Too often, discussions about Mathematics express feelings of anguish and despair; and, indeed Mathematics results in general in South Africa can be described as dismal. The Department of Education (DoE) reported that in the 2010 National Senior Certificate examinations, 52.6% of learners obtained less than 30% in Mathematics and 69.1% of learners obtained less than 40% (DoE, 2010). This implies that a very small percentage of grade 12 learners would be eligible to further their studies in the fields of Mathematics and science at tertiary level, resulting in a depletion of science and Mathematics-oriented professionals. This study explored the mathematical attitudes and achievement strategies of successful Mathematics learners to overcome the factors that might impede achievement. This study has the potential to improve practice because the findings of the study and recommendations are made implicit in the discussion. In particular this study sought to investigate the following issues: (a) What are secondary school learners' attitudes towards Mathematics? (b) In what ways are these attitudes linked to factors to which the learners attribute their achievement in Mathematics? (c) What strategies do successful Mathematics learners use to overcome the factors that they identify as impeding their performance in Mathematics? This research involved a case study approach. The study solicited both quantitative and qualitative data from the participants. The participants comprised 95 Grade 10, 11 and 12 Mathematics learners. The Fennema-Sherman Mathematics Attitude Scales (FSMAS) questionnaire was used to collect data from participants. The data was analysed using Attribution Theory and Achievement Theory. Two learners, who obtained more than 60% in the 2011 half-year Mathematics examination, from grades 10, 11 and 12 respectively, constituted the focus group. The focus group interview enhanced the study by clarifying the responses to the questionnaire and providing answers to the second and third research questions. The findings of the research include the following: teachers play an important role in shaping learners’ attitudes toward Mathematics; learners are anxious when asked to solve mathematical problems; parents are very encouraging of their children learning Mathematics; the importance of Mathematics for future careers exerted a significant effect on mathematical achievement; and finally the various strategies that learners employ that positively impact on their achievement in mathematics include mastery experience, motivation, private tuition and peer group teaching-learning. The final section of this dissertation discusses the implications of this study for practising Mathematics teachers and suggestions for further research in the area of affect. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2011.

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2007 / Twelve years into a democracy, South Africa still faces many developmental challenges. Since 2002 Universities of Technology in South Africa have introduced Foundational Programmes/provisions in their Science and Engineering programmes as a key mechanism for increasing throughput and enhancing quality. The Department of Education has been funding these foundational provisions since 2005. This Case Study evaluates an aspect of a Foundational provision in Mechanical Engineering, from the beginning of 2002 to the end of 2005, at a University of Technology, with a view to contributing to its improvemenl The Cape Peninsula University of Technology {CPUn, the locus for this Case Study, is the only one of its kind in a region that serves in excess of 4.5 million people. Further, underpreparedness in Mathematics for tertiary level study is a national and intemational phenomenon. There is thus a social interest in the evaluation of a Mathematics course that is part of a strategy towards addressing the shortage in Engineering graduates. This Evaluation of integration of the Foundation Mathematics course into Foundation Science, within the Department of Mechanical Engineering at CPUT, falls within the ambit of this social need. An integrated approach to cunriculum conception, design and implementation is a widely accepted strategy in South Africa and internationally; this approach formed the basis of the model used for the Foundation programme that formed part of this Evaluation. A review of the literature of the underpinnings of the model provided a theoretical framework for this Evaluation Study. In essence this involved the use of academic literacy theory together with learning approach theory to provide a lens for this Case Study.

M.Ed. (Education) / Please refer to full text to view abstract

These studies have focused on identifying the mathematical requirements of first-year BCom students at Nelson Mandela Metropolitan University. The research methodology used in this quantitative study was to make use of interviewing, questionnaire investigation, and document analysis in the form of textbook, test and examination analysis. These methods provided data that fitted into a grounded theory approach. The study concluded by identifying the list of mathematical topics required for the first year of the core subjects in the BCom degree programme. In addition, the study found that learners who study Mathematics in the National Senior Certificate should be able to cope with the mathematical content included in their BCom degree programme, while learners studying Mathematical Literacy would probably need support in some of the areas of mathematics, especially algebra, in order to cope with the mathematical content included in their BCom degree programme. It makes a valuable contribution towards elucidating the mathematical requirements needed to improve the chances of successful BCom degree programme studies at South African universities. It also draws the contours for starting to design an efficient support course for future “at-risk” students who enter higher education studies.

The problem of this study is to determine the needs of students who are majoring in business and to design a workbook that will best prepare these students for the business courses offered at North Texas State Teachers College and for the problems of everyday life.

It is common for students to make mistakes while solving mathematical problems. Some of these mistakes might be caused by the false ideas, or misconceptions, that students developed during their learning or from their practice. Calculus courses at the undergraduate level are mandatory for several majors. The introductory course of calculus—Calculus I—requires fundamental skills. Such skills can prepare a student for higher-level calculus courses, additional higher-division mathematics courses, and/or related disciplines that require comprehensive understanding of calculus concepts. Nevertheless, conceptual misunderstandings of undergraduate students exist universally in learning calculus. Understanding the nature of and reasons for how and why students developed their conceptual misunderstandings—misconceptions—can assist a calculus educator in implementing effective strategies to help students recognize or correct their misconceptions. For this purpose, the current study was designed to examine students’ misconceptions in order to explore the nature of and reasons for how and why they developed their misconceptions through their thought process. The study instrument—Calculus Problem-Solving Tasks (CPSTs)—was originally created for understanding the issues that students had in learning calculus concepts; it features a set of 17 open-ended, non-routine calculus problem-solving tasks that check students’ conceptual understanding. The content focus of these tasks was pertinent to the issues undergraduate students encounter in learning the function concept and the concepts of limit, tangent, and differentiation that scholars have subsequently addressed. Semi-structured interviews with 13 mathematics college faculty were conducted to verify content validity of CPSTs and to identify misconceptions a student might exhibit when solving these tasks. The interview results were analyzed using a standard qualitative coding methodology. The instrument was finalized and developed based on faculty’s perspectives about misconceptions for each problem presented in the CPSTs. The researcher used a qualitative methodology to design the research and a purposive sampling technique to select participants for the study. The qualitative means were helpful in collecting three sets of data: one from the semi-structured college faculty interviews; one from students’ explanations to their solutions; and the other one from semi-structured student interviews. In addition, the researcher administered two surveys (Faculty Demographic Survey for college faculty participants and Student Demographic Survey for student participants) to learn about participants’ background information and used that as evidence of the qualitative data’s reliability. The semantic analysis techniques allowed the researcher to analyze descriptions of faculty’s and students’ explanations for their solutions. Bar graphs and frequency distribution tables were presented to identify students who incorrectly solved each problem in the CPSTs. Seventeen undergraduate students from one northeastern university who had taken the first course of calculus at the undergraduate level solved the CPSTs. Students’ solutions were labeled according to three categories: CA (correct answer), ICA (incorrect answer), and NA (no answer); the researcher organized these categories using bar graphs and frequency distribution tables. The explanations students provided in their solutions were analyzed to isolate misconceptions from mistakes; then the analysis results were used to develop student interview questions and to justify selection of students for interviews. All participants exhibited some misconceptions and substantial mistakes other than misconceptions in their solutions and were invited to be interviewed. Five out of the 17 participants who majored in mathematics participated in individual semi-structured interviews. The analysis of the interview data served to confirm their misconceptions and identify their thought process in problem solving. Coding analysis was used to develop theories associated with the results from both college faculty and student interviews as well as the explanations students gave in solving problems. The coding was done in three stages: the first, or initial coding, identified the mistakes; the second, or focused coding, separated misconceptions from mistakes; and the third elucidated students’ thought processes to trace their cognitive obstacles in problem solving. Regarding analysis of student interviews, common patterns from students’ cognitive conflicts in problem solving were derived semantically from their thought process to explain how and why students developed the misconceptions that underlay their mistakes. The nature of how students solved problems and the reasons for their misconceptions were self-directed and controlled by their memories of concept images and algorithmic procedures. Students seemed to lack conceptual understanding of the calculus concepts discussed in the current study in that they solved conceptual problems as they would solve procedural problems by relying on fallacious memorization and familiarity. Meanwhile, students have not mastered the basic capacity to generalize and abstract; a majority of them failed to translate the semantics and transliterate mathematical notations within the problem context and were unable to synthesize the information appropriately to solve problems.

"2006" / Thesis (PhD)--Macquarie University, Australian Centre for Educational Studies, Institute of Higher Education Research and Development, 2007. / Bibliography: p. 167-173. / Introduction -- Experience and expression -- Becoming a professional -- Study design -- Graduates' experiences: a narrative -- Reflections on communication -- Examples of texts -- Reflections on learning and teaching -- Reflections and implications. / The aim of this study is to inform curriculum change in the mathematical sciences at university level. This study examines the transition to professional work after gaining a degree in the mathematical sciences. Communication is used as the basis for the analysis of the transition because of the importance of language choices in work situations. These experiences form part of the capabilities that become part of a person's potential to work as a professional. I found a subtle form of power and, of the opposite, lack of power due to communication skills. It is not as obvious as in, say, politics but it is just as critical to graduates and to the mathematical sciences. -- There were 18 participants in the study who were graduates within five years of graduation with majors in the mathematical sciences. In-depth interviews were analysed using phenomenography and examples of text from the workplace were analysed using discourse analysis. Descriptions of the process of gaining employment and the use of mathematical discourse have been reported in the thesis using narrative style with extensive quotes from the participants. -- The research shows that graduates had three qualitatively different conceptions of mathematical discourse when communicating with a non-mathematical audience: jargon, concepts/thinking and strength. All participants modified their use of technical terms when communicating with non-mathematicians. Those who held the jargon conception tried to simplify the language in order to explain the mathematics to their audience. Those who held the concepts/thinking conception believed that the way of thinking or the ideas were too difficult to communicate and instead their intention with mathematical discourse was to inspire or sell their ability to work with the mathematics. The strength conception considers the ethical responsibility to communicate the consequences of mathematical decisions. Not one of the participants believed that they had been taught communication skills as part of their degree. -- Participants gained a 'mathematical identity' from their studies and acquiring a degree gave them confidence and a range of problem-solving skills. Recommendations are made about changes in university curriculum to ensure that graduates are empowered to make a high-quality transition to the workplace and be in a position to use their mathematical skills. Mathematical skills are necessary but not sufficient for a successful transition to the workplace. Without the ability to communicate, graduates are unable to release the strength of their knowledge. / Mode of access: World Wide Web. / xi, 195 p. ill

No summary available / Mathematical Sciences/Teacher Education / D.Phil.

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

The purposes of this study were (1) to compare the achievement levels of students enrolled in a beginning college mathematics course when taught by (a) closed-circuit television followed by student-assisted study periods, (b) closed circuit television followed by access to videotape replay with no supervised study periods, (c) closed-circuit television followed by unsupervised study and discussion, and (d) regular lecture-recitation methods conducted by the television instructor, and (2) to ascertain the students' attitudes toward their instructor, course, and method of instruction.