Effects of using manipulative materials to teach remedial algebra to community college students on achievement and attitudes towards mathematics

This dissertation derived hypotheses from the theories of Piaget, Bruner and Dienes regarding the effects of using Algebra Tiles and other manipulative materials to teach remedial algebra to community college students. The dependent variables measured were achievement and attitude towards mathematics. The Piagetian cognitive level of the students in the study was measured and used as a concomitant factor in the study.^ The population for the study was comprised of remedial algebra students at a large urban community college. The sample for the study consisted of 253 students enrolled in 10 sections of remedial algebra at three of the six campuses of the college. Pretests included administration of an achievement pre-measure, Aiken's Mathematics Attitude Inventory (MAI), and the Group Assessment of Logical Thinking (GALT). Posttest measures included a course final exam and a second administration of the MAI.^ The results of the GALT test revealed that 161 students (63.6%) were concrete operational, 65 (25.7%) were transitional, and 27 (10.7%) were formal operational. For the purpose of analyzing the data, the transitional and formal operational students were grouped together.^ Univariate factorial analyses of covariance ($\alpha$ =.05) were performed on the posttest of achievement (covariate = achievement pretest) and the MAI posttest (covariate = MAI pretest). The factors used in the analysis were method of teaching (manipulative vs. traditional) and cognitive level (concrete operational vs. transitional/formal operational).^ The analyses for achievement revealed a significant difference in favor of the manipulatives groups in the computations by campus. Significant differences were not noted in the analysis by individual instructors.^ The results for attitude towards mathematics showed a significant difference in favor of the manipulatives groups for the college-wide analysis and for one campus. The analysis by individual instructor was not significant. In addition, the college-wide analysis was significant in favor of the transitional/formal operational stage of cognitive development. However, support for this conclusion was not obtained in the analyses by campus or individual instructor. ^

The effect of instruction on the study behaviors and academic achievement of community college students

The purpose of this study was twofold. It was designed to determine (a) the efficacy of an intervention designed to increase the frequencies of appropriate study behaviors on the part of community college students who were preparing for academic mathematics activities and (b) whether any increase in appropriate study behavior frequency was accompanied by increased academic achievement in college preparatory mathematics classes. A total of 126 Miami Dade College students participated in this study. Two developmental (remedial) mathematics classes were randomly assigned as the experimental group, and two others were assigned as the control group. All students also took a College Survival (SLS) class. The Study Behavior Inventory (SBI) and the Computerized Placement Test (CPT) were administered to the four classes. The SBI was used as a pre- and post-test. The SLS curriculum and classroom time were the same for both groups. However, students in the treatment groups received instruction designed to increase the frequency of effective study behaviors associated with the three factors identified in the SBI, while the students in the control group participated in activities that did not emphasize study behaviors. A series of analysis of covariance procedures were used to analyze four hypotheses. The first three hypotheses proposed that students who were instructed in the use of appropriate study behaviors would score higher on the three factors of the Study Behavior Inventory than those who were not. The fourth hypothesis proposed that a greater proportion of mathematics students who were instructed in the use of appropriate study behaviors would receive a passing grade in their course than students who were in the control group. The four hypotheses were tested at the .05 level of significance. This study revealed that students who received instruction in appropriate study behaviors scored higher in the use of appropriate study behaviors and in mathematics achievement than students who did not. Additional research is needed to investigate whether these effects would persist over time, or be found in subjects other than mathematics.

Perceptions of underprepared community college students regarding their educational achievement

The purpose of this study was to understand the perceptions of underprepared college students who had participated in learning communities and who persisted to complete developmental classes and earned at least 30 college-level credit hours to graduate and the perceptions of their peers who had dropped out of college. The theories posed by Tinto, Astin, and Freire formed the framework for this case study. The 22 participants were graduates or transfer students now attending a public university, currently-enrolled sophomores, and students no longer enrolled at the time of the study. Semi-structured individual interviews and a group interview provided narrative data which were transcribed, coded, and analyzed to gain insights into the experiences and perspectives of the participants. The group interview provided a form of member checking to increase accuracy in interpreting themes. A peer reviewer provided feedback on the researcher’s data analysis procedures. The analysis yielded four themes and 14 sub-themes which captured the essence of the participants’ experiences. The pre-college characteristics/traits theme described the students’ internal values and attributes acquired prior to college. The external college support/community influence theme described the encouragement to attend college the students received from family, friends, and high school teachers. The social involvement theme described the students’ participation in campus activities and their interactions with other members of the campus. The academic integration theme described students’ use of campus resources and their contacts with the faculty. The persisters reported strong family and peer support, a sense of responsibility, appreciation for dedicated and caring faculty, and a belief that an education can be a liberatory means to achieve their goals. The non-persisters did not report having the same sense of purpose, goal orientation, determination, obligation to meet family expectations, peer support, campus involvement, positive faculty experiences, and time management skills. The researcher offers an emerging model for understanding factors associated with persistence and three recommendations for enhancing the academic experience of underprepared college students: (a) include a critical pedagogy perspective in coursework where possible, (b) integrate co-curricular activities with the academic disciplines, and (c) increase student-faculty interaction.

Extending the Theory of Planned Behavior in the exercise domain: A study of community college students in an urban multicultural setting

The purpose of this study was to assess the intention to exercise among ethnically and racially diverse community college students using the Theory of Planned Behavior (TPB). In addition to identifying the variables associated with motivation or intention of college students to engage in physical activity, this study tested the model of the Theory of Planned Behavior, asking: Does the TPB model explain intention to exercise among a racially/ethnically diverse group of college students? ^ The relevant variables were the TPB constructs (behavioral beliefs, normative beliefs, and control beliefs), which combined to form a measure of intention to exercise. Structural Equation Modeling was used to test the predictive power of the TPB constructs for predicting intention to exercise. Following procedures described by Ajzen (2002), the researcher developed a questionnaire encompassing the external variables of student demographics (age, gender, work status, student status, socio-economic status, access to exercise facilities, and past behavior), major constructs of the TPB, and two questions from the Godin Leisure Time Questionnaire (GLTQ; Godin & Shephard, 1985). Participants were students (N = 255) who enrolled in an on-campus wellness course at an urban community college. ^ The demographic profile of the sample revealed a racially/ethnically diverse study population. The original model that was used to reflect the TPB as developed by Ajzen was not supported by the data analyzed using SEM; however, a revised model that the researcher thought was theoretically a more accurate reflection of the causal relations between the TPB constructs was supported. The GLTQ questions were problematic for some students; those data could not be used in the modeling efforts. The GLTQ measure, however, revealed a significant correlation with intention to exercise (r = .27, p = .001). Post-hoc comparisons revealed significant differences in normative beliefs and attitude toward exercising behavior between Black students and Hispanic students. Compared to Black students, Hispanic students were more likely to (a) perceive “friends” as approving of them being physically active and (b) rate being physically active for 30 minutes per day as “beneficial”. No statistically significant difference was found among groups on overall intention to exercise. ^

Effects of student-faculty interactions on persistence of underprepared community college students

The high concentration of underprepared students in community colleges presents a challenge to educators, policy-makers, and researchers. All have pointed to low completion rates and caution that institutional practices and policy ought to focus on improving retention and graduation rates. However, a multitude of inhibiting factors limits the educational opportunities of underprepared community college students. Using Tinto's (1993) and Astin's (1999) models of student departure as the primary theoretical framework, as well as faculty mentoring as a strategy to impact student performance and retention, the purpose of this study was to determine whether a mentoring program designed to promote greater student-faculty interactions with underprepared community college students is predictive of higher retention for such students. While many studies have documented the positive effects of faculty mentoring with 4-year university students, very few have examined faculty mentoring with underprepared community college students (Campbell and Campbell, 1997; Nora & Crisp, 2007). In this study, the content of student-faculty interactions captured during the mentoring experience was operationalized into eight domains. Faculty members used a log to record their interactions with students. During interactions they tried to help students develop study skills, set goals, and manage their time. They also provided counseling, gave encouragement, nurtured confidence, secured financial aid/grants/scholarships, and helped students navigate their first semester at college. Logistic regression results showed that both frequency and content of faculty interactions were important predictors of retention. Students with high levels of faculty interactions in the area of educational planning and personal/family concerns were more likely to persist. Those with high levels of interactions in time-management and academic concerns were less likely to persist. Interactions that focused on students' poor grades, unpreparedness for class, or excessive absences were predictive of dropping out. Those that focused on developing a program of study, creating a road map to completion, or students' self-perceptions, feelings of self-efficacy, and personal control were predictive of persistence.

The mathematics anxiety of bilingual community college students

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument. Bilingual and monolingual students reported comparable mean AMAS scores (20.6 and 20.7, respectively) and comparable proportions of math anxious individuals (50% and 48%, respectively). Factor analysis of AMAS scores, using principal component analysis by varimax rotation, yielded similar two-factor structures for both populations -- assessment and learning content -- accounting for 65.6% of the trace for bilingual AMAS scores. Statistically significant predictor variables for levels of math anxiety for the bilingual participants included (a) preparatory course enrollment (β = .236, p = .041) with those enrolled in prior preparatory courses scoring higher, (b) education major (β = .285, p = .018) with education majors scoring higher, and (c) business major (β = .252, p = .032) with business majors scoring higher. One statistically significant predictor variable emerged for monolingual students, gender (β = -.085, p = .001) with females ranking higher. Age, income, race, ethnicity, U.S. origin, science or health science majors did not emerge as statistically significant predictor variables for either group.^ Similarities between monolingual and bilingual participants included statistically significant negative linear correlations between AMAS scores and course grades for both bilingual (r = -.178, p = .017) and monolingual participants (r = -.203, p = .001). Differences included a statistically significant linear correlation between AMAS scores and final exam grades for monolingual participants only (r = -.253, p < .0009) despite no statistically significant difference in the strength the linear relationship of the AMAS scores and the final exam scores between groups, z = 1.35, p = .1756.^ The findings show that bilingual and monolingual students report math anxiety similarly and that math anxiety has similar associations with performance measures, despite differences between predictor variables. One of the first studies on the math anxiety of bilingual community college students, the results suggest recommendations for researchers and practitioners.^

The Theory of Planned Behavior and Ethnically Diverse Community College Students and Their Intentions to Exercise: A Preliminary Analysis

Although regular exercise is the key to a healthy lifestyle, college students are insufficiently active to maintain good health. Motivations to exercise may vary among different ethnic groups. The results of a pilot study using the Theory of Planned Behavior (Gordon, 2008) showed that ethnically diverse college students can rate their beliefs (behavioral, social, and cognitive) pertaining to physical activity.

A comparison of the self -esteem of freshman community college students enrolled in remedial and regular academic programs

This study examined relationships among self-esteem, remedial academic placement, ethnicity, gender, and enrollment status, using a nonexperimental, ex post facto research design. Participants were 113 freshman community college students attending Broward Community College in South Florida. The Coopersmith Self-Esteem Inventory (Adult Form) was used to measure the self-esteem of the participants. The results of this study indicate a significant difference between the mean self-esteem levels of the students enrolled in remedial academic classes (m = 66.08) and those enrolled in regular academic classes (m = 73.97). An independent samples t-test at the.05 significance level indicated that regular students were found to have higher levels of self-esteem than remedial students (t(112) = 2.14, p =.03). Two-way analyses of variance of placement status by ethnicity, of placement status by gender, and of placement status by enrollment status on self-esteem were also conducted. Interactions between placement status and the other factors were not found to be significant (p $>$.05). However, a significant main effect for ethnicity was found (p $<$.05). The results indicated that white students had a mean self-esteem level (m = 75.30) significantly higher than non-white students (m = 62.76, p =.002).^ The results of this study suggests that many community college students have problems related to self-esteem. Further research should be conducted on remedial and minority college students using a larger sample size and additional variables, such as socio-economic status. ^

Effects of student-faculty interactions on persistence of underprepared community college students.

The high concentration of underprepared students in community colleges presents a challenge to educators, policy-makers, and researchers. All have pointed to low completion rates and caution that institutional practices and policy ought to focus on improving retention and graduation rates. However, a multitude of inhibiting factors limits the educational opportunities of underprepared community college students. Using Tinto's (1993) and Astin's (1999) models of student departure as the primary theoretical framework, as well as faculty mentoring as a strategy to impact student performance and retention, the purpose of this study was to determine whether a mentoring program designed to promote greater student-faculty interactions with underprepared community college students is predictive of higher retention for such students. While many studies have documented the positive effects of faculty mentoring with 4-year university students, very few have examined faculty mentoring with underprepared community college students (Campbell and Campbell, 1997; Nora & Crisp, 2007). In this study, the content of student-faculty interactions captured during the mentoring experience was operationalized into eight domains. Faculty members used a log to record their interactions with students. During interactions they tried to help students develop study skills, set goals, and manage their time. They also provided counseling, gave encouragement, nurtured confidence, secured financial aid/grants/scholarships, and helped students navigate their first semester at college. Logistic regression results showed that both frequency and content of faculty interactions were important predictors of retention. Students with high levels of faculty interactions in the area of educational planning and personal/family concerns were more likely to persist. Those with high levels of interactions in time-management and academic concerns were less likely to persist. Interactions that focused on students' poor grades, unpreparedness for class, or excessive absences were predictive of dropping out. Those that focused on developing a program of study, creating a road map to completion, or students' self-perceptions, feelings of self-efficacy, and personal control were predictive of persistence.

Perceptions of Underprepared Community College Students regarding their Educational Achievement

The purpose of this study was to understand the perceptions of underprepared college students who had participated in learning communities and who persisted to complete developmental classes and earned at least 30 college-level credit hours to graduate and the perceptions of their peers who had dropped out of college. The theories posed by Tinto, Astin, and Freire formed the framework for this case study. The 22 participants were graduates or transfer students now attending a public university, currently-enrolled sophomores, and students no longer enrolled at the time of the study. Semi-structured individual interviews and a group interview provided narrative data which were transcribed, coded, and analyzed to gain insights into the experiences and perspectives of the participants. The group interview provided a form of member checking to increase accuracy in interpreting themes. A peer reviewer provided feedback on the researcher’s data analysis procedures. The analysis yielded four themes and 14 sub-themes which captured the essence of the participants’ experiences. The pre-college characteristics/traits theme described the students’ internal values and attributes acquired prior to college. The external college support/community influence theme described the encouragement to attend college the students received from family, friends, and high school teachers. The social involvement theme described the students’ participation in campus activities and their interactions with other members of the campus. The academic integration theme described students’ use of campus resources and their contacts with the faculty. The persisters reported strong family and peer support, a sense of responsibility, appreciation for dedicated and caring faculty, and a belief that an education can be a liberatory means to achieve their goals. The non-persisters did not report having the same sense of purpose, goal orientation, determination, obligation to meet family expectations, peer support, campus involvement, positive faculty experiences, and time management skills. The researcher offers an emerging model for understanding factors associated with persistence and three recommendations for enhancing the academic experience of underprepared college students: (a) include a critical pedagogy perspective in coursework where possible, (b) integrate co-curricular activities with the academic disciplines, and (c) increase student-faculty interaction.

Extending the Theory of Planned Behavior in the Exercise Domain: A Study of Community College Students in an Urban Multicultural Setting

The purpose of this study was to assess the intention to exercise among ethnically and racially diverse community college students using the Theory of Planned Behavior (TPB). In addition to identifying the variables associated with motivation or intention of college students to engage in physical activity, this study tested the model of the Theory of Planned Behavior, asking: Does the TPB model explain intention to exercise among a racially/ethnically diverse group of college students? The relevant variables were the TPB constructs (behavioral beliefs, normative beliefs, and control beliefs), which combined to form a measure of intention to exercise. Structural Equation Modeling was used to test the predictive power of the TPB constructs for predicting intention to exercise. Following procedures described by Ajzen (2002), the researcher developed a questionnaire encompassing the external variables of student demographics (age, gender, work status, student status, socio-economic status, access to exercise facilities, and past behavior), major constructs of the TPB, and two questions from the Godin Leisure Time Questionnaire (GLTQ; Godin & Shephard, 1985). Participants were students (N = 255) who enrolled in an on-campus wellness course at an urban community college. The demographic profile of the sample revealed a racially/ethnically diverse study population. The original model that was used to reflect the TPB as developed by Ajzen was not supported by the data analyzed using SEM; however, a revised model that the researcher thought was theoretically a more accurate reflection of the causal relations between the TPB constructs was supported. The GLTQ questions were problematic for some students; those data could not be used in the modeling efforts. The GLTQ measure, however, revealed a significant correlation with intention to exercise (r = .27, p = .001). Post-hoc comparisons revealed significant differences in normative beliefs and attitude toward exercising behavior between Black students and Hispanic students. Compared to Black students, Hispanic students were more likely to (a) perceive “friends” as approving of them being physically active and (b) rate being physically active for 30 minutes per day as “beneficial”. No statistically significant difference was found among groups on overall intention to exercise.

The Mathematics Anxiety of Bilingual Community College Students

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument. Bilingual and monolingual students reported comparable mean AMAS scores (20.6 and 20.7, respectively) and comparable proportions of math anxious individuals (50% and 48%, respectively). Factor analysis of AMAS scores, using principal component analysis by varimax rotation, yielded similar two-factor structures for both populations -- assessment and learning content -- accounting for 65.6% of the trace for bilingual AMAS scores. Statistically significant predictor variables for levels of math anxiety for the bilingual participants included (a) preparatory course enrollment (β = .236, p = .041) with those enrolled in prior preparatory courses scoring higher, (b) education major (β = .285, p = .018) with education majors scoring higher, and (c) business major (β = .252, p = .032) with business majors scoring higher. One statistically significant predictor variable emerged for monolingual students, gender (β = -.085, p = .001) with females ranking higher. Age, income, race, ethnicity, U.S. origin, science or health science majors did not emerge as statistically significant predictor variables for either group. Similarities between monolingual and bilingual participants included statistically significant negative linear correlations between AMAS scores and course grades for both bilingual (r = -.178, p = .017) and monolingual participants (r = -.203, p = .001). Differences included a statistically significant linear correlation between AMAS scores and final exam grades for monolingual participants only (r = -.253, p < .0009) despite no statistically significant difference in the strength the linear relationship of the AMAS scores and the final exam scores between groups, z = 1.35, p = .1756. The findings show that bilingual and monolingual students report math anxiety similarly and that math anxiety has similar associations with performance measures, despite differences between predictor variables. One of the first studies on the math anxiety of bilingual community college students, the results suggest recommendations for researchers and practitioners.

A retrospective-longitudinal examination of the relationship between apportionment of seat time in community-college algebra courses and student academic performance

During the past decade, there has been a dramatic increase by postsecondary institutions in providing academic programs and course offerings in a multitude of formats and venues (Biemiller, 2009; Kucsera & Zimmaro, 2010; Lang, 2009; Mangan, 2008). Strategies pertaining to reapportionment of course-delivery seat time have been a major facet of these institutional initiatives; most notably, within many open-door 2-year colleges. Often, these enrollment-management decisions are driven by the desire to increase market-share, optimize the usage of finite facility capacity, and contain costs, especially during these economically turbulent times. So, while enrollments have surged to the point where nearly one in three 18-to-24 year-old U.S. undergraduates are community college students (Pew Research Center, 2009), graduation rates, on average, still remain distressingly low (Complete College America, 2011). Among the learning-theory constructs related to seat-time reapportionment efforts is the cognitive phenomenon commonly referred to as the spacing effect, the degree to which learning is enhanced by a series of shorter, separated sessions as opposed to fewer, more massed episodes. This ex post facto study explored whether seat time in a postsecondary developmental-level algebra course is significantly related to: course success; course-enrollment persistence; and, longitudinally, the time to successfully complete a general-education-level mathematics course. Hierarchical logistic regression and discrete-time survival analysis were used to perform a multi-level, multivariable analysis of a student cohort (N = 3,284) enrolled at a large, multi-campus, urban community college. The subjects were retrospectively tracked over a 2-year longitudinal period. The study found that students in long seat-time classes tended to withdraw earlier and more often than did their peers in short seat-time classes (p < .05). Additionally, a model comprised of nine statistically significant covariates (all with p-values less than .01) was constructed. However, no longitudinal seat-time group differences were detected nor was there sufficient statistical evidence to conclude that seat time was predictive of developmental-level course success. A principal aim of this study was to demonstrate—to educational leaders, researchers, and institutional-research/business-intelligence professionals—the advantages and computational practicability of survival analysis, an underused but more powerful way to investigate changes in students over time.

The relationship between the secondary mathematics curriculum, college persistence, and success at an urban community college

According to Venezia, Kirst, and Antonio (2003) and Barth’s 2002 Thinking K16 Ticket to Nowhere report, the disconnect between K-12 and postsecondary education was a contributing factor to high attrition rates. Since mathematics emerged as a primary concern for college readiness, Barth (2002) called for improving student transitions from K-12 to postsecondary institutions through the use of state or local data. The purpose of the present study was to analyze mathematics course-taking patterns of secondary students in a local context and to evaluate high school characteristics in order to explore their relationships with Associate degree attainment or continuous enrollment at an urban community college. Also, this study extended a national study conducted by Clifford Adelman (The Toolbox Revisited, 2006) as it specifically focused on community college students that were not included his study. Furthermore, this study used the theoretical framework that human capital, social capital, and cultural capital influence habitus—an individual’s or a group’s learned inclination to behave within the parameters of the imposed prevailing culture and norms. Specifically, the school embedded culture as it relates to tracking worked as a reproduction tool of ultimate benefit for the privileged group (Oakes, 1994). ^ Using multilevel analysis, this ex post facto study examined non-causal relationships between math course-taking patterns and college persistence of public high school graduates who enrolled at the local community college for up to 6 years. One school-level variable (percent of racial/ethnic minorities) and 7 student-level variables (community college math proportion, remedial math attempts, race, gender, first-year credits earned, socioeconomic status, and summer credits earned) emerged as predictors for college persistence. Study results indicated that students who enter higher education at the community college may have had lower opportunities to learn and therefore needed higher levels of remediation, which was shown to detract students from degree completion. Community college leaders are called to partner with local high schools with high percentages of racial/ethnic minorities to design academic programs aimed at improving the academic preparation of high school students in mathematics and promote student engagement during the first year and summers of college. ^

A Retrospective-Longitudinal Examination of the Relationship between Apportionment of Seat Time in Community-College Algebra Courses and Student Academic Performance

During the past decade, there has been a dramatic increase by postsecondary institutions in providing academic programs and course offerings in a multitude of formats and venues (Biemiller, 2009; Kucsera & Zimmaro, 2010; Lang, 2009; Mangan, 2008). Strategies pertaining to reapportionment of course-delivery seat time have been a major facet of these institutional initiatives; most notably, within many open-door 2-year colleges. Often, these enrollment-management decisions are driven by the desire to increase market-share, optimize the usage of finite facility capacity, and contain costs, especially during these economically turbulent times. So, while enrollments have surged to the point where nearly one in three 18-to-24 year-old U.S. undergraduates are community college students (Pew Research Center, 2009), graduation rates, on average, still remain distressingly low (Complete College America, 2011). Among the learning-theory constructs related to seat-time reapportionment efforts is the cognitive phenomenon commonly referred to as the spacing effect, the degree to which learning is enhanced by a series of shorter, separated sessions as opposed to fewer, more massed episodes. This ex post facto study explored whether seat time in a postsecondary developmental-level algebra course is significantly related to: course success; course-enrollment persistence; and, longitudinally, the time to successfully complete a general-education-level mathematics course. Hierarchical logistic regression and discrete-time survival analysis were used to perform a multi-level, multivariable analysis of a student cohort (N = 3,284) enrolled at a large, multi-campus, urban community college. The subjects were retrospectively tracked over a 2-year longitudinal period. The study found that students in long seat-time classes tended to withdraw earlier and more often than did their peers in short seat-time classes (p < .05). Additionally, a model comprised of nine statistically significant covariates (all with p-values less than .01) was constructed. However, no longitudinal seat-time group differences were detected nor was there sufficient statistical evidence to conclude that seat time was predictive of developmental-level course success. A principal aim of this study was to demonstrate—to educational leaders, researchers, and institutional-research/business-intelligence professionals—the advantages and computational practicability of survival analysis, an underused but more powerful way to investigate changes in students over time.