This study explores adult returning students' mathematical experience and ways of thinking prior to enrolling in a community college arithmetic review course. It further examines one student's experience of the course. The first part of the study documents everyday activities adult students perceive as mathematical using Bishop's pan-cultural mathematical activities (Bishop, 1994), and queries students' prior experience with mathematics in school. The second part examines students' ways of thinking about proportion prior to instruction, using a framework developed from previous research (e.g., Lamon, 1993). The third part of the study examines the interaction between informal ways of thinking about mathematics that adult students bring to school and the mathematics they encounter in the classroom. Findings include: (1) Adult students view a variety of activities from their everyday lives as mathematical, (2) adult students' reasoning about proportional situations varies along a developmental trajectory described in previous research on proportional reasoning conducted with younger students, and (3) one student's experience in the arithmetic review course illustrates that she typically suppressed contextual ways of reasoning about problems she brought to the course and, when she did share prior experience, it was not leveraged to support the development of her and other students' mathematical understanding. These findings suggest that adult students' experience of everyday mathematics and ways of thinking about proportion should be the foundation that support students as they build upon informal ways of thinking toward the more formal ways of reasoning expected in school.

Although the importance of problem solving as an essential component of mathematics learning and doing has consistently been recognized, recent research has only just begun to identify and describe the complex set of variables influencing the endeavor. Therefore, the aim of this study was to empirically investigate the relationships between several of these variables: mathematical expertise (as measured by the advanced nature of the mathematics courses students have taken, and are enrolled in), the cognitive ability known as inhibitory control (the ability to inhibit or suppress an immediate response to a stimulus, and engage in deeper, more reflective thought), and facets of college students’ psychoeducational profile (e.g., academic habits of mind, future orientation, self-limiting beliefs), which provide information about the nature of college students’ learning and development. In this study, one hundred and thirty college students, enrolled in different levels of mathematics courses (from introductory courses to major courses in mathematics) were administered a modified version of the Cognitive Reflection Test (an instrument designed to measure the ability to activate one’s inhibitory control capacities) and a survey instrument designed to measure domain-general and mathematics-specific psychoeducational facets of their academic profile. Information about membership to other subgroups (e.g., gender, academic major, mathematics courses taken in high school) helped to further contextualize the findings. The majority of all participants did not correctly solve any of the problems of the modified version of the Cognitive Reflection Test which required inhibitory control. However, those with a greater level of mathematical expertise (i.e., those taking more advanced mathematical courses) performed significantly better than their peers on these problems and exhibited more desirable responses on the psychoeducational survey instrument. Responses to items of the survey instrument that measured behaviors, habits, and experiences that limit students in their conception of, approach to, and engagement with mathematics indicate the presence of a psychoeducational facet specific to mathematics that cannot be sufficiently explained by domain-general facets also under measure. These limiting characteristics related to mathematics were also significantly related to students’ performance on the modified version of the Cognitive Reflection Test, indicating a potential relationship between such characteristics and problem solving success on inhibitory control tasks. Considering the measures of mathematical expertise utilized in the current study, the social nature of mathematics learning may help explain the development of both inhibitory control ability and limiting beliefs in mathematics. The current study extended the methods utilized in previous research to examine the relationships between inhibitory control and mathematical expertise in college students while also investigating these in relation to particular psychoeducational variables known to influence learning and development of college students. The findings of this small-scale empirical study provide a modest step forward in these areas of research by providing another lens through which to view several phenomena already being extensively investigated by other researchers.

This study was an exploration into the effects of four categories of extra-student variables: high school performance, demographic characteristics, Myers-Briggs personality preferences and mathematics attitudes on three measures of college mathematics achievement (a Problem-Solving Test, an Algebra Skills Final Examination and course grade for all seven classes of 175 undergraduate students taking Pre-Calculus I Fall semester 1993). High school performance explained the most variation for all measures of mathematics achievement. Demographic characteristics and mathematics attitudes do not significantly influence any measure of mathematics achievement. The Myers-Briggs Type Indicator (MBTI) preference Extravert versus Intraverts (E versus 1) was a significant predictor for the Problem-Solving Test; the Judging versus Perception a versus P) preference was a significant predictor for the Algebra Skills Final Examination, and both E versus I and J versus P were predictors for the course grade. An experimental design was used to explore four classroom variables--3 class times, 2 instructional settings, MBTI E versus I and J versus P-- in six classes. Students taking 8:00 classes averaged 9 points lower than students taking 10:00 classes and 11 points lower than students taking 1:00 classes for all measures of mathematics achievement. There was no significant difference for the two instructional settings--cooperative learning or traditional lecture--for any measure of mathematics achievement. Students who were Introverted averaged 8 points higher on the Problem-Solving Test. Students who had the Judging preference averaged 11 points higher on the Algebra Skills Final Examination and 5 points higher for the course grade. There was a significant interaction (p<.01) for the Problem-Solving Test of class Time x instructional setting caused by the poor performance of the 8:00 Cooperative Learning class. The interaction of E versus I x J versus P or the EIJP learning styles was significant (p<.05) for the Algebra Skills Final Examination and course grade. The students with the IJ learning style averaged 13 to 20 points higher for scores on the Algebra Skills Final Examination and 11 points higher for scores on the course grade than students with the other three learning styles--EP, EJ and IP. / Ph. D.

Non-math majors enrolled in lower-division math courses at an urban university were surveyed on their math attitudes, coping behaviors, and math anxiety (MATHANX). The Revised Ways of Coping Checklist (RWCC), Revised Math Anxiety Rating Scale, and other questions were presented to 30 men and 32 women. Hierarchical regressions showed that after controlling for attitudinal covariates, emotion-focused coping behaviors (EMOTFOC) were strongly associated with MATHANX (F(5,54)=18.66, 12 < .0001), but problem-focused coping behaviors (PROBFOC) were not. The RWCC subscale most highly correlated with MATHANX was Wishful Thinking (r = .70, p < .0001). Ss were then dichotomized on PROBFOC and EMOTFOC, providing four behavioral groups. An ANCOVA controlling for attitudinal covariates showed behavioral group membership significant with respect to MATHANX (F(3,58)=6.07, p < .001), and an ANOVA revealed that students who reported high EMOTFOC coupled with low PROBFOC experienced the greatest MATHANX (,E(3,58) = 12.66, p < .0001). Males and females reported virtually identical MATHANX (M=36.30 for males, 36.44 for females), and the only significant gender difference was for avoidance coping, which was used more by males (F(1,60) = 5.43, p < .03]. Results from this study suggest that fewer gender differences may exist in MATHANX and coping than have been found in the past. Additionally, this study identifies the need for future research to determine whether EMOTFOC is the behavioral component, or one of the determinants, of math anxiety.

D. Tech. Education / The study reports on a teaching strategy for active learning using clicker mobile technology with mathematics students. The study focuses on the large class groups, poor class attendance and lack of student participation. It also focuses on lack of immediate feedback on student learning throughout the lesson and the insufficient time for regular formative assessment.

D. Tech. Education / The aim of the study is to explore the extent to which a University of Technology prepares pre-service teachers to teach the school Mathematics and Technology curriculum in South Africa. The study employed a combination of a qualitative method and case study approach. Participants were ten (10) Mathematics and nine (9) Technology pre-service teachers, totaling nineteen (19) participants. Data collection were done through an exploratory approach of document analyses, semi-structured interviews, and non-participant observations. The study was guided by two (2) conceptual frameworks, that is, Knowledge-Based for Teaching (Shulman, 1987) and the 7E instructional model from Eisenkraft (2003). This study found that Mathematics and Technology teacher training were not comprehensive enough to prepare pre-service teachers to teach the South African school curriculum.

The student success rates for three developmental mathematics courses (prealgebra, elementary algebra, and intermediate algebra) taught through four instructional methods (lecture, personalized system of instruction [PSI], hybrid, and online) were examined. The sample consisted of 9,211 students enrolled in a large Texas community college from fall 2009 through spring 2011. Student success was defined as a grade of C or better. Chi-square tests were used to compare the three developmental mathematics courses success rates. Statistically significant differences in student success were found between all four methods of instruction for all three mathematics courses (prealgebra: χ2 [df = 3] = 107.90, p < 0.001; elementary algebra: χ2 [df = 3] = 88.39, p < 0.001; intermediate algebra χ2 [df = 3] = 254.18, p < 0.001). Binary logistic regression modeling was used to determine to what extent age, gender, ethnicity, residency, Pell eligibility and mode of instruction accounted for the community college students’ course success for each of the three developmental mathematics courses. For prealgebra, the independent variables of gender, race, age, residency, and mode of instruction made statistically significant contributions to the model (χ2 [df = 14, n = 1,743] = 159.196, p < .001; Nagelkerke R2 = .119), with greater success among female, White, younger, out of country students taking the course through lecture. For elementary algebra, the independent variables of race, age, residency, and mode of instruction made statistically significant contributions to the logistic regression model (χ2 [df = 14, n = 2,731] = 816.223, p < .001; Nagelkerke R2 = .358), with greater success among , younger, out of country students taking the course through lecture, hybrid or PSI. For intermediate algebra, only race and Pell eligibility made a statistically significant contribution to the logistic regression, with greater success among White, Pell-eligible students, and mode of instruction did not contribute significantly to the model (χ2 [df = 14, n = 3,936] = 53.992, p < .001; Nagelkerke R2 = .019). Recommendations for research and implications for practice are provided.

Almost twenty-one percent of the United States population spoke a language other than English in 2011. Furthermore, there has been a dramatic increase in the enrollment of students of Hispanic and other ethnic backgrounds in U.S. post-secondary institutions between 1976 and 2013 (from 4% to 16%) (National Center for Education Statistics NCES, 2016). Until now, no systematic research has focused on the differential effects of selfefficacy on academic achievement in monolingual and bilingual undergraduate college students. The present study aimed to investigate this relationship, as well as contribute additional insight on whether the academic self-efficacy of monolingual and bilingual undergraduate college students plays a role in their academic success specifically in science and math courses. Additionally, the findings of this research study were expected to provide data to inform the development of educational programs that might specifically target monolinguals or bilinguals in enhancing students’ self-efficacy. Seven instructors of foundational undergraduate science courses and math courses at a southeastern university agreed to contribute to the study by asking their students for their voluntary participation in the data collection. A total of 361 students participated in the study. Overall, 256 (70.9%) participants reported being monolingual and 105 (29.1%) reported being bilingual; 335 (92.8%) students were enrolled in science courses and 26 (7.2%) were registered in math courses; 237 (65.7%) were female students and 124 (34.3%) were male. Demographics, self-efficacy, and sociolinguistic data were collected using the Self-Efficacy Research Study Online Questionnaire. Final science and math grades were also collected from the instructors at the end of the semester for all students who volunteered to participate in the study. The findings of this research study revealed that the self-efficacy levels of undergraduate college students in science and math predict their academic achievement in these subjects. They also showed that the self-efficacy levels of bilingual participants are higher than those of their monolingual counterparts. Findings also indicated that when the relationship between final grade and self-efficacy was examined separately in each linguistic group the correlation was significant and positive for monolinguals. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert consensus protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students answered open-ended versions of the question set. The questions were converted to multiple-choice format from these responses and disseminated to an additional 476 students over two rounds. Through follow-up interviews intended for validation, and test analysis processes, the questions were refined to best target conceptions and strengthen validity measures. The GCI consists of seventeen questions, each targeting a different concept in introductory group theory. The results from this study are broken into three papers. The first paper reports on the methodology for creating the GCI with the goal of providing a model for building valid concept inventories. The second paper provides replication results and critiques of previous studies by leveraging three GCI questions (on cyclic groups, subgroups, and isomorphism) that have been adapted from prior studies. The final paper introduces the GCI for use by instructors and mathematics departments with emphasis on how it can be leveraged to investigate their students' understanding of group theory concepts. Through careful creation and extensive field-testing, the GCI has been shown to be a meaningful instrument with powerful ability to explore student understanding around group theory concepts at the large-scale.

M.Ed. / South Africa is faced with the challenge of reconstruction and social recovery having held its .first democratic elections in 1994. Education was central to the discursive process of racial and cultural segregation (Baxen & Soudien 1999: 131). After the 1994 elections the whole education dispensation in South Africa was bound to change dramatically. This is a logical deduction since new role players will always have a new vision, in order to spell out the new roads to be embarked upon. Jansen (1999:145) puts it as follows: "...OBE as primarily a political response to apartheid schooling rather than one which is concerned with the modalities of change at classroom level". A multitude of changes have taken place in the interim. One of the major changes was legislation that provided for the establishment of SAQA (South African Qualifications Authority). The Act was promulgated in 1996, Act 58 of 1996. The main objective of SAQA is to provide for the development and implementation of the NQF (National Qualifications Framework). The NQF brought about a new structure regarding bands of education and levels of qualifications within the said bands. (Refer to diagram 1). According to Pretorius (1998:4) the framework of the NQF makes provision for life-long learning opportunities and levels of qualifications nationally agreed upon.