published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

From Introduction: As the headmaster of a large co-educational High School in East London, I have to counsel Standard 7 pupils at the end of each year with regard to their subject choices for the Senior Secondary phase. In consultation with the teacher-psychologists and the Standard 7 teachers, one has to make decisions with regard to subjects which could have far-reaching effects on the pupil. Year after year the greatest discussion and most difficult decisions concern whether or not to continue with mathematics. At the end of the Standard 7 year, the pupil is faced with a choice of subjects, one of which is usually mathematics. Depending on the school, this choice is often wide and the average Standard 7 pupil can, in spite of careful counselling and advice, still be bewildered and confused. One of the best methods of objectively predicting pupil performance is through the use of various standardised tests. Although some norm-based tests exist, very few schools apply these tests to help predict mathematics performance in the Senior Secondary Course. To aid the pupil in deciding whether or not mathematics should be taken in Standards 8, 9 and 10 it would be extremely useful if there were some guide or predictor on which this decision could be based, as it is generally accepted amongst teachers that mathematics can be a stumbling block in the Cape Senior Certificate, particularly by the weaker candidate. If it could be shown that the Standard 7 year-end mathematics mark could be used to help predict whether :- •the pupil would be likely to pass or fail mathematics in the Cape Senior Certificate; •what symbol the pupil would obtain; a decision as to whether or not he should continue with the subject could be made at this stage, and, depending on his Standard 7 mark, what the likely consequences of this decision would be. In the United Kingdom in particular, the use of A-level examination results have been used as predictors in subsequent educational courses and this has been the subject of fairly extensive research during the 1970's. The extent to which O-level examination results are predictive of A-level achievement has, however, received very little attention. The situation in South Africa is very similar and very little, if any, work has been done in assessing the effectiveness of using school marks in the lower standards of high school to predict marks in the upper standards. It is difficult to suggest a reason for this as such work would be of inestimable value in providing information for use in the counselling and selection of subjects for pupils embarking on the Senior Secondary Course.

This study reports on an investigation into the manner in which mathematical symbols influence learners’ understanding of mathematical concepts. The study was conducted in Greater Sekhukhune and Capricorn districts of Limpopo Province, South Africa. Multistage sampling (for the district), simple random sampling (for the schools), purposive sampling (for the teachers) and stratified random sampling with proportional allocation (for the learners) were used. The study was conducted in six schools randomly selected from rural, semi-urban and urban settings. A sample of 565 FET learners and 15 FET band mathematics teachers participated in the study. This study is guided by four interrelated constructivist theories: symbol sense, algebraic insight, APOS and procept theories. The research instruments for the study consist of questionnaires and interviews. A mixed method approach that was predominantly qualitative was employed. An analysis of learners’ difficulties with mathematical symbols produced three (3) clusters. The main cluster consists of 236 (41.6%) learners who indicate that they experience severe challenges with mathematical symbols compared to 108 (19.1%) learners who indicated that they could confidently handle and manipulate mathematical symbols with understanding. Six (6) categories of challenges with mathematical symbols emerged from learners’ encounters with mathematical symbols: reading mathematical text and symbols, prior knowledge, time allocated for mathematical classes and activities, lack of symbol sense and problem contexts and pedagogical approaches to mathematical symbolisation. Two sets of theme classes related to learners’ difficulties with mathematical symbols and instructional strategies emerged. Learners lack symbol sense for mathematical concepts and algebraic insight for problem solving. Learners stick to procedurally driven symbols at the expense of conceptual and contextual understanding. From a pedagogical perspective teachers indicated that they face the following difficulties when teaching: the challenge of introducing unfamiliar notation in a new topic; reading, writing and verbalising symbols; signifier and signified connections; and teaching both symbolisation and conceptual understanding simultaneously. The study recommends teachers to use strategies such as informed choice of subject matter and a pedagogical approach in which concepts are understood before they are symbolised. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education)

M.Ed. (Subject Didactics) / It is important that allowances be made for the Mathematics gifted pupil, who is seen as the problem solver of the future. Mathematics gifted pupils, on the average, use half their time to work thoroughly through the average syllabus and achieve 90% plus. The average subject teacher does not always have the necessary time for the gifted pupil. He is thus left to his own devices. The lack of facilities, sufficient qualified teachers, support from like-minded people, stimulating opportunities, resource centres and other stimulating factors add further to the pupils' frustrations. Enrichment of syllabi is seen as one of the most prominent provisional possibilities for the gifted child. The reason for this is found in the fact that the gifted child does not constitute even 5% of the population. They are kept mainly in the mainstream and are in no way identified as a group for any type of special educational need, like acceleration. Enrichment by means of educational computer programmes does not need individual teaching or a faster pace, but an adjustment in the activities within the classroom. Teaching, with the aid of computers, offers an educational aid which offers the opportunity for more effective provision for the gifted child ...

This research report focuses on an investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms in the Grahamstown region, South Africa. Boredom seems to be strongly evident in our classrooms. Quantitative data was derived from an initial survey questionnaire while semi-structured interviews were used to elicit qualitative data. The data from the survey was analysed quantitatively using descriptive statistics. The quantitative data was categorised according to the structure of the survey. The data was represented in bar graphs and then discussed accordingly. In the final narrative I infused extracts from the interviews with my quantitative analysis. The qualitative data was analysed and coded according to different categories and themes that emerged through repeated engagement with the interview transcripts. The findings revealed that boredom is a common problem in the 8 Grade 10 Mathematics schools in the Grahamstown region and this finding answered my first research question. To answer my second research question, the results showed that learners were bored due to many factors, such as; lack of understanding, repetition and the teacher’s actions and many more. My findings align with what is highlighted by Nett, Goetz, & Hall. (2011) that many learners from particularly the senior secondary schools frequently report episodes of boredom. The study recommends that teachers make their teaching more interesting, much use of concrete teaching materials and make mathematics tasks to be relevant and real.

Thesis (M.Ed.)--University of South Africa, 2002.

M. Tech. Education / The study investigated the extent to which Grade 11 learners were able to formulate Mathematics and Mathematical Literacy problems from a given soccer context and to determine the extent to which the problems formulated by learners reflect the given soccer context. Engaging learners in the activity of task formulation within the context of soccer was an attempt to enable the learners to appreciate the mathematics concepts can be extracted from familiar or everyday situations.