The researcher's experience as a high school mathematics teacher in several African countries convinced her that a good number of mathematics learners exhibit serious difficulties in conceptualising mathematics properly. Her experience in teaching the subject in the Ciskei since 1990 reinforced this conviction. The researcher's natural curiosity to probe into the causes of the poor state of mathematics education in the region served as the springboard into her investigation. Her thoughts developed in line with the emerging educational theories of social constructivism. This provided a conceptual framework for the solution of the problem, the feasibility of which was put to test practically in a Ciskeian classroom. She explicates that the difficulties experienced by the pupils in conceptualising mathematics are philosophically deep rooted and latent in the present system of mathematics education itself, which, in Ciskei, impedes the learners' conceptualisation owing to numerous problems related to their linguistic and cultural situatedness. In the analysis of the present system of mathematics education in the Ciskei she reviews a few recently published mathematics text books in the context of the topics chosen for her research study. The results of her classroom investigation establish that a possible solution to the problem lies in the social constructivist teaching approaches.

Like many South African high school mathematics teachers I have followed the development of computers with interest and I have tried wherever possible to gain some experience on them. Thus when microcomputers became more readily available the mathematics department at our school, Graeme College in Grahamstown, motivated for the school to acquire this powerful new tool. The eventual outcome was that the Old Boys' Association donated to the school 3 BBC B microcomputers with monitors, a disc drive, a printer and two tape recorders. These have now been in the school for three years. The acquisition prompted this research project which takes the following form:- 1) An investigation into some of the uses of microcomputers in schools and, in particular, in the mathematics classroom. 2) A statement on the present position adopted by the Cape Education Department on the use of computers in schools. 3) A study of what the experience has been in other countries, particularly in Britain and the United States of America. 4) A description of an investigation which was undertaken at our school using the method of Action Research and Triangulation. Its aim was to investigate the feasibility of using a microcomputer to aid in the teaching of mathematics and the reaction of the pupils to this innovation. Three different approaches were implemented. a) The algorithmic approach: In this investigation a class of standard eight pupils were required, with the help of the teacher, to write, enter and test a short computer program which would solve any pair of simultaneous linear equations of the form, ax + by = c. Their reaction to this form of instruction was noted by myself and a non-participant observer. The pupils themselves were also asked to express their reactions, both verbally and by filling in a prepared questionnaire. Examples of worksheets, exam questions and analysed questionnaires are given in the appendix. Short programs which examine various other mathematical concepts are also listed and discussed. b) The audio-visual approach: In this case use was made of a graphs software package in which the computer would draw either a straight line, circle, parabola or hyperbola when the appropriate variables were entered. This package also includes a graph game facility where participants are required to find the equation of the graph which will pass through three given points. Points are awarded if the correct type of graph is chosen and the variables are entered within a certain time interval. The pupils involved in this investigation were standard eight higher grade mathematics pupils and their reaction to this form of instruction was again noted using the methods described in (a) above. c) Computer Aided Instruction: Here I was most fortunate to be able to make use of the Rhodes University PLATO Centre. This allowed me to take a class of eighteen standard eight higher grade mathematics pupils to the Centre. Here during four sessions, each of just over an hour, the pupils interacted with the software on the computer terminal. The software used was a set of five lessons written by Barbara Lederman of the Community College Maths Group, of the University of Illinois in 1976. The lessons give instruction and require the pupils to transform, plot and draw the graphs of linear equations of the form, ax + by + c = 0, x = c and y = b. They are also taught and required to find the equations of given straight lines. Their reactions to this form of instruction are discussed after each session. 5) In conclusion some thoughts are given on how computers can best be utilised in the school situation, with particular reference to the teaching of mathematics.

I embarked upon this study to investigate mathematics teachers' practices that have led to the persistence of traditional teaching methods in grade 9 mathematics classrooms in Rundu. The study was conducted from a learner-centred (L-C) perspective or reform approach in the Namibian context. It is a qualitative study oriented in the interpretive paradigm- a paradigm that seeks to understand the meanings attached to human actions. The participants involved in this study were purposively selected and they are composed of two mathematics teachers and their grade 9 learners. This study was conducted at two schools in Rundu. One is an urban school while the other one is a rural school on the outskirts of Rundu. The research tools employed in this study are questionnaires, interviews and observations. The questionnaires were used to identify and select my participants while the observations were used to investigate the participants teaching strategies. The purpose of the interviews was mainly to investigate teachers' understanding, interpretation and implementation of learner-centre education (LCE). Amongst other findings, this study reveals that inadequate teacher-training, controversial educational policies and challenges such as overcrowdedness in mathematics classrooms, lack of teaching and learning materials, lack of cooperation among mathematics teachers and learners' negative attitude towards mathematics are some of the contributing factors to the persistence of traditional teaching methods in mathematics classrooms. Moreover, the study reveals that the persistence of traditional teaching methods in mathematics classes can no longer be attributed to the lack of understanding of LCE. The teachers in this study seem to be well acquainted with the theoretical aspect of the LCE framework while the implementation aspect seems to be a concern.

This qualitative investigation took the form of a case study and fell within the interpretive research paradigm. The Mathematics Chair at the Education Department of Rhodes University launched the Mathematics Teacher Enrichment Programme (MTEP) in 2010 in order to combat poor Mathematics performance of learners in the lower Albany district of the Eastern Cape. The challenge that the participating MTEP teachers faced was a lack of time available to implement new teaching ideas. This was because most of their time was spent catching up “lost” or untaught concepts in the classroom. To address this problem, the Catch-Up Project was launched, whereby selected Mathematics teachers in the area taught lost concepts to Grade Ten learners during afternoon classes in an attempt to improve their fundamental Mathematics knowledge. In order to establish which sections of Mathematics were more difficult for the learners in this programme, bench mark tests were administered biannually. Whilst these tests certainly identified deficient areas within their Mathematics knowledge, the poorest performance areas were the sections of the syllabus which were spatial in nature, such as Space and Shape and Geometry. However, a more in depth assessment tool was required to establish which specific spatial skills the learners were not able to employ when doing these Geometry tasks. To this end, the Spatial Skills Assessment Tasks (SSAT) was developed. It consisted of traditional text book type Geometry tasks and real-world context tasks, both of which were used to assess six spatial skills deemed crucial to successfully facilitate learning Geometry. The case study took place in two of the schools which participated in the Grade Ten Catch-Up project. The case was focused on Grade Ten learners and the unit of analysis was their responses to the SSAT instrument. The learners that participated all did so on a strictly voluntary basis and great care was taken to protect their wellbeing and anonymity at all times. The results of the SSAT instrument revealed that the real world context tasks were in general far more successfully answered than the traditional text book type questions. Important trends in learner responses were noted and highlighted. For example, geometric terminology remains a huge challenge for learners, especially as they study Mathematics in their second language. The ability of the learners to differentiate between such concepts as congruency and similarity is severely compromised, partly due to a lack of terminological understanding but also due to a perceived lack of exposure to the material. Concepts such as verticality and horizontality also remain a huge challenge, possibly for the same reasons. They are poorly understood and yet vital to achievement in Geometry. Recommendations for the development and strengthening of spatial skills support the constructivist approach to learning. Hands on activities and intensive sustained practice over a period of a few months, in which both teachers and learners are actively involved in the learning process, would be considered most beneficial to the long term enhancement of these vital spatial skills and to the learning of Geometry in general.

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Thesis submitted in fulfilment of the requirements for the degree Master of Education in the Faculty of Education at the Cape Peninsula University of Technology 2014 / This study investigates the effects of code switching in the learning of mathematics word problems in Grade 10. The research used Cummins’ language acquisition theory to inform the study. The study employed ethnographic qualitative research design whereby classroom observations and semi-structured interviews were used as data collection techniques. The use of multiple data collection techniques was to ensure validity and credibility of the study. The sample consisted of sixty learners and two mathematics teachers. The sample was drawn from a population of one thousand two hundred and thirty five learners and forty nine teachers.The study has shown that even though code switching could be beneficial in the learning and teaching of mathematics, it was difficult for learners and teachers to use it in a way that enhances the learning of mathematics word problems because of the barriers in the use of mathematical language. It is recommended that teachers should exercise care when using code switching, especially with the topics that involve word problems; as such topics are more aligned to certain mathematical language that could not be translated to IsiXhosa.

Thesis (MEd (Education))--Cape Peninsula University of Technology, 2017. / Learning Management Systems (LMS) have come into common use recently and most educational institutions from basic to higher education are increasingly adopting them, mainstreaming them into their daily teaching and learning of functions. The Western Cape Education Department piloted the Moodle (Modular Object Oriented Dynamic Learning Environment), a Learning Management System (LMS) aimed at improving teaching and learning. The aim of this research was to ascertain the effectiveness of this LMS in developing Grade 10 learners’ conceptual understanding of Functions in Mathematics with minimum educator assistance. The research investigated two classes; one class used the traditional chalk and talk teaching (control) while the other class was exposed to the Moodle LMS. The thesis unpacked the functionalities in Moodle that makes learning of Functions in Mathematics easier. Learners constructed their knowledge by using resources embedded in Moodle using “ScenTRLE” learning model that follows Vygotsky‘s Theory of Social Constructivism. The hybrid e-learning framework was used, where learners were expected to gain pedagogically by interacting with computers. Their interaction was monitored and results are recorded using online surveys and tests. A quasi-experimental design was used to compare the groups, then statistically analysed in comparison with the traditional way of learning. Results showed that the functionalities embedded within the Moodle LMS were instrumental in improving the learning and understanding of Functions in Mathematics.

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. / The aim of this theses is to find out whether there is any relationship between learners' attitudes and learning difficulties in mathematics: To investigate whether learning difficulties in mathematics are associated with learners' gender. To establish the nature of teachers' perceptions of the learning problem areas in the mathematics curriculum. To find out about the teachers' views on the methods of teaching mathematics, resources, learning of mathematics, extra curricular activities and multiracial schools

The research study focuses on assessment in Mathematics in Grade 10. The purpose is to identify problems which educators are experiencing in the assessment of Mathematics and to find possible solutions for the problems. This will enable the researcher to develop guidelines for facilitators at District Offices which in turn will contribute to more effective guidance and support for educators regarding assessment in Mathematics. The implementation of the National Curriculum Statement (“NCS”) in Grade 10 with a focus on outcomes-based assessment necessitates changes in the assessment practices in Mathematics. The literature examined views at the nature of Mathematics, constructivism and approaches to learning in Mathematics over the past century, outcomes-based education in the “NCS” and outcomes-based assessment in Mathematics. A pragmatic philosophy was followed. Both quantitative and qualitative methods of data collection were used in the study. Questionnaires were used to collect quantitative information and interviews made it possible to collect qualitative information. Questionnaires and interviews were administered, analysed and interpreted. From the analyses of the questionnaires, it was found that there is the perception that Mathematics is a subject with fixed knowledge, procedures and formulae. The educator still plays the dominant role in assessment and learners are passive in the construction of knowledge. The findings of the study revealed that the recording of outcomes-based assessment is too much and is time consuming. From the interviews it was found that the biggest changes that occurred in the Mathematics classroom because of the “NCS” were the assessment forms, - instruments and - methods. Factors that influence the assessment results in Mathematics are language, time, background and attitude of the learner and the training and experience of the educator. The recommendations of the researcher, based on the findings of the study, focus on the development of guidelines for assessment in Mathematics. The guidelines and recommendations are in the following areas: · Cognitive levels for the development of assessment tasks in Mathematics; · Outcomes in the determining of assessment strategies; · Daily assessment and formal assessment; · The development of assessment strategies; · The process of assessment; · Practical steps in the preparation of the assessment techniques; and · Guidance and support with regard to assessment to the teacher. Though the educators in this study could not solve many problems in assessment, bad planning and time-management created some of the problems. Furthermore, educators received guidelines for assessment from facilitators at District Offices, but they did not make it their own. Some educators did not take the responsibility to do research themselves and failed to adjust their assessment strategies. However, District Officials can still play a crucial role in initiating in-service training and projects that will focus on assessment. Furthermore, if facilitators at District Offices have good insight into the problems which educators are experiencing in Mathematics, they can guide and support educators effectively in the assessment processes in their classrooms. Good application of assessment in the Mathematics classroom, definitely contributes to improved quality of teaching of the subject and consequently a more skillful learner in the community. / Prof. J. Strauss