With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject will develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is assessed which influences the focus of ML in the classrooms. With this in mind, this study set out to explore the ways in which a class of Grade 12 learners engaged with a preparatory examination designed and administered by the KZN Department of Education. This is a qualitative study carried out with seventy-three grade 12 mathematical literacy learners from an urban school in North Durban. The purpose of this research is to explore the learners’ engagement with the examination tasks, thereby identifying possible factors which influence learners’ success in these items. Data were gathered from a document analysis of the 2009 KZN Trial Examination question paper and marking memorandum; 73 learners’ written responses to the examination tasks, and interviews with ten of these learners. The purpose of the document analysis was to identify contexts in which learners performed well or poorly, as well as to assess the design of the instrument. Semi-structured interviews were conducted individually with ten learners and video recorded. The purpose of the interviews was to explore some of the factors which influenced their written responses. The findings revealed that the task design was problematic for learners in terms of the order of the questions and the placement of the crucial information necessary to answer the questions. Some tasks also contained errors. The complexity of the scenario in terms of the amount of information, the language used, and the presence of distracters further influenced the way in which learners responded to the task. Learners’ personal experience of the context also affected the way they interpreted and responded to the task. Factors that constrained learners’ success in the examination task included poor conceptual understanding, misconceptions and language-related misinterpretation. It was also found that learners did not consider it a priority to make sense of the context: they focused on identifying formulae or information that could be used to present answers with little concern about the reasonableness of their responses. Some strategies used by learners in responding to the task included number grabbing, guessing without checking, scanning for crucial information and assumption-making. The study recommends that provincial examination papers be subject to the same stringent moderation requirements of the national examinations. It also recommends that should diagrams be used, they must be relevant to the context and should not conflict with the subject matter. The use of contexts should cater for alternate answers and multiple approaches and the marking memorandum should be flexible to accommodate these multiple approaches. Care must be taken in the presentation and placement of crucial information, so that learners do not miss the information they need to answer the questions. When familiar contexts are being used, task designers should also consider whether learners’ everyday experiences may conflict with these scenarios. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2011.

The proposed research is about the introduction of Continuous Assessment (CA) in Grade 12 Higher Grade Mathematics, as part of the learner's overall assessment. Schools are required by policy laid down by the Department of Education to implement CA in Grade 12 Mathematics. The introduction of CA is a new development. It is important to study how it is being implemented and the effect it has on the quality of Mathematics Education. The goals of this research are to: • investigate Grade 12 Mathematics teachers' understanding and views of CA; • the strategies that they are implementing in CA; • how CA is impacting on the conceptual understanding of their learners and • to what extent are teachers' assessment practices consistent with the Rationale of Continuous Assessment? The data was collected by means of a questionnaire which consisted of both close-ended and semi-structured questions. The Statistical Package for the Social Sciences (SPSS) was used to analyze the quantitative data. The findings show that continuous assessment is not being implemented in terms of a wide range of alternate assessment strategies as it was intended to be, with pen and paper testing still being the more dominant practice. The findings also show that whilst Continuous Assessment is having a measured educational impact on teachers and learners, there are still problems experienced by educators. These problems are hampering its implementation. Teachers require more workshops on the Continuous Assessment strategies. / Thesis (M.Ed.)-University of Durban-Westville, 2004.

The present project is part of a larger research programme focussed on the analysis of change; one aspect being educational transformation and in particular an emphasis on the explication of the contentless processes (eg. logical operations, reasoning styles, analysis and synthesis) which underlie both learning and teaching at university level. The present project is aimed at an analysis of the teaching-learning dialectic in mathematics courses. This analysis has two major focal points, that is, making explicit the often tacit and mostly inadequate and/or inappropriate rules for engaging in mathematical tasks which the under-prepared learner brings to the teaching-learning situation, and secondly the teaching strategies which may enable these learners to overcome their past (erroneous) knowledge and skills towards the development of effecient, autonomous mathematical problem-solving strategies. In order to remedy inadequate and inappropriate past learning and/or teaching, the present project presents a set of mediational strategies and regulative cues which function both for the benefit of the teacher and the learner in a problematic teaching-learning situation and on the meta and epistemic cognitive levels of information processing. Furthermore, these mediational strategies and regulative cues fall on a kind of interface between contentless processes and the particular content of the teaching-learning dialectic of mathematics in particular, as well as between the ideal components of any instructional process and the particular needs and demands of under-prepared learners engaged in mathematical tasks. / Thesis (M.Ed.) - University of Natal, Durban, 1988.

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

Thesis (MTech (Design))--Cape Peninsula University of Technology, 2015. / Mathematical literacy among the citizenry of a nation is considered indispensable to the economic welfare and global competitiveness of that nation (World Economic Forum, 2013a). In a world governed by technology, quantitative literacy is crucial (Colwell cited by Steen, 2002:8) and becomes a “most important professional and life skill” (Maloney et al., 2012:380). It is also seen as an individual’s ability to “manage situations or solve problems in practice” (Frith & Prince, 2006). Lastly, Jansen (2012) believes that sound mathematical literacy leads to an understanding of cause and effect and would guide citizens in their choices of actions. Yet, the belief that mathematical competence (or even just quantitative literacy) is the privilege of a small group of intellectually predisposed individuals is widely accepted in society, further entrenched by erroneous stereotyping (Eccles et al., 1990; Bonnot & Croizet, 2007; Mangels et al., 2011), as well as inadequate teaching methods in the Mathematics classroom/lecture theatre (Artigue, 1999; NSTF, 2009, 2010; Department of Basic Education, 2014). The consequences of this skewed view of Mathematics, and the emotional stress caused by regular failure at the subject, have resulted in wide-spread maths anxiety and maths avoidance among scholars and students. This dissertation examines an intervention programme which was designed to alter students’ negative perceptions of their intellectual ability to grasp mathematical concepts. Instead of attributing their past failures to internal, stable and uncontrollable causes, such as cognitive inability (Weiner, 1985), they were asked to consider factors which were internal or external, but certainly unstable and controllable, and which played a major role in their disappointing history in Mathematics. The interventions were aimed at bringing about a paradigm shift from a fixed mindset (entity theory) to a growth mindset (increment theory) as researched by Dweck since the 1980s. The intervention programme was implemented in the Foundation Course of a South African university of technology. It involved four interventions spread over roughly four months of the first semester and was comprised of the following lecture units and activities: a session of free-writing (Elbow, 1973), lectures on the plasticity of the brain (Hebb, 1949; Diamond 2001, Zull, 2002), the three memory systems (Eysenck & Calvo, 1992), a very basic version of Kolb’s experiential and reflective learning cycle (Atherton, 2009), and the notion of threshold concepts (Meyer & Land, 2003)

D.Ed. (Didactics) / The purpose of this research project was to ascertain whether the Mathematics curriculum for apprentices comply with scientifically defensible criteria. Important conclusions regarding characteristics of Mathematics, tuition and learning guides, and the aims of Mathematics, were reached ...

D.Ed. / Please refer to full text to view abstract

A number of tertiary institutions offer bridging courses and intervention programmes in order to increase the number of students performing well in first year mathematics. At the university of Namibia, the science faculty provides educational opportunities to students who have not met the requirements to proceed with MAT 3511 (Basic Math). Unfortunately, the majority of students are not able to cope with the first year modules in Mathematics and the pass rates are unacceptably low. In the interest of supporting students, the University was prompted to introduce a two mode intervention programme in first year mathematics, namely: the normal mode and the alternative mode intervention. The alternative mode intervention was designed to improve the mathematics achievement of first year students who are considered low achieving or at risk of failure. This programme involves the identification of the lowest attainers in first year mathematics, and the provision of professional and faculty trained tutors and individualized teaching to these students in order to advance them to a level at which they are likely to learn successfully in a normal mode system. This research explores the experience and perceptions of first year students on the alternative mode, in particular as it relates to mathematical strands of proficiency. A second step was to explore how teaching contributes to the learning of mathematics on the intervention programme. The empirical investigation was done in 4 phases. A questionnaire on mathematics teaching and learning was given to the students during the first phase. During the second phase, two focus group discussions were conducted. Thereafter four interviews were carried out with lecturers, and finally tutorial and lecture observation were conducted. An analysis of these findings led to the identification of the students’ experiences on the alternative mode. Analysis of the results indicate that the students identified mathematical proficiency as the central element to their learning, and pedagogical knowledge and exploratory talk were critical aspects of good teaching in the mathematical intervention programme.

The problem with which this investigation is concerned is that of determining whether utilizing self-help groups for remedial mathematics students would improve their course completion rates, achievement, and attitudes toward learning mathematics. The methods of determining the success/failure of self-help groups in this study were the Z-test from inferences concerning two proportions, the t-test from inferences concerning the difference between two independent means, and the t-test from inferences concerning the difference between two dependent means. The participants of the study were chosen from the students enrolled in "daytime" mathematics classes at Tarrant County Junior College - Northeast Campus, Hurst, Texas. The experiment was conducted over two semesters and the data combined for statistical analysis. There were one hundred four students involved in the study. Fifty-two students comprised each of the experimental and control classes. The term self-help group was utilized to describe a small group of two-to-fifteen people who engaged in discussion of responsibility, standards, confession, lay leadership, and action. The students did not study mathematics in self-help group sessions. The group meetings dealt with anxieties, attitudes, and commitment that may be associated with mathematics in general. To investigate the hypotheses of this study, data was collected to calculate the percentage completion rates, the means of the final exams taken by students, and the differences of the Semantic Differential scores given to students in the experimental class at the beginning and the end of the semester. This data was utilized for statistical analysis to determine if the experiment was successful. The report concludes that self-help groups did not significantly improve course completion rates, achievement, or attitudes of students toward learning mathematics. Forty-four per cent of the students that completed the experimental class participated in self-help groups.

The purpose of this study was to identify the nature of students' conceptual understanding of two concepts of calculus namely, derivative and function. As a way of collecting data two methods were employed: (a) modification of Piagetean clinical interview; and, (b) tutorial sessions. Whenever the students seemed to be confused about the issues being discussed, the researcher provided instructions through the tutorial sessions. The analysis of data was done by developing individual profiles and by response categories. It was found that the interview methodology was effective in revealing some aspects of students' concept images. The students were found to have little meaningful understanding of derivative. A number of students held proper concept images of function which should lead to the development of an appropriate concept definition. It was also evident from the study that students had adequate skill in using algorithm to solve problems. The results of the study would be useful to the instructors of calculus. It was suggested that introducing a concept by its formal definition would contribute to students' confusions and difficulties. Yet if a concept is presented by means of meaningful examples, students had better opportunity to develop their concept images. Thus leading them to form concept definitions. The researcher strongly recommended that more challenging exercises be posed to the students in problem-solving situations. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate