when I was down and kept me going when I wanted to give up. I thank God for giving me parents who have always been there and love me unconditionally. This is for you. To my siblings, Randall (Rachella) and Cres, thank you for being supportive and showing me what it takes to be successful in spite of any obstacle. To my nieces and nephews, know that you can do anything you desire with hard work and determination. I love you all. To the rest of my family (Fannins, Askews and Fraziers), thank you for believing in me and encouraging me. Even if you do not know what you said or did to help, your words did not go unnoticed and were vii greatly appreciated. Your prayers, jokes, hugs, and phone calls boosted my confidence and determination to complete this degree. Thank you all for supporting me as I achieved this dream. To my friends, fellow doctoral buddies, and work family, thank you for all of your prayers and words of encouragement. To Dr. Rosalyn Walker, thank you for taking me under your wing when I first began the doctoral program back in 2009. Meeting you was truly a blessing. To Rayna Matthews, it has been a pleasure experiencing this educational journey together; you mean more to me than just a colleague, I consider you my friend and my sister. A special thank you to Anastasia Lankford and my friends at the writing center for taking my mind off things when I needed to lighten up. Thank you to my church families, New Life Baptist Church (Quitman, Texas) and North Dallas Community Bible Fellowship (Plano, Texas). Thank you to my sisters in Alpha Kappa Alpha Sorority, Incorporated, specifically to my line sisters, E.S.O.E, Fall 2003. To the faculty and staff at Texas A&M UniversityCommerce, I would like to thank you all for your guidance and support. To my committee, Dr. Madeline Justice, Dr. Joyce A. Scott, and Dr. Joyce Miller, I thank you for your support, wisdom, and supervision. Each of you continuously pushed me to be better and raise my expectations. Your support has truly been unconditional. A special thank you goes to Dr. Katy Denson for her time and assistance. To Dr. Rodger Pool, you are the reason I started this journey. You saw greatness in me when I did not see it myself, and you gave me the confidence to do more with my education and my career. I will forever be grateful to all who have assisted me in realizing this dream. “But thanks be to God, who gives us the victory through our Lord Jesus Christ” (1 Corinthians 15:57) viii TABLE OF CONTENTS LIST OF TABLES ....................................................................................................................... xi LIST OF FIGURES .................................................................................................................... xii CHAPTER 1. INTRODUCTION ........................................................................................................ 1 Statement of the Problem ....................................................................................... 4 Purpose of the Study .............................................................................................. 5 Research Questions ................................................................................................ 5 Research Hypotheses ............................................................................................. 6 Significance of the Study ....................................................................................... 6 Method of Procedure............................................................................................ 12 General Procedures .................................................................................. 12 Design of Study........................................................................................ 13 Selection of Location Site ........................................................................ 13 Preliminary Procedures ............................................................................ 14 Selection of Sample Population ............................................................... 14 Selection of Participant Criterion............................................................. 16 Description of Instruments ....................................................................... 16 Collection of Data .................................................................................... 17 Treatment of the Data .............................................................................. 19 Definitions of Terms ............................................................................................ 21 Limitations ........................................................................................................... 22 Delimitations ........................................................................................................ 23 ix CHAPTER Assumptions ......................................................................................................... 23 Organization of Dissertation Chapters ................................................................. 23 2. REVIEW OF LITERATURE ..................................................................................... 25 Developmental Education .................................................................................... 25 Issues in Developmental Education ......................................................... 25 Initiatives and Alternatives in Developmental Education ....................... 30 Developmental Mathematics ............................................................................... 34 Issues in Developmental Mathematics..................................................... 36 Initiatives in Developmental Mathematics .............................................. 38 Math Anxiety ....................................................................................................... 42 Attitudes toward Mathematics ................................................................. 42 Studies of Math Anxiety in Preservice Teachers ..................................... 45 Studies of Math Anxiety in Students ....................................................... 49 Summary .............................................................................................................. 50 3. METHOD OF PROCEDURE..................................................................................... 52 Design of Study.................................................................................................... 52 Description of Sample Population ........................................................... 52 Description of Participant Criterion ......................................................... 53 Description of Instruments ....................................................................... 54 Collection of Data .................................................................................... 55 Treatment of Data .................................................................................... 57 Summary .............................................................................................................. 58 x CHAPTER 4. PRESENTATION OF FINDINGS ............................................................................. 60 Descriptive Analysis ............................................................................................ 60 Description of Participants ....................................................................... 60 Statistical Analysis of the Research Questions and Hypotheses ......................... 63 Research Question 1 ................................................................................ 64 Research Question 2 ................................................................................ 67 Research Question 3 ................................................................................ 69 Research Question 4 ................................................................................ 71 Summary ........................................................................................................... 74 5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH ..... 75 Summary of the Findings ..................................................................................... 76 Conclusions .......................................................................................................... 78 Implications.......................................................................................................... 79 Recommendations for Further Research .............................................................. 80 Summary .............................................................................................................. 81 REFERENCES ............................................................................................................................ 83 APPENDICES ............................................................................................................................. 91 Appendix A. Instrument Permission Letter and Response ........................................................ 92 B. Recruitment Letters .............................................................................................. 95 C. Participant Survey Packet .................................................................................... 98 VITA……………. ..................................................................................................................... 106 xi LIST OF TABLES TABLE 1. Number of Sections by Course Name .................................................................. 15 2. Level of Difficulty by Course Name ................................................................... 20 3. NCES Remedial Math Statistics: 2009 ................................................................ 35 4. Returned Survey Packets Breakdown .................................................................. 56 5. Descriptive Statistics for Variables ...................................................................... 61 6. Mean and Standard Deviation of RMARS Anxiety Score by Course Difficulty Level .................................................................................................... 66 7. ANOVA Statistics for RMARS Anxiety Score by Course Difficulty Level ....... 66 8. Mean and Standard Deviation of RMARS Anxiety Score by Age Group .......... 68 9. ANOVA Statistics for RMARS Anxiety Score by Age Group ........................... 69 10. Mean and Standard Deviation of RMARS Anxiety Score by Gender................. 70 11. ANOVA Statistics for RMARS Anxiety Score by Gender ................................. 71 12. Correlation Results of RMARS Anxiety Score and Final Course Grade ............ 73 13. Regression Statistics for RMARS Anxiety Score and Final Course Grade ......... 73 xii LIST OF FIGURES FIGURES 1. RMARS total score .............................................................................................. 62 2. RMARS anxiety level by course difficulty level ................................................. 65 3. RMARS anxiety level by age group .................................................................... 67 4. RMARS anxiety level by gender ......................................................................... 70 5. RMARS anxiety level by final course grade ....................................................... 72 1 Chapter 1 INTRODUCTION Understanding mathematics has become more challenging for many high school and college students compared to any other subject. Research shows that many students do not have basic mathematics skills when they enter college (Achieve, 2011; ACT, 2010c; Haycock, 2010). As students transition into institutions of higher education, their academic skills and comprehensive knowledge are questioned and tested, and many students realize their lack of skills needed to succeed at the college level. As the demand for higher education and the need to address the inadequacy of mathematics skills has increased, community colleges have begun to help students transition from high school to college. According to Cohen and Brawer (2003), The percentage of those graduating from high school grew from 30 percent in 1924 to 75 percent by 1960, and 60 percent of the high school graduates entered college in the latter year. Put another way, 45 percent of eighteenyearolds entered college in 1960, up from 5 percent in 1910. (p. 6) The creation of community colleges began as an idea to lessen the burden of teaching general education courses to younger students. The first junior or community colleges were proposed in 1851 by the President of the University of Michigan, Henry Tappan, in 1859 by a University of Georgia trustee, William Mitchell, and in 1869 by the President of the University of Minnesota, William Folwell (Cohen & Brawer, 2003; Jurgens, 2010). These educational leaders noted that providing general education skills to high school graduates presented a challenging responsibility to universities and required more research. In the late 19th Century, William Rainey Harper of the University of Chicago, Edmund J. James of the University of Illinois, and David Starr Jordan of Stanford 2 promoted the idea of creating institutions that were extensions of secondary schools. In 1901, these ideas and the passion of William Rainey Harper led to the founding of the first junior college, Joliet Junior College, located in Chicago (Cohen & Brawer, 2003). The growth of community colleges continued as the United States realized that the rapid increase in high school graduates and the need for a more skilled workforce called for more communitybased institutions to fulfill the demand (American Association of Community Colleges [AACC], 2008; Cohen & Brawer, 2003). As community colleges became more popular, state legislators and policymakers placed more responsibility upon these schools. Community colleges were designed to provide appropriate curricular functions including “academic transfer preparation, vocationaltechnical education, continuing education, developmental education and community service” (Cohen & Brawer, 2003, p. 20). The roles and responsibilities of community colleges continued to expand, and the education of their students was top priority. As the United States continued to seek methods to increase the quality of education of high school graduates who were transitioning to postsecondary education, community colleges were faced with the challenge of meeting the needs of students who lacked basic reading, writing, and mathematics skills. At local community colleges, many students found themselves in developmental education programs. As such, developmental education, sometimes called remedial education, had become the driving force behind the mission of most community colleges. According to Bailey (2009), Community colleges are charged with teaching students collegelevel material, yet a majority of their students arrive with academic skills in at least one subject area that are judged to be too weak to allow them to engage successfully in collegelevel work. Thus, 3 a majority of community college students arrive unprepared to engage effectively in the core function of the college. (p. 11) Community colleges strive to provide a quality education to all students, and structure developmental programs to ensure that additional instruction in basic skills is available to and adequate for these students. Courses that are designed to assist underprepared college students with basic skills and college aspirations are considered part of developmental education (Boylan, 2002). According to Boylan (1999a), “almost every community college campus in the country offers some combination of remedial and developmental courses, learning labs, and tutoring programs” (p. 5). Boylan also identified a spectrum of developmental education interventions including “tutoring programs, special academic advising and counseling programs, learning laboratories, and comprehensive learning centers [and] developmental courses” (p. 2). From 2000 to 2010, nearly 100% of public 2year institutions offered remedial services or developmental education courses (National Center for Educational Statistics [NCES], 2011). Boylan and Saxon (1998) evaluated developmental education in Texas public colleges and universities. The following findings pertain to the 44 community colleges that participated: 1. 37.7% of students surveyed were placed in developmental reading. 2. 40.4% of students were placed in developmental writing. 3. 61.8% of students were placed in developmental mathematics. 4. 70.7% of firsttime students who failed at least one section of the Texas Academic Skills Program (TASP) test took at least one developmental course. (pp. 23) As enrollment numbers in community colleges nationwide have steadily risen over last 10 years, these colleges have also experienced drastic increases in the number of students requiring 4 developmental courses (NCES, 2010). Across the nation, 19.1% of all firstyear undergraduate students took a remedial course from 20032008. By the 20072008 academic year, this rate had increased to 20.2% (NCES, 2010). The NCES (2004) found that, nationally, fewer than 30% of entering freshmen had registered for at least one remedial (developmental) course. The report also indicated that more students were enrolling in developmental mathematics courses than in developmental writing and reading courses nationwide (NCES, 2004). Among students enrolled in developmental mathematics courses, the fear of not succeeding is omnipresent. Researchers have found that the negative perception of mathematics is a contributing factor to the failure of mathematics students (Mji & Mwambakana, 2008; Suinn & Edwards, 1982). Some developmental mathematics students are faced with the task of completing several remedial mathematics courses prior to beginning collegelevel mathematics courses. Therefore, the anxiety to succeed looms over the heads of these students. Research has also found that math anxiety, coupled with poor mathematics skills, is interlinked as a possible causal relationship (Bai, Wang, Pan, & Frey, 2009; Brady & Bowd, 2005; Cates & Rhymer, 2003; Chinn, 2009; Lavasani & Khandan, 2011; Mji & Mwambakana, 2008; Prevatt, Welles, Li & Proctor, 2010). However, developmental mathematics students continue to struggle, as they are required to take a variety of noncredit courses before enrolling in college algebra. Statement of the Problem Various researchers have conducted studies to determine the influence of math anxiety on students (Bai et al., 2009; Boylan, Bonham & White, 1999; Chinn, 2009; Meece, Wigfield, & Eccles, 1990). Research has shown that the level of a student’s math discomfort and anxiety directly affects his or her achievement and progress (Brady & Bowd, 2005; Bull, 2009; Cates & Rhymer, 2003). As negative reactions and attitudes toward mathematics increase, student 5 successes and understanding of mathematics concepts decrease (Lavasani & Khandan, 2011; Mji & Mwambakana, 2008; Prevatt et al., 2010). Research has also found that students who were enrolled in developmental courses are faced with a greater challenge of academic success and have a higher risk of developing math anxiety than do students who were not enrolled in developmental courses (Asera, 2011; Brothen & Wambach, 2004; Fike & Fike, 2012; Kolajo, 2004; Phipps, 1998). The problem of this study was to examine the level of math anxiety in developmental mathematics students at community colleges and its effect on academic success. Purpose of the Study The purpose of this study was to examine the relationship between math anxiety and academic achievement among developmental mathematics students to determine the following: 1. The level of math anxiety in developmental mathematics students at a Texas community college based on age, gender, and developmental program level. 2. The effect of high and low levels of math anxiety on academic success in developmental mathematics courses. Research Questions The following research questions guided this study: 1. Does a difference exist in math anxiety among developmental mathematics students who take lower levels or higher levels of developmental mathematics courses? 2. Does a difference exist in math anxiety of developmental mathematics students between age groups (i.e., 1822, 2327, 2832, 3337, 38 and older)? 3. Does a difference exist in math anxiety among developmental mathematics students by gender? 6 4. Does a difference exist between math anxiety of developmental mathematics students and final course grades? Research Hypotheses The following null hypotheses guided this study, and were tested at the 0.05 level of significance: 1. No significant differences exist in the level of math anxiety of students who take higher difficulty levels of developmental mathematics courses compared to those who take lower difficulty levels of developmental mathematics courses. 2. No significant differences exist in the level of math anxiety of developmental mathematics students based on age. 3. No significant differences exist in the level of math anxiety of developmental mathematics students based on gender. 4. No significant relationship exists in overall developmental mathematics final course grades and level of math anxiety of developmental mathematics students. Significance of the Study Researchers have examined the increased need for programs that promote academic preparation and success among students, including those in community college (Conley, 2008; Phipps, 1998; Southern Regional Education Board [SREB], 2001). College readiness has become a global issue for high school students, parents, high school principals, high school counselors, admissions counselors, and college professors. Conley (2008) defined college readiness “as a level of preparation a student needs in order to enroll and succeed, without remediation, in a creditbearing general education course at a postsecondary institution” (p. 4). Students who are deemed collegeready must possess a strong foundation in reading, writing, 7 mathematics, science, and history. They must also have adequate critical thinking skills and a strong work ethic (ACT, 2010a; SREB, 2001). Therefore, a strong academic curriculum in high school must include courses that challenge and motivate students. Further, alignment of high school graduation requirements and college readiness standards is needed to ensure the sufficient preparation of high school graduates (ACT, 2010c). Conley (2008) identified the following four components necessary for a student to be collegeready: Key cognitive strategies Academic knowledge and skills Academic behaviors Contextual skills and awareness Key cognitive strategies consist of problemsolving skills, research capabilities, reasoning, interpretation of literature, and precision of tasks. Collegeready students must “encompass behaviors that reflect greater student selfawareness, selfmonitoring, and selfcontrol of processes and actions” (Conley, 2008, p. 9). Conley also noted that, for a student to possess adequate academic knowledge and skills, he or she must develop comprehensive skills in all core subjects. Several academic concerns have elicited questions surrounding the academic preparedness of many students who enroll in college as the United States continues to fall behind other countries in science and mathematics. Lack of adequate preparation to complete collegelevel coursework has become a focal point of many K12 systems and higher education institutions in the United States. The Alliance for Excellent Education (AEE, 2006) reported that students who complete the more strenuous track of 4 years of advanced English and at least 3 years of advanced mathematics, science, and social sciences are more prepared for collegelevel 8 curriculum than those that do not take advanced and honors courses in high school. Several policymaking entities have conducted research that suggest college readiness requires global attention (Achieve, 2011; ACT, 2010d, SREB, 2001), and have convened conferences, initiatives, and summits to work on aligning high school curricula and expectations with the standards of postsecondary education (Achieve, 2008; ACT, 2010b, Haycock, 2010). President Barak Obama asked for a new Elementary and Secondary Education Act (ESEA) to “require states to set college and careerready standards” (Haycock, 2010, p. 19). The nation’s mission is to align the curriculum and expectations of high schools with the expectations and needs of postsecondary institutions and employers. The United States has become aware of the significant influence that college readiness has on producing stability in the economy and understands that the students of the future will lead the way. Whether students are heading to college or entering the workforce, their levels of education influence all aspects of their lives. Graduating from high school is an important milestone, and educators, policy makers, and legislators must strengthen the educational foundation of the United States. The educational spotlight is on adequate student preparation for college and career, and the debate as to who is to blame for deficiencies has become more intense. College readiness is more than just how much a student knows; rather, it also involves understanding basic skills and possessing a higher work ethic to shift successfully to postsecondary education. With the federal government advocating K16 alignment of core curriculum standards, institutions of higher education work with high schools to develop partnerships to ensure student success in higher education and the workforce. According to Achieve, Inc. (2011), 47 states and the District of Columbia have developed and implemented 9 alignment of high school standards and postsecondary expectations; 20 states and the District of Columbia have raised the bar on graduation requirements; and 14 of the 50 states administered assessments that produced adequate readiness data. In addition, 22 states have created P20 data systems that connect K12 data with postsecondary systems (Achieve, 2011). Concerning the accountability systems standard, only one state, Texas, met the four indicators; however, Achieve reported optimism that more states would follow in providing data that show improvement in college readiness criteria. Various studies have provided insight into the enrollment and retention rates of developmental students (Boylan et al., 1999; Umoh, Eddy & Spaulding, 1994). Findings suggest that students who successfully pass their first developmental courses are more likely (66.4%) to stay enrolled at the institution the following year (Boylan & Saxon, 1998). Retention has become a focal point for many higher education institutions, and community colleges are no different. The NCES (2004) reported the following enrollment pattern in developmental courses: The proportion of freshman enrolling in at least one remedial reading, writing, or mathematics course was higher at public 2year colleges than it was for all other types of institutions; 42 percent of freshman at public 2year colleges compared with 12 to 24 percent of freshmen at other types of institutions enrolled in such courses. (p. 32) Research has also shown that students in remedial courses are less likely to complete their degrees (AEE, 2006). The National Conference of State Legislatures (NCSL, 2011) stated, “less than 25 percent of remedial students at community colleges earn a certificate or degree within eight years” (p. 2). Rather, many students drop out of community college because of the cost of remedial education and the time required. 10 Developmental mathematics has been placed under a microscope as academic preparedness and developmental education continue to be focal points of higher education. The academic success of developmental mathematics students is at the forefront of many institutional leaders’ and department chairs’ concerns. Of specific concern in the current study is that findings suggest that poor academic performance among developmental mathematics students may be linked to math anxiety (Brady & Bowd, 2005). Many researchers have discussed math anxiety and its influence on various programs and groups such as nursing, finance, teaching, middle school students, and secondary students (Abidin, Alwi & Jaafar, 2010; Brady & Bowd, 2005; Bull, 2009; Chinn, 2009; Wigfield & Meece, 1988). Studies have also reported a variety of findings on the effects of gender and math anxiety. Additionally, several math anxiety assessments and scales have been created, modified, or adapted to identify the indicators and effects of math anxiety (Bai et al., 2009; Baloğlu, 2005; Deniz & Üldaş, 2008; Hopko, 2003; Miller & Mitchell, 1994; Richardson & Suinn, 1972; Suinn & Edwards, 1982). Continuous research has been conducted to test the validity and reliability of these scales (Baloğlu, 2005; Deniz & Üldaş, 2008; Hopko, 2003). Cates and Rhymer (2003) administered the FennemaSherman Mathematics Anxiety Scale (FSMAS) to identify the level of math anxiety and its effect on the fluency and accuracy of college students. The researchers found that participants with higher math anxiety had lower fluency and accuracy than did those with lower levels of math anxiety. Deniz and Üldaş (2008) developed a 39item scale, the Mathematics Anxiety Scale toward Teachers (MAST), to measure math anxiety in teachers and prospective teachers. Bai et al. (2009) used a 14item Mathematics Anxiety ScaleRevised (MASR) to determine the reliability and validity of the bidimensional affective scale, and found that this tool was an authentic measure of math anxiety. 11 Chinn (2009) examined secondary students in England using a 20item questionnaire with a variety of items that focused on different activities and situations in mathematics that may correspond with math anxiety. He found that formal and informal assessments in mathematics increased math anxiety among participants. Abidin et al. (2010) used an adapted version of Richardson and Suinn’s (1972) Mathematics Anxiety Rating Scale (MARS) and found that males in a mathematics of finance course experienced lower levels of anxiety than did female students. The researchers also reported that students’ anxiety levels increased as final examination time arose. Brady and Bowd (2005) examined the level of math anxiety in preservice teachers by combining Richardson and Suinn’s (1972) MARS and a demographic questionnaire. The researchers found that female teachers had higher levels of math anxiety than did male teachers. The findings also indicated, “Mathematics anxiety correlated negatively with confidence to teach mathematics” (Brady & Bowd, 2005, p. 42). Gresham (2007) administered the Richardson and Suinn’s MARS in fall of 2003 and then again in the fall of 2005 to 246 early childhood and elementary teachers. Findings indicated that math anxiety decreased over the course of 2 years. Few researchers have focused solely on the effects of math anxiety on the academic success of developmental mathematics students. A single study was conducted that examined the effects of math anxiety on developmental mathematics students at the community college level. Johnson and Kuennen (2004) applied a mixed methods design and administered a 10question math anxiety test, developed by Ellen Freedman, as a pre and posttest to determine whether math anxiety could be reduced following an intervention. The researchers found a significant difference between the treatment and control groups; however, no statistically 12 significant difference in math anxiety was found between developmental mathematics students and college algebra students. The current study attempted to determine the effect of math anxiety in community college developmental mathematics students. The focus was to understand the effect of math anxiety on the academic success of developmental mathematics students, which has received little attention in recent years. Waycaster (2001) found that 40% of students who transitioned directly to a community college from high school needed some remediation in mathematics. The need to understand more about math anxiety and its effects on developmental mathematics students’ academic achievement was the focus of this study. Method of Procedure To investigate the effect of math anxiety on the academic achievement of developmental mathematics students at various levels of a program, the researcher applied a variety of quantitative research methods and procedures. The methodology of this study is presented in sections dedicated to (a) General Procedures, (b) Design of the Study, (c) Selection of Location Site, (d) Preliminary Procedures, (e) Selection of the Participants, (f) Selection of the Instruments, (g) Collection of the Data, and (h) Treatment of Data. General Procedures Written permission to conduct the study was obtained from the Texas A&M UniversityCommerce (TAMUC) Internal Review Board (IRB) for the Protection of Human Subjects. Following IRB approval, permission to use and reproduce the Revised Mathematics Anxiety Rating Scale (RMARS) was obtained from the author (Appendix A). Permission was acquired from the administrators and developmental mathematics instructors at the selected Texas 13 community college to collect data from students enrolled in the colleges’ developmental mathematics program during the spring 2013 semester. Design of Study This study sought to explain the effects of math anxiety on the academic achievement of developmental mathematics students. The study design was quantitative and used a causalcomparative method. According to Gall, Gall, and Borg (2007), causalcomparative research is a quantitative investigation “in which researchers seek to identify causeandeffect relationships" (p. 306). Within this quantitative study design, four null hypotheses were formulated and tested for statistical significance. A null hypothesis is “a prediction that no relationship between two measured variables will be found, or that no difference between groups on a measured variable will be found” (Gall et al., 2007, p. 646). The criterion to measure math anxiety was the RMARS. The criterion to measure academic achievement was the final developmental course grade during the spring 2013 semester. Selection of Location Site To gain access to developmental mathematics students at a Texas community college within driving distance of Dallas County, inquiries were made at seven 2year community college campuses to generate an accessible population of participants. An accessible population is defined as a population in which “all members of a set of people, events, or objects [that] feasibly can be included in the researcher’s sample” (Gall et al., 2007). The application of accessible population resulted in the selection of a single community college as the research site. The selected college is a large, public 2year institution in a multicampus community college district. Using the Carnegie Classification of Institutions of Higher Education (CCIHE) system from the Carnegie Foundation for the Advancement of Teaching (CFAT) to ensure 14 population validity, the selected community college met the classification parameters of being an associate’s degreegranting institution that served a public, urban community in Texas. The researcher sent the selected institution’s dean of College Readiness and Mathematics and the appropriate department chairperson a letter that detailed the study and requested participation. The researcher completed all requirements for institutional approval, including submitting TAMUC IRB forms. Preliminary Procedures Following permission from the selected institution and college instructors, the researcher sent a letter to each developmental mathematics instructor during the spring 2013 semester (Appendix B). The letter described the purpose of the study and sought consent from instructors to allow their classes to participate. All developmental mathematics instructors were required to have at least 18 graduate hours of mathematics and have been a faculty member at the institution for at least 2 years. The researcher was available to visit the institution’s mathematics department during the spring 2013 semester, and answered all questions and concerns prior to beginning the study. Selection of Sample Population Participants included students enrolled in a developmental mathematics course at the selected Texas community college. All students were enrolled in various courses and levels of the developmental mathematics program during a traditional semester (16 weeks) and remained enrolled for the duration of the study. The selected institution had five courses and levels that were identified as developmental mathematics courses. The courses included (1) Concepts in Basic Mathematics, (2) PreAlgebra Mathematics, (3) Algebra Fundamentals I, (4) Algebra 15 Fundamentals II, and (5) Algebra Fundamentals III. The course catalog was used to identify and categorize the course names into levels of difficulty (low and high). The target population included 224 sections of developmental mathematics offered during the spring 2013 semester. Five sections of each of the five developmental mathematics courses were selected. Stratified random sampling was used to ensure that adequate representation of each level of developmental mathematics was selected and represented in the sample. The sample was chosen from 16week, lecturebased sections in which students received direct instruction and could only complete one level of developmental mathematics per semester. Sections listed as Computerized Modular Math (CMM), Personalized System of Instruction (PSI), and online were excluded from the sample because students were able to complete more than one level of developmental mathematics in these courses, and they did not receive direct instruction in the case of the online sections. The selected institution had 76 courses that met the criteria set by the researcher for the sample population. A goal of 25 total developmental mathematics sections was desired (see Table 1). Table 1 Number of Sections by Course Name Course Name Sections Offered: Spring 2010 16Week Lecture Sections (N) DMAT 0066: Concepts in Basic Mathematics 23 13 DMAT 0090: PreAlgebra Mathematics 36 16 DMAT 0097: Algebra Fundamentals I 57 18 DMAT 0098: Algebra Fundamentals II 55 15 DMAT 0099: Algebra Fundamentals III 53 14 16 Selection of Participant Criterion Twentyfive sections of developmental mathematics courses were chosen with 2025 students enrolled in each class, which yielded a sample size of 500625 students. The researcher applied the following participant criteria: 1. At least 18 years old. 2. Currently enrolled in a 16week, lecture developmental mathematics course. 3. Has never taken the RMARS test. 4. Willing to participate in the study. If a student did not meet all of the criteria, he or she was not included in the study. Instructors read participants a letter of recruitment prior to the data collection window (Appendix B). Description of Instruments Instructors of the randomly selected course sections were given an approximate number of survey packets for enrolled students. The survey packets contained study directions, an informed consent letter, a demographic questionnaire, the RMARS, and an optional puzzle activity in a sealable envelope (Appendix C). The informed consent letter briefly described the study and the criteria to participate. The letter also described the potential risks and benefits of participating in the research. The letter informed students that their spring 2013 final developmental mathematics course grade would be obtained from the institution at the conclusion of the semester. Students who chose to participate signed with their initials and campus identification number as a verification of voluntary participation. A brief demographic questionnaire was included for students to complete prior to beginning the RMARS. Participants were asked to write their campus identification number at the top of the questionnaire and to complete the remaining information by circling the 17 appropriate response. The questionnaire asked participants to indicate their age group (1822, 2327, 2832, 3337, 38 and older), gender (male or female), and the level of developmental mathematics enrolled in during the spring 2013 semester (course name). Only the researcher had access to the information on the demographic questionnaire, and all information remained confidential. The RMARS, developed by Plake and Parker (1982), was used to collect data pertaining to level of math anxiety. The RMARS was adapted from Richardson and Suinn (1972) MARS and is a 24item scale that consists of items concerning anxiety about the process of mathematics learning and testing situations. Responses are answered on a 5point Likerttype scale that ranges from 1 (not at all) to 5 (very much) (Hopko, 2003). According to Plake and Parker (1982), the RMARS, “which yielded a coefficient alpha reliability estimated at .98, was correlated at .97 with a full scale MARS” (p. 551); therefore, the revised scale generated a more adequate score of the level of math anxiety. The puzzle activity was a word search that was optional for all students to complete. Students who chose not to participate had the option of completing only the puzzle activity. Students who chose to participate could also complete the puzzle activity if time permitted. Collection of Data At the beginning of the spring 2013 semester, the researcher randomly selected five sections from each developmental mathematics course (25 sections in total) to participate in the study. The researcher spoke with the department chairperson and determined that no chosen section had more than 25 students enrolled. The researcher combined approximately 25 survey packets for each instructor, rubber banded and labeled them by course section number, and placed the survey packets in the College Readiness and Mathematics office for pick up. The 18 survey packets were available to instructors on the first day of the study distribution window set by the researcher. The instructor handed out the survey packets to the enrolled students during a single class period at their convenience during the 2week study distribution window. On the day chosen by the instructor for study distribution, each student was given a survey packet. Students were instructed to remove the items from the sealable envelope and read directions as the instructor read them aloud. The instructor allowed students 30 minutes to complete the survey packet materials. All students then read the informed consent letter for further explanation of the study and decided if they wanted to participate. Students who chose to participate (from this point referred to as participants) signed the informed consent letter with their initials, campus identification number, and the date. After signing the informed consent letter, participants completed the demographic questionnaire, the RMARS, and the optional puzzle activity if they so desired. Students were assured that their responses to the demographic questionnaire and the RMARS would be confidential and have no effect on their course grades. Only participants’ campus identification numbers were used to keep responses and final course grades confidential. Students who chose not to participate had the option to complete the puzzle activity during the 30 minutes allotted for participants to complete the forms. All students sealed their survey packets at the conclusion of the data collection period and then returned the packets to the instructor. When all survey packets were returned, the instructors returned the exact number of survey packets distributed to the institution’s division office. The researcher gathered all survey packets at the conclusion of the 2week distribution window. Data for the investigation were collected from the brief demographic questionnaire and the RMARS, which was administered by the instructor during the data collection window. The questionnaire was used to categorize the responses by gender, age, and developmental 19 mathematics course level. The puzzle activity was not used as a form of data collection; rather it was used as an optional activity. At the end of the spring 2013 semester, the participants’ final developmental mathematics course grades were obtained from the institution’s Decision Support department using participants’ campus identification numbers to ensure confidentiality. Treatment of the Data The researcher accessed and analyzed data collected from the brief demographic questionnaire, RMARS, and the final course grades using the computer package software Statistical Package for the Social Sciences (SPSS) version 16.0. The researcher generated a total math anxiety score by obtaining the sum of the items on the RMARS instrument from each participant; higher totals indicated higher levels of math anxiety (Baloğlu, 2005, Richardson & Suinn, 1972). The researcher coded each participant’s total score as lowlevel or highlevel math anxiety. The RMARS median score was 72, meaning that participants with a score below 72 had low math anxiety and those with 72 or above had high math anxiety. The researcher formed various comparison groups based on the level of developmental mathematics program in which each student was enrolled by gender and age group. Descriptive statistics were obtained using frequencies and the explore procedure to test the assumption for the categorical and continuous variables. The researcher obtained descriptive statistics output for all variables. The group mean, standard deviation, range of scores, skewness and kurtosis were calculated for each comparison group. Each developmental mathematics course was categorized as low or highlevel of difficulty using the course descriptions from the institution’s course catalog (see Table 2). 20 Table 2 Level of Difficulty by Course Name Course Name Level of Difficulty DMAT 0066: Concepts in Basic Mathematics Low DMAT 0090: PreAlgebra Mathematics Low DMAT 0097: Algebra Fundamentals I High DMAT 0098: Algebra Fundamentals II High DMAT 0099: Algebra Fundamentals III High The researcher conducted a oneway Analysis of Variance (ANOVA) to find differences within and between comparison groups among the RMARS scores as the dependent variable and age, gender, and developmental mathematics level of difficulty as the independent variables. The researcher conducted an ANOVA to address Research Questions 13 and test Hypotheses 13. Differences were reported at a confidence level of 95% (p < 0.05) to generate a wide range of practical significance and decrease the risk of Type I and Type II errors. The Levene’s Test for Equality of Variance and effect sizes were also calculated. The researcher used a simple linear regression to determine the correlation between academic achievement and the presence of high levels of math anxiety among developmental mathematics students. Research Question 4 and Hypothesis 4 were analyzed using linear regression. The correlation coefficient (R) and the coefficient of determination (R2) were calculated to establish the relationship between academic success (participants’ final course grades) and level of math anxiety. The F statistic was also calculated during the regression test. 21 Definitions of Terms The following terms are defined for clarification as used in this study: Academic success. For the purpose of this study, academic success refers to the completion of a course by earning a letter grade of C or better (ACT, 2010c). College readiness. College readiness is “a level of preparation a student needs in order to enroll and succeed, without remediation, in a creditbearing general education course at a postsecondary institution” (Conley, 2008, p.4). Developmental education. According to the National Association of Developmental Education [NADE] (2011), “Developmental education is a field of practice and research within higher education with a theoretical foundation in developmental psychology and learning theory” (para. 2). High difficulty level developmental mathematics course. For the purpose of this study, courses listed as Algebra Fundamental I, Algebra Fundamentals II, and Algebra Fundamentals III in the institution’s course catalog indicated a highlevel of developmental mathematics courses. Highlevel math anxiety. For the purpose of this study, a total score of 72 or higher on the RMARS indicated a highlevel of math anxiety (Plake & Parker, 1982). Low difficulty level developmental mathematics course. For the purpose of this study, courses listed as Concepts in Basic Mathematics and PreAlgebra Mathematics in institution’s course catalog indicated lowlevel developmental mathematics courses. Lowlevel math anxiety. For the purpose of this study, a total score of 71 or lower (below 72) on the RMARS indicated a lowlevel of math anxiety (Plake & Parker, 1982). 22 Math anxiety. Math anxiety includes “feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (Richardson & Suinn, 1972, p. 551). Mathematics Anxiety Rating Scale (MARS). The MARS is a 98item, Likertstyle assessment that was “constructed to provide a measure of anxiety associated with the single area of the manipulation of numbers and the use of mathematical concepts” (Richardson & Suinn, 1972, p. 551). Revised Mathematics Anxiety Rating Scale (RMARS). Plake and Parker (1982) developed the RMARS, which “a 24item version of the Mathematics Anxiety Rating Scale” (Mji & Mwambakana, 2008, p. 24). Remedial. In this study, remedial is synonymous with developmental (NADE, 2011). Traditional developmental mathematics course. For the purpose of this study, developmental mathematics courses refer to full 16week semester courses with direct instruction and lecture as the modality of instruction in the institution’s course catalog. Limitations The following limitations were applied to this study: 1. The researcher was an employee at the selected Texas community college used in this study. 2. Instructors did not use any strategy to decrease math anxiety during the study. 3. Students may or may not have responded to the study instruments with candor and seriousness. 4. The researcher did not control for the experience or expertise of the developmental mathematics instructors used in this study. 23 Delimitations The following delimitations were applied to this study: 1. Only one public community college in Dallas County, Texas was selected using the Carnegie Classification of (a) medium public urbanserving multicampus or (b) large public urbanserving multicampus. 2. Only community college students enrolled in a developmental mathematics course during the selected Spring 2013 semester were invited to participate in the study. 3. Only traditional 16week semester developmental mathematics courses using a lecturebased mode of instruction were included in the sample population. 4. Academic success was determined by the successful completion of a developmental mathematics course with a letter grade of C or better. Assumptions This study was based on the following assumptions: 1. The Revised Mathematics Anxiety Rating Scale instrument accurately measured the level of anxiety of each participant. 2. Participants responded to the items on the Revised Mathematics Anxiety Rating Scale thoroughly. 3. Participants understood each item of the Revised Mathematics Anxiety Rating Scale. Organization of Dissertation Chapters This study investigated the influence of math anxiety on the educational achievement of developmental mathematics students at a Texas community college. A review of the literature is presented in Chapter 2 and addresses the research pertaining to the topics of developmental education, developmental mathematics, math anxiety, and the effect of math anxiety on students 24 and teachers. The methodology used in this study is described in detail in Chapter 3. Chapter 3 also includes the selection of participants, collection of data, and the treatment of data. An analysis of the data is provided in Chapter 4, in which the research questions and hypotheses are addressed. Chapter 5 includes a summary of the study, a report of the findings, and the researcher’s conclusions concerning possible implications for practice and recommendations for further research. 25 Chapter 2 LITERATURE REVIEW Developmental mathematics programs at community colleges are scrutinized, revised, and restructured continuously in an effort to create the most effective sequence of learning mathematics for students who do not possess these basic skills. According to Bonham and Boylan (2011), “developmental mathematics as a barrier to educational opportunity represents a serious concern for the students as well as higher education policy makers” (p. 2). Remediation in mathematics is also a source of frustration for community college leaders and students (Bonham & Boylan, 2011). The current developmental mathematics programs have become a target for criticism and attack from all fronts (Boylan, 1999b; College Complete America [CCA], 2012). Developmental Education Community colleges across the United States are charged with the task of building the skills of underprepared high school students who enter college. According to Kolajo (2004), “Nearly all community colleges nationwide offer developmental education to underprepared students as a prerequisite for collegelevel courses” (p. 365). Developmental education has continued to be essential to community colleges (Kolajo, 2004). However, because the cost of remedial education is a burden on community colleges, they tirelessly debate whether keeping these programs is worthwhile. Issues in Developmental Education In addressing the problems surrounding developmental education, Phipps (1998) indicated that structural questions exist about earlier education and students’ academic backgrounds, which may affect the amount of remediation needed. One major finding was that 26 developmental education is a common part of postsecondary education (Phipps, 1998); in fact, it has been an essential component of higher education since the early 17th Century (Phipps, 1998; Kolajo, 2004). Phipps also noted the following: A 1995 survey by the National Center for Education Statistics (NCES) found that 78 percent of higher education institutions that enrolled freshman offered at least one remedial reading, writing, or mathematics course. One hundred percent of public twoyear institutions and 94 percent of institutions with high minority enrollments offered remedial courses. Twentynine percent of firsttime freshmen enrolled in at least one of these courses in the fall of 1995. Freshmen were more likely to enroll in a remedial mathematics course than in a remedial reading or writing course, irrespective of the institution they attended. (p. vvi) This conclusion indicated that remediation or developmental programs would continue to be cornerstones of colleges and universities. Phipps (1998) also found the costs of remediation are typically equal to the costs of other academic programs. The researcher stated that, on a national level, remediation programs cost “approximately $1 billion annually in a public higher education budget of $115 billion—less than 1 percent of expenditures” (p. vii). This national cost estimate includes costs for students, regardless of age or demographics; however, it does not include costs incurred in private or corporate sectors because of a lack of education and preparedness of potential employees (Phipps, 1998). Phipps suggested that the national cost estimation “could be twice as high as previously reported or closer to $2 billion” (p. 13), meaning that it is still a low amount to spend on such an important program. Phipps (1998) also reported that consistent standards do not exist for collegelevel work, the investment in remediation benefits all stakeholders, and not providing 27 remedial education results in social and economic repercussions. Phipps provided several strategies to improve the effectiveness of remediation and ultimately to reduce the need for these courses such as promoting collaboration between colleges and universities within states, redesigning remedial programs to include more than tutoring, and increasing the use of technology in the courses. Brothen and Wambach (2004) attempted to redefine the core elements and components of developmental education to address structural concerns. With pressure to reduce remediation programs, researchers have questioned whether these efforts are effective in preparing students for collegelevel work and degree completion. Brothen and Wambach noted the increase in enrollment at 4year institutions because of openadmission policies in the 1960s and 1970s. These openenrollment policies have caused many schools to develop courses that focus primarily on remediation and developmental education. Another concern the researchers addressed is whether these courses adequately serve developmental education students (Brothen & Wambach, 2004). Finally, they addressed research on the effect of having underprepared students in collegelevel courses, and cited that having underprepared students in their courses has resulted in teachers adapting and modifying their teaching styles as preemptive responses. This finding suggests that teachers have lowered their expectations of student achievement and may cover less material in an effort to maintain high retention and success rates (Brothen & Wambach, 2004). Brothen and Wambach (2004) offered the following seven concepts to improve developmental education: 1. Continue and refine literary skill development courses. 2. Vary course placement requirements based on student goals and program of study. 28 3. Develop a range of placement testing procedures. 4. Integrate alternative teaching/learning approaches. 5. Use theory to inform practice. 6. Integrate underprepared students into mainstream curriculum. 7. Adjust program delivery according to institutional type. (p. 1822) The implementation of these critical concepts and approaches would assist in creating a more successful future for developmental education. The researchers suggested a continuation of supplemental instruction that incorporates study skills, developing consistency in cut scores for placement assessments, and infusing the curriculum with theory and quality instruction that meets the needs of all students. A reconfiguration of developmental education would promote motivation and progression of students and encourage teachers to be openminded about applying methods and strategies to aid in the academic success of all students (Brothen & Wambach, 2004). Smith (2012) discussed student readiness in Texas and stated that less than 50% of students met the required standardized assessment scores necessary to be considered collegeready. Smith also reported that identifying college readiness skills is easy, but it is the actual measurement of these skills that presents incomplete evidence. A debate over who is to blame for the low performance and lack of student preparedness for postsecondary education has resulted in finger pointing and blaming (Smith, 2012). Smith (2012) reported that experts believe some students are placed in remediation courses because of scores that may have been affected by the lack of preparation or focus during the admission exam, rather than low skill level. He questioned whether state standardized or 29 college admissions exams provide accurate data about college preparedness. In fact, Smith reported the following: Studies support the theory that high school grades, not placement or admissions exams, give a better picture of whether students are ready for college, said Pamela Burdman, an education policy analyst who recently wrote a report on the role of placement exams in assessing college readiness for Jobs for the Future, a Bostonbased nonprofit. And the best measures, she said, use some combination of high school gradepoint averages and standardized test scores. (p. 2) Smith (2012) suggested steps that the state is taking to develop more efficient and effective evaluation measures including creating an assessment that provides a more detailed account of what students are missing in their high school curriculum. Smith (2012) discussed a contract between Texas and the College Board “to develop a statewide placement assessment, which all institutions would be required to administer to incoming students who did not meet the benchmark scores on state standardized exams or college admissions tests” (p. 2). The purpose of this new assessment is to ensure uniformity and a better view of student deficiencies. He also provided examples of community colleges and school districts in Texas that are tackling the challenge head on. For example, El Paso Community College collaborated with their local high schools to allow students to take the college placement exam during their junior years of high school (Smith, 2012). In doing so, students are able to work with counselors to develop a plan for their senior year coursework. Another example included school districts that work in collaboration with community colleges by allowing students to take more dualcredit courses and leave high school with an associate’s degree (Smith, 2012). 30 Texas transitioned to the new standardized assessments, the State of Texas Assessments of Academic Readiness (STAAR) exams in the spring of 2012, which addressed a few of the issues with students not entering college adequately prepared for collegelevel courses. Because the STAAR exams align sufficiently with college readiness standards, school districts and colleges are obtaining a better view of entering students (Smith, 2012). However, if students choose to take dualcredit courses, they must take both the standardized STAAR exam and a college final, which often deters student from wanting to take that path and enroll in those types of courses (Smith, 2012). Initiatives and Alternatives in Developmental Education Boylan (1999b) embarked upon finding solutions to the complaints of the time and cost of remedial courses, which hinder students’ academic progress in college. The researcher noted, “Traditionally, developmental education has included such activities as remedial/developmental courses, tutoring, learning laboratories, and various forms of individualized instruction” (Boylan, 1999b, p. 2). Boylan (1999b) provided alternative approaches to current programs including a freshmen orientation, supplemental instruction (SI), paired courses, collaborative learning communities, and critical thinking courses and programs, many of which have been around since the late 1970s. The researcher supported traditional approaches because these interventions have proven effective, especially among students who may not have persisted without such instructional support (Boylan, 1999b). Freshmen seminars or orientations typically last a day or two at universities and even less time at community colleges. The alternative approach increases the time span and orientation lasts the entire academic semester. Boylan (1999b) stated the following: 31 Instead of concentrating on rules and traditions, the freshmen seminar actually explores issues in college life, the purposes of higher education, and the requirements and expectations of college attendance through the vehicle of a regular, creditbearing, college course conceived as an integral part of the firstyear experience. (p. 3) Freshmen orientation has generated opportunities for all students, including developmental students, to learn more about the campus culture and expectations. Supplemental Instruction was developed in the early 1970s at the University of MissouriKansas City to help students progress through difficult courses. Specifically, SI consists of small groups of students with one group leader who took the course during a previous semester. The group leader serves as a peer mentor to help the students develop strategies for success such as testing and notetaking skills. Using this approach in developmental education programs may result in more students being placed in remedial courses to be successful in regular college courses eventually. Since its development, SI has been incorporated into various academic programs, including developmental education (Boylan, 1999b). Another alternative is including learning communities and collaborative learning in a developmental education program. Boylan (1999b) noted, “[A] learning community is arranged by having students enroll together as a cohort in several courses linked together by a common theme” (p. 3). Course instructors also work as a team to link content so that students can make connections while working with others to study and complete assignments (Boylan, 1999b). Paired courses are another alternative that is related closely to collaborative learning. Like collaborative learning, paired courses include a cohort of students that enrolls in two courses together, a main course and a supplement to the main course (Boylan, 1999b). In the paired course approach, instructors work together to provide connections and support between the two 32 courses (Boylan, 1999b). Using paired courses in developmental education can reduce the amount of time students spend in developmental education courses and allow them to earn course credit in collegelevel courses (Boylan, 1999b). Boylan (1999b) suggested that lack of critical thinking skills is a primary cause of failure among developmental students; therefore, he suggested an alternative approach that addresses increasing these skills. Developmental educators can address the lack of critical thinking skills by providing students with single courses or workshops that focus on these skills or by integrating critical thinking into the curriculum. Boylan (1999b) concluded by stating that implementing strategies for interventions and alternatives to remedial education requires organization, training, and collaboration of advisors and faculty, as well as consistency in availability and resources. Kozeracki and Brooks (2006) evaluated the effectiveness of the developmental education program at Davidson County Community College (DCCC) in North Carolina as it prepared for its 2002 accreditation. Specifically, the college engaged in a selfassessment of developmental education strategies applied on each campuses. The college chose developmental education as the selfassessment focus for the following reasons: 1. There had been a dramatic increase in the number of underprepared students enrolling at the college in recent years. 2. There was also a concern that the developmental courses did not create a sound foundation for success in collegelevel courses and programs. 3. Faculty and staff were aware that a disproportionate amount of time and resources were being dedicated to the placement and advising of underprepared students. 33 4. A number of projects conducted by the college in the mid1990s had helped familiarize faculty with how to teach to students’—especially developmental students’—learning styles. (Kozeracki & Brooks, 2006, pp. 6869) The committee in charge of conducting the selfassessment hired an outside consultant experienced in developmental education who recommended, “Subcommittees explore the following areas: advisement, assessment, coordination and learning support, communication, evaluation, and curriculum and development” (Kozeracki & Brooks, 2006, p. 69). The advisement subcommittee found that students need immediate advising following their first assessment, and advisors need continuous training to communicate the requirements of the developmental education program effectively (Kozeracki & Brooks, 2006). The assessment subcommittee found that benchmark scores should be consistent and compatible with aiding students in proper placement and skills intervention (Kozeracki & Brooks, 2006). The coordination and learning support subcommittee reviewed the organizational structure and alignment between developmental education and the mission of the institution (Kozeracki & Brooks, 2006). This subcommittee found that the preparatory (developmental) education mission statement and that of the college were aligned, and the program was essential to the mission of the college (Kozeracki & Brooks, 2006). The college decided that “A hybrid organization model, in which developmental courses are housed in their own disciplines but support services and other activities are centrally coordinated, would be most appropriate” (Kozeracki & Brooks, 2006, pp. 6970). The curriculum and development subcommittee discovered that no explicit expectations existed for students in the developmental courses and many courses were inconsistent because faculty added activities or requirements (Kozeracki & Brooks, 2006). Therefore, 34 recommendations included standard student expectations related to student behavior, class and homework, grading policies, and academic integrity. The evaluation subcommittee discovered that onethird of the 389 students who graduated in 19992000 had taken at least one developmental course; however, some students graduated from the college without taking the recommended developmental education courses (Kozeracki & Brooks, 2006). The communications subcommittee discovered that faculty who taught the same developmental education courses had no consistency in syllabi formatting, which caused difficulties for students in understanding the expectations and goals of the courses (Kozeracki & Brooks, 2006). Additionally, this subcommittee revealed that faculty exuded a negative tone and attitude toward the program in the language they used when speaking of developmental education programs (Kozeracki & Brooks, 2006). Kozeracki and Brooks (2006) urged community colleges to address the needs of underprepared students and to evaluate their developmental education programs. The realization that underprepared students can be in any class meant that faculty in every division and department should be prepared to address and meet students’ needs to achieve success (Kozeracki & Brooks, 2006). Full institutional support, from the administration to the faculty and students, is necessary for the growth and success of developmental education programs (Kozeracki & Brooks, 2006). Developmental Mathematics Radford and Horn (2012) reported on NCES data that listed precollege credits; remedial education participation; withdrawals and repeated courses; and credits earned in science, technology, engineering, and mathematics (STEM) from 20032004 for firsttime postsecondary students who were followed for 6 years. Table 3 offers an abbreviated version of the data from 35 the NCES on percentages of students that took a remedial mathematics course and the average number of remedial mathematics courses taken and passed (Radford, & Horn, 2012). Over the course of the 6year period, nearly 17,000 students participated in the survey and 42.2% took at least one remedial mathematics course at a postsecondary institution, The average was two mathematics courses taken during the 6year period and students passed an average of 1.3 mathematics courses (Radford & Horn, 2012, p. 15). Most participants who took a remedial mathematics course were female (44.0%), Black (51.6%), and 2023 years of age when first enrolled in 2003 (Radford & Horn, 2012, p. 15) (see Table 3). Table 3 NCES Remedial Math Statistics: 2009 Took remedial math course (%) Remedial math courses taken (M) Remedial math passed (M) Total 42.2 2.0 1.3 Sex Male 39.8 2.0 1.2 Female 44.0 2.0 1.3 Race/ethnicity White 39.4 1.9 1.3 Black 51.6 2.2 1.3 Hispanic 49.5 2.3 1.4 Asian 31.2 2.0 1.3 Other or Two or more 40.6 2.1 1.2 Age when enrolled in 20032004 18 or younger 38.2 2.0 1.3 19 42.0 2.0 1.3 2023 50.3 2.1 1.3 24 or older 46.3 2.0 1.4 36 Issues in Developmental Mathematics In an interview with Dr. Paul Nolting, Boylan (2011) posed several questions on improving developmental mathematics programs. Nolting stated that the levels of developmental mathematics may vary by state or university, and some universities had as many as four or even five levels of developmental mathematics, which increases the likelihood that students will enroll in developmental mathematics (Boylan, 2011). Nolting also noted several possible reasons why so many incoming students are placed in developmental mathematics courses. First, placement cut scores, which determine whether a student is required to enroll in a developmental mathematics course, vary by institution, which implies that benchmark scores to enter collegelevel mathematics courses may be harder to reach than those for reading and English (Boylan, 2011). Nolting also suggested that the time between mathematics courses, the inability to use calculators on placement tests, students entering college on a General Equivalency Diploma (GED), and test anxiety are factors that may result in students being placed in developmental mathematics courses (Boylan, 2011). Nolting also discussed the low prevalence of passing collegelevel algebra among students who take lower level developmental mathematics. Reasons for this low pass rate in collegelevel mathematics includes the length of developmental courses, high failure rates, inability to develop the necessary skills for college math, deficiencies in abstract reasoning and math anxiety. These factors result in students who avoid math and develop poor study habits. Nolting also suggested that failing mathematics is socially acceptable among the college student population, and “students with personal problems usually withdraw from math first, and repeating students usually get the same type of instruction that originally led to their failure” (Boylan, 2011, p. 21). Nolting also commented on the linear nature of developmental 37 mathematics, the notion of math phobia, and student procrastination as factors that may exist more among developmental mathematics students than other students (Boylan, 2011). Nolting proposed initiating an open conference to address the issues and concerns of developmental mathematics programs where administrators, faculty, and students could discuss factors that plague the program (Boylan, 2011). Nolting also provided two options for students who fail a developmental mathematics course, “retaking the placement test to score out of the developmental math course or retaking the final exam” (Boylan, 2011, p. 21). However, these choices pose more questions than they offer solutions to the problem, including whether the score on college placement assessments better shows students’ skills and knowledge than the final grade in previous mathematics courses (Boylan, 2011). Finally, Nolting discussed the role that math and test anxiety play in developmental mathematics students. He believed that math anxiety over the tests and content materials affect how students perform in class, on homework and on assessments (Boylan, 2011). To address these issues, Nolting suggested that universal placement assessments, resources for developmental mathematics, adequate preparation for the workforce, and effective teaching for developmental students are appropriate approaches that colleges should consider (Boylan, 2011). Fike and Fike (2012) surveyed 3,476 firsttime college students to compare those who enrolled in developmental mathematics during their first semester compared to those who delayed enrollment at an urban, private Hispanicserving university in the Southwest United States. The researchers suggested that delayed enrollment in developmental mathematics courses may have a negative effect on academic success. The researchers also suggested a more indepth look at the placement policies and examinations to determine their influence on 38 academic success. Of firsttime students, “884 (25%) were college ready in mathematics at initial enrollment, 1,139 (33%) enrolled in developmental mathematics during their first semester, and 1,453 (42%) deferred enrollment in developmental mathematics during their first semester” (Fike & Fike, 2012, p. 3). Findings revealed that students who were college ready in mathematics were more academically prepared than were students who either deferred enrollment or were enrolled in developmental mathematics (Fike & Fike, 2012). Additionally, 71% of students enrolled in developmental mathematics successfully completed with a grade of A, B, or C (Fike & Fike, 2012). These findings suggested that students in developmental mathematics were as successful as were those in college mathematics, which supports the need for developmental mathematics courses in college (Fike & Fike, 2012). Additional findings showed that final grade point averages (GPA) of students who passed developmental mathematics courses were higher than were those of students who deferred their developmental mathematics courses or failed their developmental mathematics courses (Fike & Fike, 2012). This finding implies that developmental mathematics students reach the same level of achievement as do collegeready students (Fike & Fike, 2012). Additionally, universities should not allow students to postpone enrollment into developmental mathematics courses. Fike and Fike (2012) concluded that requiring all students who are not prepared for collegelevel courses to take a developmental mathematics course within their first year might be the best solution. Initiatives in Developmental Mathematics Mireles, Offer, Ward, and Dochen (2011) examined study strategies among students in developmental mathematics and college algebra programs. Specifically, the researchers 39 addressed the problem of developmental mathematics as a barrier that results in many students repeating these courses. The researchers applied a mixed methods design to assess 47 students who participated in a rigorous summer hybrid program of developmental mathematics and college algebra. The program integrated mathematics and science, and used “peerled team learning and computer theme modules that link content” (Mireles et al., 2011, p. 12). Mireles et al. (2011) measured students using the Learning and Study Strategies Inventory (LASSI; 2nd edition), LASSI PrePost Achievement Measure, and the Mathematics Information Survey. The program length was 5.5 weeks with the developmental mathematics course for 2 hours in the early morning and the college algebra course for 2 hours in the late afternoon. The program integrated study strategies into the developmental mathematics course curriculum and reinforced those study strategies during the college algebra course. Mireles et al. (2011) found that incorporating study skills, supplemental instruction, and learning strategies improved program success. Specifically, the findings showed that students were more aware of their anxiety, attitudes, and motivation levels, and were able to monitor their concentration levels (Mireles et al., 2011). This finding implies that over the duration of the summer program, students decreased their math anxiety and increased their level of motivation (Mireles et al., 2011). Additionally, the program design aided students’ overall feelings of success and achievement (Mireles et al., 2011). Students were also aware of the resources available to them. They learned study strategies and continued to use those strategies in other classes (Mireles et al., 2011). Mireles et al. (2011) suggested that additional research investigate the effect of introducing study skills at an earlier stage in the developmental mathematics program. Additionally, the researchers noted that the study “highlighted positive impact on the strategies utilized by developmental 40 mathematics students through study strategy incorporation in both a developmental mathematics and college algebra class” (pp. 4041). Asera (2011) explored interventions for a developmental mathematics program at 11 California community colleges. The project Strengthening PreCollegiate Education in Community Colleges (SPECC) was designed in 2005 to allow colleges to redesign and improve their developmental education programs and focus on the program effects on student learning and achievement (Asera, 2011). According to Asera (2011), The SPECC campuses offered the range of the intervention programs that are common across community colleges: different configurations of learning communities; firstyear experiences; various uses of technology in both math and English classrooms; as well as use of tutors and instructional aides in the classroom, in scheduled study sessions, and in labs. Many of these interventions were small programs, nurtured by the faculty and staff responsible for them. (p. 28) The SPECC program had some limitations including the realization that a high number of mathematics students failed developmental mathematics courses regardless of strategies and interventions (Asera, 2011). Other findings discussed the use of technology in the classroom. While the researcher found technology had a moderate effect, it was helpful as a means of tutoring. Additionally, redesigning course materials and examinations to be the same in similar courses created a more consistent developmental mathematics program but did not seem to affect students’ results (Asera, 2011). At the conclusion of the SPECC program, the Carnegie Foundation shifted its focus to developmental mathematics with the induction of the new president, Tony Bryk (Asera, 2011). Along with other organizations, educational reform initiatives begun including Achieving the 41 Dream Developmental Education Initiative (ADDEI), National Center for Academic Transformation (NCAT), Changing the Equation (CtE), the California State Basic Skills Initiative (CTBSI), and Global Skills for College Completion (GSCC). Many of these initiatives focused on the sequence of developmental mathematics programs and challenges to completion. One study from the Community College Research Center (CCRC) revealed the following: The studies pointed out the low percentage of students who complete the sequence (overall 31% of students who start anywhere in developmental mathematics) and the somewhat counterintuitive finding that more students are lost before initial enrollment and between courses than from courses. The very length of the sequence is problematic because the longer the sequence, the more chances there are—in every course and between courses—for students to leave. (Asera, 2011, p. 29) To address the sequencing issue, the Carnegie Foundation and others created new sequencing pathways to align course materials with academic and professional goals (Asera, 2011). Asera (2011) stated that minimal changes to the system would not be adequate and that major course and program reform would be needed. The Carnegie Foundation began by forming two initial pathways, the Mathway and the Statway. The Mathway started “with a onesemester experience of integrated problem solving and critical thinking called Mathematical Literacy for College Students (MLCS)” (Asera, 2011, p. 29). The Statway was “an integrated pathway from developmental mathematics (starting with students who place into elementary algebra) through collegelevel statistics in 1 year” (Asera, 2011, p. 29). The program design aimed to avoid the possibility of a limited pathway by a higher level of rigor in mathematics, to connect both pathways, and to gather data and evidence to support findings (Asera, 2011). Asera (2011) concluded that it would not be easy redesigning 42 and restructuring the current model of developmental mathematics courses into specific pathways that focused on student learning and achievement. She also noted that neither design would meet the needs of all developmental students, but either program design may work for the right set of students. Math Anxiety Various studies have been conducted to discover the possible effect of math anxiety on mathematics performance. Richardson and Suinn (1972) characterized math anxiety as “feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (p. 551). Gresham (2007) defined math anxiety as “a feeling of helplessness, tension, or panic when asked to perform mathematics operations or problems” (p. 182). Furner and GonzalesDeHass (2011) stated the following: Mathematics anxiety can be defined as feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations. Some students tend to be more anxious about the testing process and can often freeze up (math test anxiety), others just cringe when they are confronted with any form of computational exercise (number anxiety), and others dread taking math classes which can occur in the elementary school, middle school, high school, or college levels (math course anxiety). (p. 228) Attitudes toward Mathematics Geist (2010) examined the root causes of math anxiety in the classroom and the negative attitudes toward mathematics. The researcher stated that many children develop math anxiety early in life, especially if their parents are from low socioeconomic backgrounds and have math 43 anxiety (Geist, 2010). Additionally, the role that gender plays on math anxiety suggests that more female students have math anxiety because of their negative attitudes toward testing compared to male students (Geist, 2010). Considering the gender gap in academic achievement, it is possible that gender is influential and math anxiety or negative attitudes toward mathematics are more influential in this gap (Geist, 2010). Geist (2010) offered the following: Studies have shown that at this time in children’s learning of mathematics, textbooks take over the process of teaching and the focus on shifts from construction of concepts using children’s own mathematical thinking to teacher imposed methods of getting the correct answer (Geist, 2000). Teachers begin to focus on repetition and speed or “timed tests” as important tools for improving mathematical prowess and skill which can undermine the child’s natural thinking process and lead to a negative attitude toward mathematics (Popham, 2008; Scarpello, 2007; Thilmany, 2004; Tsui & Mazzocco, 2007). (pp. 2425) As children develop and enter formal schooling, math anxiety is a serious obstacle at all levels and for all groups, which produces an achievement gap in mathematics (Geist, 2010). Geist (2010) examined gender differences in negative attitudes toward mathematics, and found that female students develop negative attitudes because of the timed and highstakes testing, which results in higher levels of math anxiety. Gender differences increase because of the assumption that one teaching method or style meets all students’ learning needs and abilities (Geist, 2010). Geist (2010) also examined teacher’s beliefs and instructional approaches as factors that influence students’ attitude toward mathematics. The researcher revealed the belief that mathematics achievement among females is because of hard work, while that among males is because of natural talent. Thus, children may adopt their teachers’ attitudes and the confidence level of female students pertaining to their performance may decrease as selfdoubt increases 44 (Geist, 2010). According to Geist (2010), anxiety develops in individuals when the focus is on the correct answers, speed, and repetition instead of ensuring that students can critically think through and process the answers and concepts. Students may inherit their teachers’ negative attitudes about areas of mathematics, which develop from teachers’ own levels of math anxiety and inadequacies (Geist, 2010). Geist (2010) also expressed the need to examine how mathematics is taught because of the global necessity of mathematics. Geist (2010) traced the cause of negative attitudes toward mathematics to poverty and family. He noted that a low household income and low level of education in parents are risk factors for low achievement in mathematics (Geist, 2010). Concerning attitudes toward mathematics and parental education, Geist noted the following: This data shows that the father’s education level seems to have a greater effect in almost all groups. Yet studies have shown that a mother’s attitude and encouragement toward mathematics was a significantly more important factor to children having a positive attitude toward mathematics (Scarpello, 2007) (p. 27). The parents may have less knowledge of mathematical concepts, lower comfort level with mathematics and a negative attitude toward mathematics leading to math anxiety and an aversion to mathematics. (p. 28) Geist (2010) expressed concern for developing students who shy away from higher levels of mathematics, which leads to avoidance of postsecondary education. He concluded by stating that educators must remember their experiences in mathematics so as not to repeat the same mistakes (Geist, 2010). Amirali (2010) examined attitudes and perceptions toward mathematics of eighthgrade private school students in Pakistan. Overall, the researcher found that a dislike of mathematics 45 was universal. She also stated that most secondary students believed mathematics is difficult and not very interesting. Convenience sampling and accessibility strategies were used to locate the research site and sample population. Amirali noted she used eighthgrade students as the sample population because eighthgrade mathematics represents the middle point of attainment in skill level for secondary mathematics. Eightytwo students from an Englishspeaking school participated in the study and were mostly between the ages of 13 and 15. To examine attitudes toward mathematics in Pakistan, Amirali (2010) used four foci, “usefulness of mathematics, the nature of mathematics, attitude towards the subject as well as mathematics anxiety” (p. 29). The researcher developed an instrument consisting of 35 items that were rated on a 5point Likert scale to address the four areas (Amirali, 2010). Amirali (2010) found little difference between male and female responses. Findings suggested that most students had a positive outlook and felt confident about their mathematics skills and ease in learning the content. Additionally, more female students had positive attitudes toward mathematics compared to male students, which produced lower levels of math anxiety among female students. Amirali implied that further research needed to be conducted regarding students learning mathematics because most students considered mathematics as highly important. The researcher also suggested research address the issue of engaging students in learning problemsolving skills that are relevant to their lives. Studies of Math Anxiety in Preservice Teachers Sloan (2010) conducted a mixed methods study of math anxiety with future teachers to examine the prevalence of teachers with math anxiety passing it along to students. The researcher cited additional research that included the following ideas: 46 Mathanxious teachers actually teach differently than teachers who are less anxious about mathematics, teachers who do not enjoy mathematics spend 50 percent less time teaching this subject than teachers who feel comfortable with this subject, and teachers with negative attitudes toward mathematics frequently rely on teaching algorithms while neglecting cognitive thought processes and mathematical reasoning. (Sloan, 2010, p. 243). Sloan (2010) also stated that a number of future teachers had math anxiety and negative attitudes and perceptions towards mathematics. To examine these claims and to add to the literature, Sloan (2010) examined “72 preservice teachers from three sections of an undergraduate mathematics methods course” (Sloan, 2010, p. 243). Participants ranged in age from 18 to 27, and the sample included 66 females and 6 males. Among participants, 61 had taken high school algebra, 45 had taken high school geometry, 72 had taken high school trigonometry, 41 had taken college algebra, four had taken college calculus, and five had taken college precalculus. The intervention was a mandatory course to aid future elementary teachers in the preparation for and evaluation of mathematics teaching (Sloan, 2010). This course incorporated a variety of topics including “basic mathematics content for preschool through third grade; an examination of learning principles; an exploration of various instructional strategies, techniques, and materials; and other issues related to teaching mathematics to children in the primary grades” (p. 244). Course requirements included presenting instruction to peers, working with mathematics manipulatives, using technology in the classroom, and field experience (Sloan, 2010). The researcher used the Mathematics Anxiety Rating Scale (MARS) to measure the levels of math anxiety before and after the methods course to determine the effectiveness of the 47 15week course (Sloan, 2010). The researcher also interviewed 12 participants who yielded the greatest differences on the MARS pre and posttest (Sloan, 2010). The researcher found statistically significant differences between pre and post course math anxiety among all participants, and attributed these differences to participation in the methods course (Sloan, 2010). Findings revealed, “At the completion of the standardsbased mathematics course, mathematics anxiety levels of preservice elementary teachers were significantly reduced from their initial levels at the beginning of the course” (Sloan, 2010, p. 246). Specific intervention methods, such as required time in the field and overall course atmosphere, helped reduce math anxiety levels, while intervention, such as course examinations, increased math anxiety levels (Sloan, 2010). Sloan (2010) exposed the emergence of the following nine categories of antecedents of math anxiety: (a) parental influences, (b) negative school experiences, (c) methodology of former mathematics teachers, (d) low mathematics achievement, (e) test anxiety, (f) lack of confidence, (g) negative attitudes, (h) mathematics avoidance, and (i) mathematics background (p. 250). Sloan (2010) offered several implications and recommendations for further study. 1. A required mathematics methodology course for all future teachers. 2. Developing a positive and encouraging learning environment. 3. Continued research using the same participants at the end of their course work and field experience to reassess math anxiety levels. Isiksal (2010) studied “the relationship among Turkish preservice elementary teachers’ mathematics teaching efficacy beliefs, mathematics anxiety, and mathematical selfconcept” (p. 501). In this study, “data were collected from 276 Turkish preservice elementary teachers enrolled in teacher education programs of two universities in the Southwest part of Turkey” (p. 48 504). The study used the Mathematics Teaching Efficacy Belief Instrument (MTEBI), the Abbreviated Mathematics Anxiety Scale (AMAS), and the Experience with Mathematics Questionnaire (EMQ) to examine the variables (Isiksal, 2010). The MTEBI is a 21item scale used to measure teaching efficacy beliefs and perceptions of teaching abilities. The AMAS is a 9item scale used to measure anxiety in certain mathematical situations, including learning process and mathematics test anxiety. The EMQ is a 27item questionnaire used to measure perceived mathematics learning ability. The researcher found the following: 1. Preservice teachers who had higher beliefs in their ability in learning new topics in mathematics and in translating teachers’ action into student learning also had higher beliefs in their own ability to teach mathematics effectively. (Isiksal, 2010, p. 508) 2. Preservice teachers’ higher beliefs in their own ability to teach mathematics and higher anxiety during testing situations were associated with higher beliefs in translating teachers’ action into student learning. (Isiksal, 2010, p. 508) 3. Higher anxiety about process of learning mathematics affected test anxiety positively and increased preservice teachers’ mathematics evaluation anxiety. (Isiksal, 2010, p. 508) 4. Preservice teachers with higher anxiety had lower beliefs in their ability to learn and perform task in mathematics. (Isiksal, 2010, pp. 508509) Isiksal (2010) stated that courses for teacher preparation have been structured successfully to implement new curriculum changes, strategies, and requirements effectively. The researcher further concluded that preservice teachers should be allowed to practice and experience the mathematics curriculum, and the teacher preparation curriculum should be aligned with the school curriculum to lower math anxiety and increase confidence levels (Isiksal, 2010). 49 Studies of Math Anxiety in Students Zakaria and Nordin (2008) “investigated the effects of mathematics anxiety on matriculation students as related to motivation and achievement” (p. 27). The researcher aimed to determine whether study relationships existed between math anxiety and motivation, and math anxiety and achievement (Zakaria & Nordin, 2008). The researchers administered the Mathematics Anxiety Scale (MAS), Effectance Motivation Scale (EMS) and the Mathematics Achievement Test (MAT) to 73 female students and 15 male students (Zakaria & Nordin, 2008). Participants were divided into three groups based on their math anxiety scores: (1) low math anxiety group (lower 33%), (2) moderate anxiety group (between 33% and 67%), and (3) high math anxiety group (33%) (Zakaria & Nordin, 2008). The results revealed a significant difference in achievement between the low and high anxiety groups, but no significant difference between the low and moderate and between the moderate and high anxiety groups (Zakaria & Nordin, 2008). The results showed that students with high math anxiety had low achievement scores (Zakaria & Nordin, 2008). The results also revealed significant differences for motivation between the low and moderate, low and high, and moderate and high anxiety groups. This finding indicates that the level of math anxiety affects student motivation in such a way that the higher the level of math anxiety, the less motivation to complete any mathematicsrelated tasks (Zakaria & Nordin, 2008). In other words, the relationship between math anxiety and achievement indicates that as math anxiety scores increase, achievement scores decrease (Zakaria & Nordin, 2008). The researchers implied that teachers should be mindful that student academic success is tied to their levels of anxiety, and teachers should vary their teaching methods and strategies to meet all student needs (Zakaria & Nordin, 2008). 50 Kesici and Erdogan (2010) sought to determine whether social comparison affected student motivation and anxiety levels by studying students in Turkey. Participants included 156 eighthgrade students (86 males and 70 females). The instruments included the MARS, Achievement Motivation Scale (AMS), and Social Comparison Scale (SCS) (Kesici & Erdogan, 2010). The MARS consists of 98 items aimed to determine the level of math anxiety (Kesici & Erdogan, 2010). The AMS measures consist of 14 items aimed to determine the level of motivation to achieve (Kesici & Erdogan, 2010). The SCS consists of 18 selfevaluation items to determine the perception of abilities and skills compared to peers (Kesici & Erdogan, 2010). The results revealed a significant difference in math anxiety and achievement motivation between students classified as high achievement motivation and those classified as low achievement motivation (Kesici & Erdogan, 2010). Results showed that students with high achievement motivation scores had a higher level of math anxiety than did those with low achievement motivation (Kesici & Erdogan, 2010). Concerning math anxiety and social comparison, the results revealed that math anxiety was higher among students with negative selfesteem compared to those with positive selfesteem (Kesici & Erdogan, 2010). Kesici and Erdogan (2010) concluded that math anxiety among students varies depending on their motivation to succeed and their perceptions of their capabilities within their peer group. The researchers suggested that students set goals and develop motivation based on personal expectation, not peer achievements and scores (Kesici & Erdogan, 2010). Summary Extensive research has been conducted on developmental education, developmental mathematics, and math anxiety among teachers and students. This literature review outlined the body of knowledge available that addresses the developmental education world, specifically, 51 developmental mathematics programs. In regard to the developmental education system, the CCA (2012) stated, “While more students must be adequately prepared for college, this current remediation system is broken. The very structure of remediation is engineered for failure” (p. 2). According to Furner and GonzalesDeHass (2011), increased advertisement of STEM fields is generating more interest in those areas, which is causing universities and community colleges to focus on adequate preparation in those areas. Bonham and Boylan (2011) concluded, “It is unfortunate that developmental courses, once envisioned as a gateway to educational opportunity, have become barriers to that opportunity for many students” (p. 8). As the sequencing of the developmental mathematics program continues to present challenges for students, the likelihood that more students will feel the effect of math anxiety increases (Bai et al., 2009; Boylan et al., 1999; Chinn, 2009; Meece et al., 1990). 52 Chapter 3 METHOD OF PROCEDURE The purpose of this study was to examine the relationship between the achievement of developmental mathematics students and math anxiety. This study sought to determine whether a significant difference exists in levels of math anxiety based on age, gender, and developmental mathematics program level. Additionally, this study strived to establish a connection between the effects of high and low levels of math anxiety and academic success. Design of Study This quantitative, casualcomparative study focused on the effect of math anxiety on the academic achievement of developmental mathematics students at a Texas community college. The researcher formulated four null hypotheses and then tested for statistical significance to determine whether each null hypothesis could be rejected. The researcher administered the Revised Mathematics Anxiety Rating Scale (RMARS) to students enrolled in various levels of developmental mathematics programs during the spring 2013 semester to measure the level of math anxiety. The researcher also collected students’ final spring 2013 semester developmental mathematics course grades from the institution to explore the effect of math anxiety on academic achievement. Description of Sample Population The researcher sent letters to the dean of mathematics and the mathematics department chairperson at the selected Texas community college and obtained IRB approval to conduct this study. Following approval, the researcher reviewed the spring 2013 course listing for developmental mathematics and found 224 sections of developmental mathematics. A letter detailing the study and the amount of participation by the instructor was placed in each 53 developmental mathematics instructors’ campus mailbox and sent via email. The researcher narrowed the target population by selecting only traditional, 16week, lecturebased sections, which resulted in 76 sections. The selected college had five levels of mathematics in the developmental program, which included two lowlevel difficulty courses (DMAT 0066: Concepts in Basic Mathematics and DMAT 0090: PreAlgebra Mathematics), and three highlevel difficulty courses (DMAT 0097: Algebra Fundamentals I; DMAT 0098: Algebra Fundamentals II; and DMAT 0099: Algebra Fundamentals III). The researcher selected five sections of each level of developmental mathematics using stratified random sampling. Three of the 28 developmental mathematics instructors declined participation following an email about the study and an informal meeting to answer questions and concerns. Description of Participant Criterion Twentyfive sections of developmental mathematics were chosen to participate in the study, and the instructors were notified via email. The researcher gave participating instructors a letter of recruitment (Appendix B) and asked them to read the letter to the selected section 1 week prior to the distribution of the survey packets. The scripted letter detailed the study and the criteria to participate. The student participation criteria included the following: 1. At least 18 years old. 2. Currently enrolled in a 16week, lecture developmental mathematics course. 3. Have never taken the RMARS test. 4. Willing to participate in the study. Each section had no more than 25 students enrolled; therefore, a sample size of 625 potential participants was generated. 54 Description of Instruments The survey packets contained five items, study directions, informed consent letter, demographic questionnaire, the RMARS, and an optional puzzle activity (Appendix C). The researcher created color duplicates of each instrument and copied, collated, folded, and placed them into 6x9 inch sealable brown envelopes. The study directions were included in the survey packet and given to the instructor to read aloud to students on the day of data collection. A onepage summary included the research process and length of time allotted to complete the packet. The informed consent letter briefly explained the study, criteria for participation, and any foreseeable risks and benefits. The letter also explained that the researcher could obtain students’ final spring 2013 developmental mathematics course grades from the institution. Also included in the letter were the confidentiality procedures to ensure security of all information provided. Students who chose to participate signed and dated the consent form with their initials and campus identification number. Students were also given the opportunity to receive the results of their RMARS by listing their personal email addresses. The researcher designed the demographic questionnaire to obtain certain descriptive data about each participant. Participants were asked to write their campus identification number at the top and then circle the appropriate response to questions about their age, gender, and developmental course level. The age groups were categorized as follows: 1822, 2327, 2832, 3337, and 38 and older. The developmental course levels were listed with full course name and corresponding course number. The RMARS was duplicated with permission from the creator. The instrument includes a 24item scale for level of math anxiety that uses 5point Likerttype scale (1 = not at all, 2 = a little, 3 = moderate, 4 = much, and 5= very much) to depict the level of fear or apprehension. 55 Statements include, “Walking into a math class,” “Watching a teacher work an algebraic equation on the blackboard,” “Thinking about an upcoming math test on the day before,” and “Taking an examination (final) in a math class.” The researcher created the optional puzzle activity using an online word search puzzle making system. Fortyfive words were selected from basic Texas eighthgrade Algebra vocabulary. The puzzle activity was designed to provide students something to work on while waiting for others to complete the survey packets. The puzzle activity was optional and no data were obtained. Collection of Data At the beginning of February 2013, during the spring 2013 semester, the developmental mathematics instructors of the selected 25 sections were notified via email that the survey packets were available in the mathematics division office for pickup. The survey packet materials were placed in empty copier paper boxes, separated by course number (i.e., DMAT 0066, DMAT 0090, DMAT 0097, DMAT 0098, and DMAT 0099), and color coded by course number as indicated on the study directions sheet (i.e., DMAT 0066red, DMAT 0090light green, DMAT 0097turquoise, DMAT 0098purple, and DMAT 0099yellow). Each DMAT instructor’s name and selected section course number were placed on the study directions sheet along with 25 survey packets and were rubberbanded together. A total of 625 survey packets were prepared for distribution. From February 18 to March 1, DMAT instructors distributed survey packets to the appropriate class section and return them to the same copier paper box. The researcher sent emails to remind DMAT instructors of the surveys, dates of the 2week data collection window, and the deadline to return all materials. The researcher returned to the division office to retrieve 56 the copier paper boxes with all the survey materials during the first week of March. At that time, the researcher sent an email to instructors indicating that the data collection window had closed and that all survey materials should have been returned. The researcher left one copier paper box in the office for an additional week to ensure that all materials had been returned. Of the 625 survey packets distributed, 542 survey packets were returned to the researcher, resulting in 86.72% return rate. Of the 542 survey packets returned, 283 were sealed but partially incomplete and discarded, and 259 were unsealed and blank and discarded (see Table 4). Table 4 Returned Survey Packets Breakdown Type Total Completed 185 Consented and Completed 93 Consented, Email Response, and Completed 92 Partially Incomplete 98 No Campus ID Number Provided 66 Demographic Questionnaire Incomplete 8 RMARS Incomplete 24 Blank 259 Total Returned 542 The consented and completed category indicates that the participant signed the consent form appropriately and completed the demographic questionnaire and the RMARS in their entirety. The consented, email response, and completed category type indicated that the participant signed the consent form appropriately, requested his or her RMARS scores be sent to him or her individually, and completed the demographic questionnaire and the RMARS in their 57 entireties. The partially incomplete category type indicates that the participant did not complete the consent form, demographic questionnaire, or RMARS adequately for the researcher to obtain all data needed. The blank category type indicated that no information within the survey packet was completed and the envelope was unsealed. The researcher first scored the RMARS documents for each participant by calculating the sum of the responses provided. Each participant’s total score was coded as lowlevel or highlevel math anxiety. The RMARS median score was 72, meaning that participants with a score below 72 were categorized as having lowlevel math anxiety and those with 72 or above were categorized as having highlevel math anxiety. The researcher then organized the data and created an Excel spreadsheet to compile the necessary information from the consent forms, demographic questionnaires, and RMARS. To obtain the final developmental mathematics course grades of all participants, the researcher created and compiled a separate Excel spreadsheet and listed only participants’ campus identification numbers and their enrolled developmental mathematics course numbers. The spreadsheet was emailed to the institution’s decision support department 2 weeks after the conclusion of the spring 2013 semester. The decision support department returned the spreadsheet with the final course grades inputted to the researcher via a file transfer. Both Excel spreadsheets were merged to show all data. Treatment of Data The data collected from the brief demographic questionnaire, RMARS, and the final course grades were accessed and analyzed using the computer software, Statistical Package for the Social Sciences (SPSS) version 16.0. Various comparison groups were formed based on the level of the developmental mathematics program in which each student was enrolled by gender and age group. Descriptive statistics were obtained using frequencies and explore procedures to 58 test the assumption for the categorical and continuous variables. The descriptive statistics output answered all four research questions. The researcher calculated group means, standard deviation, range of scores, skewness, and kurtosis for each comparison group, and categorized each developmental mathematics course as low or high difficulty level. A oneway Analysis of Variance (ANOVA) was performed to determine whether significant differences existed within and between comparison groups with RMARS scores as the dependent variable and age, gender, and developmental mathematics level of difficulty as the independent variables. The researcher formulated four null hypotheses and tested them for statistical significance to determine whether each null hypothesis could be rejected. The ANOVA tested Hypotheses 13. Differences were reported at a confidence level of 95% (p < 0.05) to generate a range of practical significance and decrease the risk of Type I and II errors. The researcher also calculated the Levene’s Test for Equality of Variance and effect sizes. The researcher used a simple linear regression to determine the correlation between academic achievement and the presence of high levels of math anxiety among developmental mathematics students. Hypothesis 4 was analyzed using linear regression. The correlation coefficient (r) and the coefficient of determination (r2) were calculated to establish the relationship between academic success (final course grades) and level of math anxiety. The F statistic was also calculated during the regression test. Summary This study used a quantitative approach to explore the effects of math anxiety on the academic success of developmental mathematics students at a Texas community college. Participants included students who were enrolled in traditional 16week, facetoface developmental mathematics courses during the spring 2013 semester. The developmental 59 mathematics department provided the researcher access to survey their students and the institution’s decision support department provided access to the final course grades for participating students. The researcher analyzed the gender, age, and difficulty level of developmental course (spring 2013) data using ANOVA and linear regression tests. 60 Chapter 4 PRESENTATION OF FINDINGS The purpose of this study was to investigate the relationship between math anxiety and student achievement among developmental mathematics students. Participants in this study were enrolled in a developmental mathematics course at a Texas community college during the spring 2013 semester. Data collection included a demographic questionnaire, a math anxiety rating scale, and participants’ final course grades to determine the effect of math anxiety on the academic success of developmental mathematics students based on age, gender, and course difficulty level. Specifically this study attempted to determine the following: 1. The level of math anxiety in developmental mathematics students at a Texas community college based on age, gender, and developmental program level. 2. The effect of high and low levels of math anxiety on academic success in developmental mathematics courses. Descriptive Analysis The researcher used an Excel spreadsheet to compile the data by students’ campus identification numbers, gender, age group, developmental mathematics (DMAT) course, Revised Mathematics Anxiety Rating Scale (RMARS) score, and final course grades. The researcher used the Statistical Package for the Social Sciences (SPSS) version 16.0 to analyze all data. Descriptive data from the instruments describe the participant characteristics. Description of Participants Of the 185 survey packets returned, fully completed, and analyzed, 61.6% (N = 114) of the participants were female, 44.3% (N = 82) of the participants were between the ages of 18 and 22 years old, 24.9% (N = 46) of the participants were enrolled in the fourth level of 61 developmental mathematics (DMAT 0098), and 28.6% (N = 53) of the participants earned a C for their final course grade. Of the 185 participants, 41.1% (N = 76) were enrolled in a low difficulty level developmental course (DMAT 0066 or DMAT 0090), and 58.9% (N = 109) were enrolled in a high difficulty level developmental mathematics course (DMAT 0097, DMAT 0098, or DMAT 0099). Of all the participants, 70.3% (N = 132) successfully completed their developmental mathematics course with a letter grade of A, B, or C, indicated academic success (see Table 5). Table 5 Descriptive Statistics for Variables Variable Frequency Percent Gender Male 71 38.4 Female 114 61.6 Age Group 1822 82 44.3 2327 31 16.8 2832 28 15.1 3337 14 7.6 38+ 30 16.2 DMAT Course 0066 45 24.3 0090 31 16.8 0097 38 20.5 0098 46 24.9 0099 25 13.5 Final Course Grade A 38 20.5 B 41 22.2 C 53 28.6 D 7 3.8 F 32 17.3 W 14 7.6 Total 185 100.0 62 Plake and Parker (1982) developed the RMARS and indicated a median score of 72, meaning that participants with a score lower than 72 are categorized as having low math anxiety and those with a score of 72 or higher were categorized as having high math anxiety. These scoring criteria were also used in the current study. A total of 57.3% (N = 106) of students scored a 71 or lower on the RMARS, which indicated a low level of math anxiety. A total of 42.7% (N = 79) of students scored a 72 or higher on the RMARS, which indicated a high level of math anxiety. The mean score was 67.82 and standard deviation was 19.318; therefore, the RMARS scores were considered normally distributed (see Figure 1). Figure 1. RMARS total score. 63 Statistical Analysis of the Research Questions and Research Hypotheses Descriptive data were generated prior to conducting the oneway analysis of variance (ANOVA) tests in which the percentages, group mean, standard deviation, and 95% confidence interval were calculated for each comparison group and math anxiety level. Regression procedures were used to analyze data regarding the association between math anxiety and final course grade in a developmental mathematics course. This output allowed the researcher to answer the following research questions: 1. Does a difference exist in math anxiety among developmental mathematics students who take lower levels or higher levels of developmental mathematics courses? 2. Does a difference exist in math anxiety of developmental mathematics students between age groups (i.e., 1822, 2327, 2832, 3337, 38 and older)? 3. Does a difference exist in math anxiety among developmental mathematics students by gender? 4. Does a difference exist between math anxiety of developmental mathematics students and final course grades? Oneway ANOVA tests were conducted to determine the overall significance of each comparison group and math anxiety level. Regression procedures were used to analyze data regarding the association between math anxiety and final course grade in a developmental math course. This output allowed the researcher to test the following research hypotheses: 1. No significant differences exist in math anxiety of students who take higher difficulty levels of developmental mathematics courses compared to those who take lower difficulty levels of developmental mathematics courses. 64 2. No significant differences exist in the level of math anxiety of developmental mathematics students based on age. 3. No significant differences exist in the level of math anxiety of developmental mathematics students based on gender. 4. No significant relationship exists in overall developmental mathematics final course grades and level of math anxiety of developmental mathematics students. Research Question 1 Most participants were enrolled in a high difficulty developmental mathematics course (DMAT 0097, DMAT 0098, or DMAT 0099) and had low math anxiety. Of the 76 participants in a low difficulty level developmental mathematics course (DMAT 0066 or DMAT 0090), 52.7% (N = 40) had low levels of math anxiety and 47.3% (N = 36) in a low difficulty level developmental mathematics course had high levels of math anxiety. Of the 109 participants in a high difficulty level developmental mathematics course, 60.5% (N = 66) had low levels of math anxiety and 39.4% (N = 43) had high levels of math anxiety (see Figure 2). 65 Figure 2. RMARS anxiety level by course difficulty level. Dotted line indicates separation between low difficulty level and high difficulty level. Participants in low difficulty level courses had a mean of 71.87 and a standard deviation of 20.139 on the RMARS, and participants in high difficulty level courses had a mean of 65.00 and a standard deviation of 18.292 on the RMARS. Participants in developmental mathematics courses with a lower difficulty level had a higher mean RMARS anxiety score than did those in higher difficulty level developmental mathematics courses. Confidence intervals revealed the true mean for level of math anxiety for participants in low level difficulty developmental mathematics courses was between 67.27and 76.47. The true mean for level of math anxiety among participants in high difficulty developmental mathematics courses was between 61.53 and 68.47 (see Table 6). 31.6% 21.1% 22.0% 21.1% 17.4% 27.6% 19.7% 12.8% 21.1% 5.5% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% DMAT 0066 DMAT 0090 DMAT 0097 DMAT 0098 DMAT 0099 Percentage DMAT Course Anxiety by Course Low Anxiety High Anxiety66 Table 6 Mean and Standard Deviation of RMARS Anxiety Score by Course Difficulty Level Course Difficulty N M SD Low Difficulty 76 71.87 20.139 High Difficulty 109 65.00 18.292 Total 185 67.82 19.318 In analyzing the level of math anxiety among participants in developmental mathematics courses with low and high levels of difficulty, the Levene’s Test indicated homogeneity of variance between the two groups. The overall F statistic was significant, which signifies that a significant difference existed between the level of course difficulty [F(1,183) = 5.808, p = .017, η2 = .03]. The very small effect size shows that 3% of the variance in the RMARS anxiety scores could be explained by the difficulty level of the developmental mathematics course. Post hoc tests were not performed because there were fewer than th 
Date  2014 
Faculty Advisor  Justice, Madeline 
Committee Members 
Miller, Joyce Scott, Joyce A 
University Affiliation  Texas A&M UniversityCommerce 
Department  EdD Supervision, Curriculum, and InstructionHigher Education 
Degree Awarded  Ed.D. 
Pages  118 
Type  Text 
Format  
Language  eng 
Rights  All rights reserved. 



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