This study seeks to determine the nature of the intellectual demands of the Higher Grade course in Mathematics with a view to early, more accurate prediction of individual pupil success in this course. The need for such early prediction is clearly indicated by the interest shown on the part of parents and pupils alike during the Standard Seven year where the realisation exists that Matriculation Mathematics is a subject sometimes found to be "overwhelmingly difficult". The "drop out" figure from the Higher Grade course to the Standard Grade course in most schools further demonstrates the need for more careful selection at the Standard Seven level. Both old (1973) and new (1984) syllabuses are analysed to determine the nature of the content and the intellectual level at which this should be taught. In addition, a series of past Cape Senior Certificate examination papers are investigated to reveal information about the nature and level of examining. Mental processes involved in the examination items are classified and the general composition of the examination papers is discussed. A test device suitable for Standard Seven pupils is developed on the basis of the composition of the Higher Grade Matriculation examination papers analysed. The object of this test is to provide that early indication to pupils of their ability to cope with the level of mental process required by the Higher Grade course in Mathematics. The investigation describes the construction, administration and further development of the test device and, furthermore, seeks to show its predictive validity for the Matriculation examination in Mathematics by comparing test results with successive school examination results over a three year period. The possibility of sex differences in Mathematics achievement and prediction are also investigated on the basis of the results obtained during the course of this experiment. General conclusions are drawn, the difficulties encountered are discussed and some suggestions for further research are offered.

D.Ed. (Subject Didactics) / The lack of explicitly formulated criteria for the writing of a mathematics textbook, has the implication that the author of a mathematics textbook has to establish his own criteria. In doing this the author may achieve his objectives but his objectives may not necessarily be those of the curriculum. The purpose of this study is to develop criteria for the writing of a mathematics textbook. In order to do this the history of mathematics from the time of the ancient Egyptians to the present and the various ways (structure) in which mathematics manifests itself have been discussed. The most prominent theories on how children learn, together with the classroom situation as far as mathematics is concerned have been discussed to determine the implications they have for the writing of a mathematics textbook...

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.

M.Ed. (Mathematics) / The rising of the problem whether competency based education (CBE) programs produce better results than conventional edu - cational report. methods has been investigated and discussed in this A comprehensive literature study indicated that the upholders of the CBE program advocated beter results than the conventional educational methods. Research showed positive results. An empirical research on the micro-level was launched to de - termine whether this was the case or not. The procedure was to use a group N1-students, at a technical college of the Department of Education and Training, who were not familiar with the N1-Mathematics syllabus. An experimental group as well as a control group was selected at random. The experimental group was subjected to the CBEmethod and the control group to the conventional method of teaching of N-Mathematics. Prior to the research both groups were subjected to a standard N1-Mathematics test without preparation. These results were used for the pretest. The national N1-Mathematics examination was used for the post test, after completion of the course. The pretest results were compared to determine whether there was a significant difference in the level of the foreknowledge of the two groups...

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

This study was motivated by the latest revision of the mathematics syllabuses of the Cape Education Department. The most important changes to content in the Senior Secondary Mathematics Syllabus (July 1984) are the introduction of calculus and linear programming, the substitution of a section on analytical geometry for vector algebra and the recall of the remainder and factor theorems. The way in which these changes were introduced left the task of integrating them into the teaching process in the hands of individual teachers. This is a task of extreme importance. If one's classroom practice is to simply plough one's way through the syllabus, one loses many opportunities to make the study of mathematics meaningful and worthwhile. Accepting the view of the spiral nature of the curriculum where one returns to concepts and procedures at increasing levels of sophistication, one needs to identify the position of topics in this spiral and to trace their conceptual foundations. Analytical geometry is in particular need of this treatment. Similarly there are many opportunities for preparing for the introduction of calculus. If the teaching of calculus is left until the last moments of the Standard 10 year without proper groundwork, the pupil will be left with little time to develop an understanding of the concepts involved. It is the advent of calculators which presents the greatest challenge to mathematics education. We ignore this challenge to the detriment of our teaching. Taken seriously calculators have the potential to exert a radical influence on the content of curricula and examinations. They bring into question the time we spend on teaching arithmetic algorithms and the priority given to algebraic manipulation. Numercial methods gain new prominence. Calculators can even breathe new life into the existing curriculum. Their computing power can be harnessed not only to carry out specific calculations but also to introduce new topics and for concept reinforcement. The purpose of this study has been to bring about a proper integration of the new sections into the existing syllabus and to give some instances of how the calculator can become an integral part of the teaching/learning process

Bibliography: pages 82-84. / This dissertation is concerned with aspects of the role of the textbook in school mathematics. An attempt is made to uncover control strategies used by the teacher in textbook use in the classroom, and those implicit in a mathematics textbook. It is argued that these forms of regulation place constraints on the transformative role sometimes attributed to textbooks. The following research question is addressed: how does the teacher recruit the textbook in the classroom, how is he/she 'recruited' by it and how are both recruited by school mathematics? A case study methodology is described, involving a video-recording of a fifty minute mathematics lesson and a follow-up interview with the teacher. Transcriptions are used and a fine-grained analysis of data is attempted. A literature survey examines other research in the areas of content selection, content control and content expression. Content selection refers to choices and omissions, content control refers to sequencing, pacing and authority in the pedagogic relationship, and content expression includes verbal and textual modes of expressing content. Theoretical ideas are drawn from Bernstein (1976, 1991, 1993) and Dowling (1993). Although these works are methodologically different, they both describe aspects of regulation and control. Of particular interest are Bernstein's notions of classification and framing, and Dowling's ideas on discourse and procedure. The hypothesis is put forward here that there is a dialectical relationship involving the positioning of teacher and textbook. The teacher recruits the textbook to regulate pupils and knowledge, but s/he is at the same time constrained by strategies implicit in the textbook. In other words the teacher both positions and is positioned by the textbook. Both in tum are positioned by school mathematics. The data analysis examines the 'how', 'what' and 'who' of control. It considers the regulation of speech, silence, working and listening, as well as the sequencing, pacing, selecting, presenting and authorising of content. It argues that the teacher both recruits and is 'recruited' by the textbook, and that although the framing is strong and the teacher has a high degree of control in the pedagogic relationship, the classification is also strong and the teacher lacks control over what she can teach and the relationship between contents. The research concludes by suggesting that the transformative role sometimes attributed to the textbook is problematic. The strategies of regulation and control operating in the classroom, implicit in the textbook and in school mathematics, limit the possibilities of how textbooks can be used by the teacher and constrain transformation to a significant degree.

Thesis (M.Ed. (Mathematics)) ---University of Limpopo, 2016 / This research explored the pedagogical content knowledge (PCK) of algebra as held by a group of senior phase teachers in Limpopo Province, South Africa. Sixty-one teachers from different districts in the province participated in this study. This qualitative study used a case study design. Data was collected using a test and content representation (CoRe) matrix. The results were analysed through analysis of narratives. The study revealed that most of the teachers could not identify the main concepts that are taught in algebra. It was discovered that some could not differentiate between algebra and arithmetic. The findings also point out that the teachers had inadequate knowledge of algebra subject matter. The participants were able to identify some of the concepts that learners were supposed to do in the next grades. The findings revealed that most of the participants did not know the importance of teaching algebra. It was revealed that most participants could not identify the learners‘ difficulties; they could not specify the procedures they followed when teaching the identified main concepts in algebra, or give reasons for using those procedures. Furthermore, they could not specify factors that influenced their teaching. However, they were able to indicate different methods they used to assess learners‘ understanding. It was concluded that these teachers had inadequate PCK of senior phase algebra. The study recommends development programmes for both subject matter knowledge and PCK for practising teachers. Keywords: pedagogical content knowledge, content representations (CoRes), algebra, senior phase mathematics teachers.

Over the past several decades there has been an emphasis on educational research pertaining to learners’ performance in Mathematics and on finding methods to improve learner performance in this subject. In South Africa, Grade 12 learners’ results in Mathematics from 2010 to 2013 were unsatisfactory as shown in DBE, 2013a. The teachers are challenged to find new teaching methods that will make the subject more interesting and appealing to the learners (Oliver & Makar, 2010 in Goos, 2010). The purpose of this study was to investigate the effect of using computers in the teaching and learning of Mathematics with special reference to the topic of linear functions in order to improve learner performance. The literature reviewed shows that the use of computers not only improves the learners’ performance but also changes their attitude towards Mathematics (Bester & Brand, 2013). The quantitative research approach was used to gather the data, namely the quasi- experimental, non-equivalent control group pre-test-post-test design. Two intact classes formed part of the research study, that is an experimental group (n=50) and control group (n=50). The experimental group learnt the concept of linear function using GeoGebra software. The control group learnt the same concept through the traditional pen and paper method. The data were analysed using the SPSS on ANOVA. The results indicated that there was a significant difference between the mean scores of the experimental group (μ=70.5) and the control group (μ=47.5). From the results it was evident that the use of computers had a positive effect on learners understanding of linear functions as reflected in their performance and on their attitude towards Mathematics, as seen in the questionnaire responses. / Mathematics Education / M. Ed. (Mathematics Education)

Over the past several decades there has been an emphasis on educational research pertaining to learners’ performance in Mathematics and on finding methods to improve learner performance in this subject. In South Africa, Grade 12 learners’ results in Mathematics from 2010 to 2013 were unsatisfactory as shown in DBE, 2013a. The teachers are challenged to find new teaching methods that will make the subject more interesting and appealing to the learners (Oliver & Makar, 2010 in Goos, 2010). The purpose of this study was to investigate the effect of using computers in the teaching and learning of Mathematics with special reference to the topic of linear functions in order to improve learner performance. The literature reviewed shows that the use of computers not only improves the learners’ performance but also changes their attitude towards Mathematics (Bester & Brand, 2013). The quantitative research approach was used to gather the data, namely the quasi- experimental, non-equivalent control group pre-test-post-test design. Two intact classes formed part of the research study, that is an experimental group (n=50) and control group (n=50). The experimental group learnt the concept of linear function using GeoGebra software. The control group learnt the same concept through the traditional pen and paper method. The data were analysed using the SPSS on ANOVA. The results indicated that there was a significant difference between the mean scores of the experimental group (μ=70.5) and the control group (μ=47.5). From the results it was evident that the use of computers had a positive effect on learners understanding of linear functions as reflected in their performance and on their attitude towards Mathematics, as seen in the questionnaire responses. / Mathematics Education / M. Ed. (Mathematics Education)