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This single case study investigated the implementation of a modularized mathematics course designed to eliminate the usage of remedial mathematics courses from post-secondary mathematics curricula. The literature review revealed that introductory college level mathematics success and student retention rates in post-secondary schools was chronically problematic due in large part to the number of students unable to advance past remedial courses. According to the findings of this study, the modularized curriculum provided the necessary remediation tools embedded within course essential to student learning and development without the psychosocial pitfalls and financial burdens that follow remedial mathematics courses. The conclusion drawn from the findings is that enrolling post-secondary students in a modularized introductory college level mathematics course with embedded remedial support can be effective in increasing student confidence in successfully completing an introductory level mathematics course

Thesis (M.Sc.)--University of the Witwatersrand, Faculty of Science (Science Education), 1996. / This study explores ways in which first-year mathematics students use calculator as a tool of semiotic mediation. Twenty students out of a class of one hundred were loaned a graphic calculator for the academic year and were encouraged to use these during support tutorials. at year-end seven students (four with graphic calculator, three without) were audio-taped while solving a mathematical problem aloud in an interview situation. Also statistical data comparing graphic calculator and non-graphic calculator students' performance on a set of five questions was collected. The qualitative analysis of the interview data suggests that the calculator functioned primarily as a tool which amplified the zones of proximal development of the students, increasing efficiency and speed, rather than a semiotic which had been internalised. The quantitative analysis of the statistical data failed to support this notion of amplification. It is suggested that the add-on status of the graphic calculator undermined the possibility for statistical significance on this amplification effect.

Please read the abstract in the section 00front of this document / Thesis (PhD)--University of Pretoria, 2006. / Humanities Education / PhD / Unrestricted

Mathematics presents a stumbling block to many students, particularly those majoring in scientific fields, business administration, or elementary education. Improvement of student achievement in mathematics at the lower division college level is needed. Seven instructional methods were investigated in terms of student achievement: programmed instruction (P.I.), individualized instruction (I.I.), computer based instruction (CBI), laboratory and discovery methods (Lab), television (TV), audio-tutorial (A-T), and tutoring. The research questions were: (1) What is the relative effectiveness of the innovative instructional methods as measured by student achievement and compared to the traditional lecture method? (2) What is the relative effectiveness of the innovative instructional methods on students of differing ability and course levels. (3) What is the effectiveness of combinations of the innovative instructional methods? A meta-analytical approach was used. Studies comparing an innovative method to the lecture or to another innovative method were located, and the summary data in each were used to calculate an "effect size"--a standardized measure of the effectiveness of the innovative method--to which statistical procedures were applied. The meta-analysis found that (1) Relative to the lecture method, six of the innovative methods produced a positive effect on student achievement. The ranking of the methods in order of decreasing effectiveness was: tutoring, CAI, A-T, I.I., P.I., Lab, TV. (2) The most effective methods by level of course were: (a) Precalculus level: CAI, A-T, and tutoring; (b) Calculus level: tutoring, I.I., P.I., and A-T; (c) Foundations of Mathematics (elementary education majors): P.I.; Descriptive Geometry: TV. The most effective methods by ability level of the student were: (a) High ability: CAI and Lab; (b) Middle ability: CAI, I.I., and P.I.; (c) Low ability: P.I. and A-T. (3) The lack of empirical studies prevent a determination of the relative effectiveness of combinations of the innovative methods. Recommendations include the following: (1) Variation of instructional methods; (2) Incorporation of specific, effective elements of innovative methods into the lower division college mathematics instructor's repertoire; and (3) Empirical investigation of the effectiveness of combinations of methods and of various instructional methods on students of different ability levels.

<p>This research provided insights into the mathematical achievement of a cohort of tertiary mathematics students. The context for the study was an entry level mathematics course, set in an engineering programme at a tertiary institution, the Cape Peninsula University of Technology (CPUT). This study investigated the possibilities of providing a bridge between the assessment of students by means of tests scores and a taxonomy of mathematical objectives, on the one hand, and the critical analysis of student produced texts, on the other hand. This research revealed that even in cases of wrong solutions, participant members' responses were reasonable, meaningful, clear and logical.</p>

D.Phil. (Mathematics Education) / In tertiary education, a statement like ‘Low graduation rates prevail around the world’ is common knowledge since the 1940s, and therefore one does not need any longer to mention references. The factors that contribute to it though, are innumerable. One of those factors is the ability of a student to solve problems. Problem solving has been accepted as a prerequisite for lifelong learning by many governments and it is enshrined in their educational policies. However, problem solving can be associated with academic performance (mastery of content knowledge being a main contributor) as well as application/transfer of content knowledge. Critical thinking on the other hand is embedded in problem solving, acquisition of knowledge and application. Then an investigation into the relationships between all these constructs is warranted. This research aimed at shedding some or more light into this proverbial problem. Problem solving is equated by some authors to learning. Learning while solving problems and solving problems result in learning. Almost all theorists see problem solving as a process and be one of the products of learning. This research concluded that problem solving is a product of its own as a result of a number of complex cognitive processes. The simple argument is: If a problem solver cannot solve a problem successfully then no product is produced by those cognitive processes. In actual fact, the possibility of the existence of misconceptions could be one of the reasons for the failure of solving the problem. If that is true, then the statement: ‘we should be diagnosing rather than teaching’ could be valid. Furthermore, teaching problem solving as a process gives rise for it to be treated as an ‘algorithm’ by students which they try to memorise without having a conceptual understanding of the problem. However if it is treated as a product the students will be encouraged to think of the various cognitive processes that are necessary to solve the problem. This research concluded that cognitive processes such as critical thinking, acquisition of (mathematical) knowledge and application thereof, can lead to a product which was guided by ‘quality control processes’. Therefore problem solving in this research is not explicitly expressed but implicitly. As a result ‘successful problem solving’, the product, is closely associated with academic achievement.

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 2002. / In this thesis I consider how mathematics students in a traditional firstyear Calculus course at a South African university appropriate mathematical objects which are new to them but which are already part of the official mathematics discourse. Although several researchers have explained mathematical object appropriation in process-object terms (for example, Sfard, 1994; Dubinsky, 1991, 1997; Tall, 1991, 1995, 1999), my focus is largely on what happens prior to the object-process stage. In line with Vygotsky (1986), I posit that the appropriation of a new mathematical object by a student takes place in phases and that an examination of these phases gives a language of description for understanding this process. This theory, which I call “appropriation theory”, is an elaboration and application of Vygotsky’s (1986) theory of concept formation to the mathematical domain. I also use Vygotsky’s (1986) notion of the functional use of a word to postulate that the mechanism for moving through these phases, that is, for appropriating the mathematical object, is a functional use of the mathematical sign. Specifically, I argue that the student uses new mathematical signs both as objects with which to communicate (like words are used) and as objects on which to focus and to organise his mathematical ideas (again as words are used) even before he fully comprehends the meaning of these signs. Through this sign usage the mathematical concept evolves for that student so that it eventually has personal meaning (like the meaning of a new word does for a child); furthermore, because the usage is socially regulated, the concept evolves so that its usage is concomitant with its usage in the mathematical community. I further explicate appropriation theory by elaborating a link between the theoretical concept variables and their empirical indicators, illustrating these links with data obtained from seven clinical interviews. In these interviews, seven purposefully chosen students engage in a set of speciallydesigned tasks around the definition of an improper integral. I utilise the empirical indicators to analyse two of these interviews in great detail. These analyses further inform the development of appropriation theory and also demonstrate how the theory illuminates the process of mathematical object appropriation by a particular student.

For several reasons, Guilford's psychological theory, "The Structure-of-Intellect" (SI), seems a good candidate for relating to the learning of mathematics. The general purposes of this study were to identify SI factors which would be significantly related to achievement in a junior-college mathematics course for non-science, non-mathematics majors and to determine whether semantic factors would be better predictors than symbolic for students classified as having high verbal ability. The two topics in the mathematics course which were selected for study were (1) numeration in other bases and (2) finite systems. / Typescript. / "August, 1975." / "Submitted to the Area of Instructional Design and Personnel Development, Program of Mathematics Education, in partial fulfillment of the requirements of Doctor of Philosophy." / Advisor: Eugene D. Nichols, Professor Directing Dissertation. / Vita. / Includes bibliographical references (leaves 151-153).

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