Submitted to the Faculty of Education in fulfilment of the requirements for the Degree of Master of Education, in the Department of Mathematics, Science and Technology Education at the University of Zululand, 2008. / The present study is about the problem solving and the use of computer in teaching and learning of mathematics. The study was conducted to grade eight learners where basic mathematics concepts are introduced. The reason is that lack of knowledge of basic mathematics concepts, irrelevant approaches and methods used in teaching mathematics are perceived as the cause of poor performance in mathematics. Therefore if learners could master these concepts and acquire problem solving skills at elementary level they can do better in upper levels especially in grade 12. In this regard the effects of problem solving involving the use of computer at grade eight level have been investigated. The first aim was to test the effects of multidimensional approach using computer in algebra problem solving. The second aim was to determine the effects multiple representations in computer environment have on mathematics problem solving. The third aim was to determine the effects of computer assisted collaborative learning on mathematics problem solving. To achieve these aims an unstandardised achievement test and a questionnaire was administered to a sample of grade eight learners from three high schools in KwaZulu Natal. The results revealed that if problem solving is integrated with other components (dimensions) such as the teaching of facts and skills, teaching for understanding and the use of technology (computer) learners are likely to achieve better results in mathematics. The results also revealed that the use of multiple representations in expressing the mathematical concept or idea and collaboration among learners in problem solving improve learners' understanding of mathematics. The discussion of the results of this study leads to the discussion of implications of the findings and recommendations. / University of Zululand.

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The purposes of the study were: (1) to determine the effects of four testing strategies upon performance in college algebra, attitude towards mathematics, and attrition rate; (2) to determine the effects of two types of frequent testing upon performance, attitude, and attrition rate, (3) to determine the effects of different frequencies of in-class testing upon performance, attitude, and attrition rate; and (4) to draw conclusions which might help in selecting testing methods for college algebra classes.

The pass rate of first-year university mathematics students at the University of KwaZulu-Natal (Pietermaritzburg Campus) has been low for many years. One cause may be weak algebra skills. At the time of this study, revision of high school algebra was not part of the major first year mathematics course. This study set out to investigate if it would be worthwhile to spend tutorial time on basic algebra when there is already an overcrowded calculus syllabus, or if students refresh their algebra skills sufficiently as they study first year mathematics. Since it was expected that remediation of algebra skills would be found to be worthwhile, two other questions were also investigated: Which remediation strategy is best? Which errors are the hardest to remediate? Five tutorial groups for Math 130 were randomly assigned one of four remediation strategies, or no remediation. Three variations of using cognitive conflict to change students’ misconceptions were used, as well as the strategy of practice. Pre- and post-tests in the form of multiple choice questionnaires with spaces for free responses were analysed. Comparisons between the remediated and non-remediated groups were made based on pre- and post-test results and Math 130 results. The most persistent errors were determined using an 8-category error classification developed for this purpose. The best improvement from pre- to post-test was 12.1% for the group remediated with cognitive conflict over 5 weeks with explanations from the tutor. Drill and practice gave the next-best improvement of 8.1%, followed by self-guided cognitive conflict over 5 weeks (7.8% improvement). A once-off intervention using cognitive conflict gave a 5.9% improvement. The group with no remediation improved by 2.3%. The results showed that the use of tutorintensive interventions more than doubled the improvement between pre-and post-tests but even after remediation, the highest group average was 80%, an unsatisfactory level for basic skills. The three most persistent errors were those involving technical or careless errors, errors from over-generalising and errors from applying a distorted algorithm, definition or theorem. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.

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 examined success rates and end-of-semester grades for three instructional methods used in developmental algebra and college algebra. The methods investigated were traditional lecture, laboratory, and computer mediated learning. The population included the 10,095 students who had enrolled in developmental algebra and college algebra at Richland College in Dallas, Texas, for five semesters. Success was defined as earning a grade of A, B, C, or D in a course.

The purpose of this study was to compare the effects of Web-based learning (WBL) versus those of traditional instructor-based learning (IBL) on student knowledge and satisfaction based on student learning styles. Other goals were to determine if WBL is more effective for those with a particular learning style. The study examined a sample of undergraduate students who were enrolled in the college algebra offered as both oncampus instructor-based (traditional) and Web-based at the university of North Texas (UNT). A total of 36 Web-based students and 58 instructor-based students participated in this study. This study utilized a posttest-only intact group. The Kolb Learning Style Inventory (LSI) measured the learning styles of students. This study used learning methods (Web-based learning (WBL), instructor-based learning (IBL)), and learning styles (Diverger, Converger, Assimilator, and Accommodator) as independent variables. Student knowledge and student satisfaction was measured at the end of the course as independent variables. Based upon the results of the LSI, post-learning exam, and satisfaction a series of two-way analysis of variance (ANOVA 4x2) techniques and independent variable tests was used for each of the dependent variables, knowledge and satisfaction, based on a student's learning styles. The results revealed that students' learning styles were statistically significant for knowledge when learning on the Web versus instructor-led. In addition, the learning style was important factor for Web-based learning. The results indicated students with Assimilator and Converger as learning styles received better result with the Web-based learning method. Furthermore, this study found there is significant difference in student satisfaction based on learning on the Web versus instructor-led. The outcome of the study could be of particular interest in educational institutions; especially those that want to transfer some of their traditional courses onto the Web. The finding also has implications for training organizations as they seek efficient and effective ways to satisfy their training needs.

The effect of an interdisciplinary algebra/science course on students' critical thinking skills was examined. A traditional college algebra course was used as a comparison group. The students in the sample enrolled in college algebra and then half were randomly placed into the interdisciplinary course. A quasi-experimental pretest-posttest comparison group design was used. The Watson-Glaser Critical Thinking Appraisal was used to measure the students' critical thinking skills. This instrument consists of an overall critical thinking score as well as five subscores in the areas of Inference, Recognition of Assumptions, Deduction, Interpretation and Evaluation of Arguments. It was found that the students in the interdisciplinary course made greater gains in the overall critical thinking score as well as in four of the five subscores. However, the differences in the gains made in the two courses were not statistically significant. Disregarding course, other factors that were found to be closely related to critical thinking were Composite ACT, grade received in the course, Math ACT and grade point average. It was also found that students whose majors were in the Schools of Arts and Letters or Science and Technology scored higher on critical thinking than students whose majors were in the Schools of Business or Education. Factors found to have no relationship to critical thinking were ethnicity, gender and classification.

This dissertation consists of three related papers. The first paper, Rethinking mathematics bridge courses--An inquiry model for community colleges, introduces the activities of conventionalizing and axiomatizing from a practitioner perspective. In the paper, I offer a curricular model that includes both inquiry and traditional instruction for two-year college students interested in mathematics. In particular, I provide both examples and rationales of tasks from the research-based Teaching Abstract Algebra for Understanding (TAAFU) curriculum, which anchors the inquiry-oriented version of the mathematics bridge course. The second paper, the role of past experience in creating a shared representation system for a mathematical operation: A case of conventionalizing, adds to the existing literature on mathematizing (Freudenthal, 1973) by "zooming in" on the early stages of the classroom enactment of an inquiry-oriented curriculum for reinventing the concept of group (Larsen, 2013). In three case study episodes, I shed light onto "How might conventionalizing unfold in a mathematics classroom?" and offer an initial framework that relates students' establishment of conventions in light of their past mathematical experiences. The third paper, Collective axiomatizing as a classroom activity, is a detailed case study (Yin, 2009) that examines how students collectively engage in axiomatizing. In the paper, I offer a revision to De Villiers's (1986) model of descriptive axiomatizing. The results of this study emphasize the additions of pre-axiomatic activity and axiomatic creation to the model and elaborate the processes of axiomatic formulation and analysis within the classroom community.

The problems with which this study was concerned were threefold: (a) to design a computer-based graphics presentation on the topics of functions and graphing, (b) to develop the presentation, and (c) to determine the instructional effectiveness of this computer-based graphics instruction. The computerized presentation was written in Authorware for the Macintosh computer. The population of this study consisted of three intermediate algebra classes at Collin County Community College (n = 51). A standardized examination, the Descriptive Tests of Mathematics Skills for Functions and Graphs, was used for pretest and posttest purposes. Means were calculated on these scores and compared using a t-test for correlated means. The level of significance was set at .01. The results of the data analysis indicated: 1. There was a significant difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 2. There was no significant gender difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 3. There was no significant difference between the pretest and posttest performance of the traditional and nontraditional age students after exposure to the computer-based graphics presentation. Females had a lower posttest score than the mean male posttest score, but an analysis of the differences showed no significance. Traditional age students had a higher posttest performance score than the mean traditional age student posttest score, but their pretest performance scores were higher as well. An analysis of the differences showed no significance. In summary, this computer-based graphics presentation was an effective teaching technique for increasing mathematics performance.