published_or_final_version / Education / Master / Master of Education

published_or_final_version / abstract / Education / Master / Master of Education

published_or_final_version / abstract / Education / Master / Master of Education

The study explored the relationship between student academic performance in an exit-level, developmental mathematics course and subsequent academic performance in a college-level mathematics course. Using an ex post facto research design, the study focused specifically on the influence of three sets of factors: (a) demographic characteristics, (b) "stopping-out," and (c) the developmental course. The criterion variables were college-level performance, defined in terms of the student's course grade, and college-level persistence, defined in terms of whether or not the student officially withdrew from the course. A convenience sample of 824 community college students who had completed both the exit-level developmental mathematics course and the entry-level college course during a three-year period from fall 1989 to summer 1992 was used for the data set; the students in the set were shown to be similar to several populations of developmental students. Discriminant function analysis indicated that the data supported the hypotheses. The discriminant function was calibrated on 364 cases randomly selected from the data set; the remainder of the cases were used to cross-validate the results. Cross-validated correct classification rates of 76.74% for academic success and 81.09% for persistence were obtained. The major conclusions of the study were: (1) Developmental course performance is a significant discriminator of college-level mathematics performance and persistence. (2) The length of time a student allows to pass between exiting the developmental course and entering the college-level course is a negatively related discriminator of both college-level performance and persistence. (3) Student age is a positively related discriminator of college-level mathematics performance. (4) The number of attempts at the developmental course is a negatively related discriminator of persistence. (5) African American completers of developmental mathematics appear to be more likely to withdraw from entry-level college mathematics than developmental completers in other ethnic groups. (6) Poor performance in exit-level developmental mathematics greatly increases the risk of failure or attrition for students in entry-level college mathematics. The implications of these results and those of several post hoc analyses were discussed in terms of their theoretical and applied contributions, the limitations of the study were detailed, and suggestions made for future research. / text

This study considered spontaneous versus feedback induced changes in probability strategies using grouped trials of two-choice problems. Third and sixth grade Anglo and Apache children were the focus of computer assisted instruction and diagnostics designed to maximize performance and measure understanding of probability concepts. Feedback, using indeterminate problems directed at specific strategies, in combination with a large problem set permitted examination of response latency and hypothesis alternation. Explicit training, in the form of computer based tutorials administered feedback as: (a) correctness and frequency information, (b) mathematical solutions, or (c) in a graphical format, targeted by weaknesses in the prevailing strategy. The tutorials encouraged an optimal proportional strategy and sought to affect the memorial accessibility or availability of information through the vividness of presentation. As the subject's response selection was based on the query to select for the best chance of winning, each bucket of the two-choice bucket problems was coded as containing target or winner (W) balls and distractor or loser (L) balls. Third and sixth grade subjects came to the task with position oriented strategies focusing on the winner or target elements. The strategies' sophistication was related to age with older children displaying less confusion and using proportional reasoning to a greater extent than the third grade children. Following the tutorial, the subjects displayed a marked decrease in winners strategies deferring instead to strategies focusing on both the winners and losers; however, there was a general tendency to return to the simpler strategies over the course of the posttest. These simpler strategies provided the fastest response latencies within this study. Posttest results indicated that both third and sixth grade subjects had made comparable gains in the use of strategies addressing both winners and losers. Based on the results of a long-term written test, sixth grade subjects appeared better able to retain or apply the knowledge that both winners and losers must be considered when addressing the two-choice bucket problems. Yet, for younger children, knowledge of these sophisticated strategies did not necessarily support generalization to other mathematical skills such as fraction understanding.

The Outreach Project of the University of the Western Cape has since 1982 through various computer supported services been assisting grade 12 mathematics learners and educators at previously disadvantaged Western Cape high schools. This thesis described and appraised the MICSES2000 program of the Outreach Program, the latest innovative computer enhancing service to schools, with respect to its implementation, perceived and achieved programs by participating educators.

<p>This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.</p>

The primary purpose of this study was to determine if the implementation of an intervention involving teachers' use of children's literature, related storybook manipulatives, and a scaffolding (LMS) approach to learning would improve preschool children's mathematics test scores. Additionally, the LMS approach was examined to determine whether teachers' perceptions of their effectiveness in mathematics instruction changed from the beginning to the end of the study. The subjects of the study included 60 preschool-aged children and six teachers from two child care centers. The preschool teachers participated in either a control or experimental condition (the LMS approach) in their daily mathematics instruction with their preschool children. The researcher tested the children using the Test of Early Mathematics Ability and an abbreviated version of the Stanford-Binet Intelligence Scale. The study was based on two main research questions. The first question asked if there was a difference in the Test of Early Mathematics Ability total posttest scores between children in the literature-manipulatives-scaffolding intervention group and children in the control group after assuring equivalency of the two groups. The second question addressed if preschool teachers believed they were more effective in their mathematics instruction after implementing the LMS approach with young children. The answer to the first research question was that there was no statistically significant difference in the Test of Early Mathematics Ability total posttest scores between children in the literature-manipulatives-scaffolding group and children in the control group. However, the answer to the second question was that preschool teachers believed they were more effective in their mathematics instruction after implementing the LMS approach with young children. Recommendations for future research on early childhood mathematics include the investigation of preschool children's ability, achievement, and interest in mathematics; teachers' use of mathematics scaffolding techniques; and longitudinal mathematics interventions beginning during the preschool years.

The purpose of this study was to determine the relationship between sixth grade students' academic achievement levels in math and their perceptions of school climate. Student characteristics of socioeconomic status and gender were used to identify groups for the purpose of data analysis. Data was gathered using the five independent variables of the My Class Inventory (satisfaction, friction, competitiveness, difficulty, and cohesiveness) and the dependent variable of the Stanford Achievement Total Math scores. The results of the data collection were tested using a Pearson product-moment analysis and a backward multiple regression analysis. A univariate analysis of variance was also used to compare the five independent variables of the My Class Inventory as well as to compare socioeconomic status and gender with the Stanford Achievement Total Math scores. The schools selected for this study were from a city in Texas with a population of approximately 100,000. The sample consisted of 262 sixth grade mathematics students. The findings of this study are as follows: (a) The Pearson product-moment correlation analysis revealed little, if any, correlation for any of the five subscale predictor variables; (b) the multiple regression analysis revealed that all five classroom climate indicators combined together could explain only 10.5% of the variance in mathematics achievement; (c) the univariate analysis of variance revealed that there is a significant relationship between the climate factors of friction and difficulty when compared to mathematics achievement; and (d) the univariate analysis of variance also revealed that mathematics achievement scores vary significantly as a function of economic category membership, but there appears to be no relationship to gender.

This study analyzed the eighth grade mathematics portion of the spring 2004 Maine Educational Assessment (MEA) achievement test and the survey questions that were also administered. The analysis was on a school-wide level (n = 182). The two survey questions used were: “Which statement best describes the use of calculators in your mathematics classes?” and "Which statement best describes how you use your laptop in mathematics class: getting data from the Web, finding mathematics problems online, creating graphs?" Correlational analysis, partial correlation, and regression were used to determine if there was any association between calculator usage, laptop usage, and mathematics achievement for girls and for boys in the first state-wide group of students to have one-to-one laptops in Maine. Calculator usage was found to be positively associated with mathematics achievement for both girls (partial correlation coefficient of .189 (p = .011)) and for boys (partial correlation coefficient of .193 (p = .010)) even after controlling for school size and socio-economic status. Though no significant association between laptop usage and mathematics achievement for either girls or boys was found, this may be more a reflection on the survey question being a weak measure than the usage of laptops. In a post-hoc analysis of findings, schools were rank ordered based on the average mathematics achievement score regardless of gender; the top 25% (n = 45) and the lower 25% (n = 45) of the schools were evaluated. In the top 25%, there was no statistically significant difference between school-wide girls' and boys' mathematics achievement scores. However, in the lower 25% of the schools, there was a statistically significant difference (p = .01) between the school-wide average of girls' and boys' mathematics achievement scores, with the girls' score being 1.49 points higher (p = .01, d = .447) than the boys'. Recommendations for refinement of MEA survey questions as well as future studies are provided.