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Browsing by Author "Mbekwa, Monde"

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An analysis of learners’ ways of working in high stakes mathematics examinations: quadratic equations and inequalities
(2012) Godden, Hebrew J.; Julie, C.; Mbekwa, Monde
Every year there is a national outcry by educationists in South Africa relating to the poor performance of grade 12 mathematics learners. This is an unsatisfactory state of affairs in a country where mathematics is seen as playing a pivotal role in the preparation of students in disciplines for careers in science and technology. Interventions by the Department of Basic Education as well as by provincial education departments do not seem to be successful in stemming the tide in the decline of standards in the mathematical performance of learners. It is this which has motivated this study.The aim of this study was to identify the types of errors committed by students in their responses to question one of Paper 1 in the final Grade 12 mathematics examinations of 2010. By reviewing the work done by different authors, an analytical framework was compiled that was used to identify and to label errors in the written responses of learners. This study has adopted a documentary analysis approach and has selected a representative sample of examination scripts of Western Cape students who wrote the first paper of the grade 12 mathematics examination in 2010. The result shows that during the analysis of 1959 scripts (the sample taken from different educational departments and districts), 4163 errors were identified. These errors have been identified based on the above-mentioned analytical framework. Comparisons were labeled according to the different types of errors, across the different ex- department schools and per districts. If the percentage is calculated based on the number of scripts analyzed, the number of errors varies from 12% careless errors to 40% calculation errors. It was also noticed that the number of errors found in the urban districts was higher than all of the errors found in the different rural districts. In return, in the urban districts, the numbers of errors found were evenly distributed over the four districts. When the different ex-department schools were compared, the numbers of application and procedural errors were significantly higher in the DET schools(Department of Education and Training, which consists of mostly black disadvantaged learners) than all the other schools. The rest of the errors were evenly distributed over all the exdepartment schools. The inability of learners solving inequality equations stood out as a major concern.
Analysis of the ways of working of learners in the final grade 12 mathematical literacy examination papers: focussing on questions related to measurement
(University of Western Cape, 2012) Simons, Marius; Julie, Cyril; Mbekwa, Monde
Mathematical Literacy has a dual meaning in South Africa. On the one hand it alludes to an understanding of the role of Mathematics in the real world. On the other hand it refers to a subject that is taken by students who generally do not do well in Mathematics and who do not wish to do a pure Mathematics course, This research focuses on the identification and investigation of errors, misconceptions and alternative ways of working in the responses of students in the final grade 12 Mathematical Literacy examination. The aim was to identify the errors, misconceptions and alternative ways of working and to discuss possible reasons for these errors and misconceptions. This aim was governed by the principle that feedback to students and teachers form a vital component in the teaching and learning process. This analysis only focused questions pertaining measurement in Mathematical Literacy. An analytical framework was constructed based on common errors and misconceptions identified by various researchers’ in the field of Mathematics. This analytical framework was used to classify and analyse the errors, misconceptions and alternative ways of working in Mathematical Literacy. The analysis was done using document analysis on a randomly selected sample of Mathematical Literacy scripts taken from across all education districts in the Western Cape. Great care was taken to prevent bias and cross checking was done by peers to ensure that the categories of errors were agreed on. The results of the analysis revealed that the errors identified for Mathematics are common to those of Mathematical Literacy. The findings in this project suggest that the analysis and feedback of errors and misconceptions may help to improve teaching and learning in Mathematical Literacy.
A case study of how learners apply a Grade 10 study skills module in a mathematics class
(University of the Western Cape, 2016) Arnold, Feeroezah; Julie, C.; Mbekwa, Monde
A qualitative case study was used to investigate how learners apply a study skills guide during the teaching of mathematics content in a Grade 10 class. A great amount of research and money is continually spent focussing on improving mathematics performance throughout the world. Performance of our learners in South Africa is of concern to the government as well as educators. Researchers agree that many learners lack effective study skills, which is the reason for their poor performance in mathematics. This study intended to infuse study skills in mathematics lessons as an intervention. The study skills intervention sessions were done over a period of 6 weeks. These study skills were infused in topics of the mathematics curriculum which was done in the previous quarter of the school program. Data was collected through interviews, journal entries and a questionnaire. The interviews were done before study skills instruction while the questionnaire was administered after completion of the sessions. Journal entries were completed during the 6 week instruction period by learners. It was found that some learners used the study guide as intended whilst others did not. Furthermore there was improvement in learners' scores for the topics focused on at the end of the study compared to the scores for similar topics in a school-based test written about two months before the intervention. It is concluded that the infusion of study skills in lessons has the potential for improving achievement in high-stakes mathematics examinations.
A comparison between the contexts grade 10 learners prefer for mathematical literacy and those reflected in the timss survey
(University of the Western Cape, 2006) Snyders, Charles John; Julie, Cyril; Mbekwa, Monde
This study focuses on the contexts grade 10 learners prefer to deal with in mathematical literacy. These preferred contexts of the learners were then compared with the contextual situations found in the Third International Mathematics and Science Study (TIMSS). The most important findings of this study are that grade ten learners from low socio-economic environments regard mathematics and mathematicians' practices as the most favoured items. The extra-mathematical clusters that they prefer are the technology and health cluster. TIMSS designers favoured the financial cluster favoured with youth cultural elements and technological devices that the youth are associated with. What learners find relevant or interesting may differ from what designers of tests may perceive to be relevant or vice versa.
A comparison between the contexts grades 10 learners prefer for mathematical literacy and those reflected in the PISA survey
(University of the Western Cape, 2008) Hartzenberg, Louis Reginald; Julie, Cyril; Mbekwa, Monde
The study focuses on the contexts grade 10 learners prefer to deal with in Mathematical Literacy. These preferred contexts of the leamers were then compared with the contextual situations found in the Organization for Economic Cooperation and Development's (0ECD) Programme for International Student Assessment (PISA). The most important findings of the study are that the grade l0 leamers from low socioeconomic environments regard the intra-mathematical clusters as the most favoured items. In the extra-mathematical cluster learners favoured technology and health. PISA designers favoured the mathematical cluster followed by physical science and the finance cluster. The context preferred by learners may differ from what designers of tests may perceive to be relevant or interesting and vice versa.
A comparison between the contexts learners in Grades 8, 9 and 10 prefer for mathematical literacy and gender
(University of the Western Cape, 2008) Cornelissen, Belinda M.; Julie, Cyril; Mbekwa, Monde; Faculty of Education
For many years, there have been calls for the mathematics curriculum in South African schools to be made more meaningful and relevant to young people's everyday lives. Despite efforts to address this issue, there is a widespread perception wihtin the mathematics education community that much remains to be seen. Broadly, this study focused on the contexts preferred by grade 8 , 9 and 10 learners as a domain in which to embed mathematics. The particular focus was on whether gender played a role in the preferences expressed by these learners for contexts.
A comparison of grade 8 to10 urban and peri-urban learners context preferences for mathematical literacy
(University of the Western Cape, 2009) Blaauw, Christopher; Julie, Cyril; Mbekwa, Monde; NULL; Faculty of Education
The study explored the comparison of grade 8 to 10 urban and peri-urban learners' contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas; least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners.
The contexts which Namibian learners in grades 8 to 10 prefer to use in mathematics
(University of the Western Cape, 2012) Shifula, Loide Ndahafa; Julie, Cyril; Mbekwa, Monde; NULL
One of the key ideas in the research on mathematics education is that the mathematical knowledge that learners acquire is strongly tied to the particular situation in which it is learnt. This study investigated the contexts that learners in grades eight, nine and ten prefer to deal with in the learning of mathematics based on their personal, social, societal, cultural and contextual concerns or affinities. The study is situated in the large-scale project called the Relevance of School Mathematics Education II (ROSMEII), which is concerned with the application and the use of mathematical knowledge and processes in real life situations. It is based on a survey of learners from ten (10) secondary schools in the Oshana and Khomas regions of Namibia. The ten schools that were sampled represent the spectrum of schools in Namibia in both urban and semi-urban areas. The Rasch model of data analysis is employed to provide some insight into the contextual situations learners would like to deal with in their mathematical learning. The data obtained for this study was analysed using the WINSTEPS Version 3.65.0 suite of computer programs. The current study arises from a concern about the absence of the voices of learners in the contextual situations in mathematics selected by adults such as mathematics teachers, inspectorates and curriculum and materials developers. The assumption is that the inclusion of learners’ insights into mathematics curricular might enhance mathematical learning. The study reveals that school children have an intrinsic desire to learn about mathematical issues embedded in real-life contexts. Several items which Namibian learners have shown interest in are issues they experience in life out of school which are not directly dealt with in school, such as managing personal and financial affairs, health matters, technology, construction, engineering and government financial matters. However, learners indicated to have a low preference in contexts like lotteries and gambling, national and international politics, cultural products, all kinds of pop music and dancing. This thesis contends that the inclusion of contexts in the mathematics curriculum which are of interest to learners will go a long way in facilitating good performance of learners in mathematics.
The effect size of an intervention focusing on the use of previous national senior certificate mathematics examination papers
(University of Venda, 2016) Julie, Cyril; Mbekwa, Monde; Simon, Marius
This study reports on an intervention that emanated from a concern a mathematics teacher had about the unsatisfactory performance of grade 12 learners in the school-based mid-year examination. The intervention was based on distributed practice and the effect size of the intervention was determined as an indicator of the effectiveness of the intervention. Different effect sizes are reported and the reasons for their acceptance or non-acceptance are presented. Overall the results indicate that if all the different effect sizes are taken into account, the intervention had a medium to high effect. Given that the intervention was driven by aspects of teaching and was done at school, it is recommended that more attention be accorded to those aspects of teaching that enhance achievement in Mathematics.
The effects of examination-driven teaching on mathematics achievement in Grade 10 school-based high-stakes examinations
(AOSIS, 2018) Okitowamba, Onyumbe; Julie, Cyril; Mbekwa, Monde
Various efforts are underway to improve achievement in high-stakes examinations in school mathematics. This article reports on one such initiative which focuses on the development of quality teaching of school mathematics by embedding it within an examination-driven emphasis. A quantitative approach was used to analyse the performance of Grade 10 learners in three consecutive end-of-year school-based examinations set by the initiative. Results indicate a trend in a positive direction over the three-year period. Nevertheless, there was a discernible decrease between the first and second administration of the examinations. It is concluded that examination-driven teaching holds a promise for enhancing achievement in high-stakes school mathematics examinations if sensibly and sensitively implemented.
Evaluation of an in-service degree programme at a Nigerian University
(University of the Western Cape, 2019) Fatoba, Abiodun Folakemi; Mbekwa, Monde
The Sandwich degree programme is an in-service training programme run by Nigerian Universities for primary and secondary school teachers who either do not have a first degree or those who do not have professional teaching qualifications. The main aim of this study was to evaluate the Sandwich degree programme at Fountain State University in Nigeria, and determine its impact on improving the subject content knowledge of teachers. This study was spurred by the poor performance of some learners in both external and internal examinations despite several efforts made by the government to improve the quality of education in Nigeria. The poor performance of learners has often been blamed on teachers who have no teaching qualifications and hence lacked pedagogical knowledge. The study therefore investigated the Sandwich degree programme at Fountain State University which was specifically designed to upgrade the qualifications of teachers. The study investigated the Sandwich degree programme to determine whether it adequately enhanced teachers’ content and pedagogical knowledge. The evaluation of the Sandwich degree programme was carried out using Kirkpatrick's Four-Level Training Evaluation Model. The study employed a qualitative research paradigm. The research sample comprised of three university lecturers (Sandwich degree lecturers), the director of the Sandwich degree programme and eight high school teachers purposively sampled who are graduates of the Sandwich degree programme. Data collection was achieved by means of questionnaires, semi-structured interviews and documentary analysis.
Exploring translanguaging practices in a multilingual grade 6 mathematics classroom
(University of the Western Cape, 2024) Claasen, Leona; Mbekwa, Monde
Even though the South-African education system has undergone profound changes in the decades of democracy, and various language policies have been implemented and re-implemented, language practices in basic and higher education still reflect the legacy of colonialism and apartheid. A particular consequence of this is evident in mathematics where learners’ poor performance can be located in a disjuncture between multilingual classrooms and the language of instruction. This study analyses how translanguaging practices are used in a multilingual grade 6 mathematics classroom to facilitate mathematical understanding. The aim of the study was to see whether, and if so how, the teacher and learners use translanguaging practices in the mathematics classroom in lessons relating to the topic in question. The research questions explored in this study examine firstly, the purpose of translanguaging in a grade 6 mathematics classroom; secondly, the dynamics of translanguaging and thirdly, perceptions and experiences of the teacher and the learners with respect to translanguaging.
Implementing an intentional teaching model to investigate grade 9 learners’ ways of working with rational algebraic fractions
(University of the Western Cape, 2019) Maphini, Nwabisa Vivian; Mbekwa, Monde; Julie, Cyril
In South Africa it is widely known that most learners struggle with mathematics. The results for mathematics are poor. The department of basic education offers a number of intervention programmes to assist learners in mathematics but the problem still persists. Algebra is the most basic and important topic in mathematics as it becomes an element in almost all the other topics in mathematics curriculum. Algebraic fractions in particular are a challenge for most leaners. Research shows that learners commit a number of errors when they work with algebraic fractions. The study investigated the implementation of an intentional teaching model into grade 9 mathematics learners’ ways of working with rational algebraic fractions. An intentional teaching model is a teaching strategy which emphasizes teaching intentions or teaching objectives are brought to the fore during a lesson, the model emphasizes the use of spiral revision and assessment for learning. Ways of working in this study refers to the way in which learners deal with algebraic fractions when they simplify them including the errors they commit from the misconceptions they have about aspects of working with fractions. The study was conducted in a group of grade 9 mathematics learners at Gugulethu High school, which is located in Guguletu, a township in the Western Cape Province of South Africa. The study is premised on a qualitative research paradigm which focuses on studying situations in their natural settings and applying an interpretive perspective. Data was collected by means of observation and video recording of lessons while learners were engaged in working with algebraic fractions. Learners’ written work was analysed as part of the data collection. The results of the study show that leaners commit a number of errors when they manipulate algebraic fractions. Among other errors are: (i) Cancellation errors which had the highest frequency of occurrence (ii) Defractionalisation (iii) No recognition of the common factor and (iv)Exponential laws error. It was found that the learners’ ways of working with algebraic fractions are mostly characterised by their misunderstanding of exponential laws and difficulty in working with fractions needing the use of factorisation to simplify and find the lowest or highest common denominator during addition or subtraction. The results of the study also reveal that learners struggle to articulate extensively or in detail what they are actually doing as they simplify rational algebraic fraction.
Implementing an intentional teaching model to investigate the algebraic reasoning of grade 9 mathematics learners
(University of the Western Cape, 2019) Davids, Jade Ethel; Mbekwa, Monde
This research has employed an intentional teaching model to investigate the algebraic reasoning of grade 9 learners from a low socio-economic background. It has also sought to study how learners engage with algebra to make generalizations and to scrutinize any misconceptions deriving from the experience. They looked for patterns, paid attention to aspects of the patterns that are important and then generalized from familiar to unfamiliar situations. Algebraic reasoning underpins all mathematical thinking including arithmetic because it allows us to explore the structure of mathematics. This study is based on the Curriculum and Assessment Policy Statement which states that learners are expected to investigate patterns to establish the relationships between variables, as well as represent and analyse the change of patterns. The study also had a huge emphasis on algebra. According to Mphuthi & Machaba (2016): “Algebraic expressions form part of the senior phase CAPS curriculum in South Africa. A substantial amount of time is allocated to this section on evaluating expressions and simplifications of algebraic expressions in grade 7-9.” The study is premised on a qualitative research paradigm and a design-based research methodology for data collection. A set of tasks based on algebraic patterns and generalizations was given to an opportunistic sample of 20 grade 9 learners in a school in Delft, a low socio-economic suburb about 30 kilometres from Cape Town in the Western Cape Province of South Africa. Three weeks after completing the tasks, learners were interviewed to identify their reasoning and how they felt about the tasks. The results of the study show that the majority of the learners struggled with tasks especially when asked what the rules they could derive from the patterns. Learners did not seem to understand what they were doing because they were unable to articulate the given tasks in words and did not have knowledge of concepts like the perimeter.
Investigating the impact of an intervention programme in a Grade 11 mathematics class : a case study
(University of the Western Cape, 2015) Mnqwazi, Xabiso Priceless; Julie, Cyril; Mbekwa, Monde
The general performance of learners in mathematics in most secondary schools in South Africa is not encouraging. Statistics reveal that there is a general poor performance in mathematics and related science subjects especially in those schools located in previously disadvantaged communities. There is just a need for appropriate interventions of the significance of mathematics in present society which is now characterised by high information and technology thrust. The objective of the study was to investigate the impact of the tutorial intervention programme on the performance of a grade eleven mathematics class with a view to improving the mathematics performance of these grade 11 learners. The selection of the action research based method was premised on the idea that it would help the researcher to improve his tutoring practice as well as contributing to better learner performance. Data was collected through the use of qualitative research methods. These involved observation, the utilisation of focus group discussions of learners, and in-depth interviews with randomly selected learners and other mathematics colleagues. A careful mix of learners of different learning abilities was made so that high performers would assist those whose performance was lower. In each group of five at least two high performers were included. Findings of the study point to the effectiveness of the tutorial process, justifying its adoption on a long term basis. In general, it can be concluded that the tutoring strategies used by the researcher had a positive effect on the knowledge retention of the learners. This conclusion was arrived at from an observation of improved test results over time, the learners‟ views in the questionnaires as well as those of peer observers.
Investigation of learners’ ways of working with algebraic graphs in high-stakes mathematics examinations
(University of the Western Cape, 2015-11) Lumbala, Paul Desire Mutombo; Julie, C; Mbekwa, Monde
Algebraic graphs are a difficult topic for most secondary school mathematics learners. My experience as a Mathematics teacher in the Further Education and Training Phase (FET) is that learners solve problems involving graphs with difficulty. Consequently, the purpose of this research was to investigate learners’ ways of working with algebraic graphs in high-stakes examinations including their errors and misconceptions in this respect. The investigation carried out to identify learners’ errors and misconceptions is based on the analysis of 444 scripts from the 2012 grade 12 final Mathematics examination. More specifically, the study aimed to investigate the ways learners used to solve questions related to graphs in this examination. The focus of the study was the algebraic graphs tested in Paper 1 of the National Senior Certificate (NSC) examination with an emphasis on the identification of errors exhibited in the learners’ scripts. The study adopted a qualitative approach using documentary analysis methodology. As data, the study used the scripts of the final grade 12 Mathematics examinations of schools participating in a project for the improvement of Mathematics based at the University of the Western Cape (UWC). The analysis of learners’ scripts reveals that learners make many errors when they work with algebraic graphs. These errors that have been found in this investigation were coordinate, intercept, domain and range, asymptote, identification, drawing and function errors. Additional errors which were identified are transformation and inverse errors.
Preferred contexts for mathematical literacy of Korean grade 8-10 learners
(University of the Western Cape, 2006) Kim, Sun Hi; Julie, C; Mbekwa, Monde; Faculty of Education
The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in comparison to those of other countries. Based on these observations, the present study was an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of the study was to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study paid more attention to mathematics education in real life situations.
Preferred contexts of Korean youth for the learning of school mathematics (grades 8-10)
(2012) Kim, Sun Hi; Julie, Cyril; Holtman, Lorna; Mbekwa, Monde
This study investigated real life situations which learners in South Korea grade 8-10 learners would prefer to be used in school mathematics.This thesis is based on the ROSMEII (Relevance of School Mathematics ducation) questionnaires and interviews, which was used to examine the preferred mathematical learning contexts for South Korean grade 8-10 learners. The study investigates the affective factors that pupils perceive to be of possible relevance for the learning and teaching of mathematic; and is aimed at providing data that might form part of a basis for a local theory of the mathematics curriculum. The standardized ROSMEII survey questionnaire of 23closeended items that relate to some aspects of mathematics on a 4-point Likert-type scale was administered to Korean grade 8-10 learners at the end of compulsory schooling, and mainly 14 to 16 year old cohorts. The data for this study were collected from a sample of 1839 learners drawn from 26 South Korean schools in the year 2009. Interviews were conducted to gauge the pupils‘ preference of the ROSMEII questionnaire contexts and used to validate learners‘ responses. In analyzing their responses, it became clear that, on the average, views expressed were common to all groups of pupils in South Korea (whether male or female, or from the metropolitan, city, or countryside). The clusters of the most preferred mathematical learning contexts are linked to youth culture, which learners are usually and easily engaged with in one way or another. These clusters include the sports, leisure and recreation cluster; planning a journey/popular youth culture cluster the technology cluster; the making of computer games, storing music and videos on CD‘s and Ipods. The lowest preferred mathematical learning contexts are: an agricultural cluster which focuses on agricultural matters and traditional games (yut). In conclusion, this study suggests that teachers should use contexts that increase learners‘ interest in classroom activities. Therefore mathematics curricula and textbooks which are appropriate to this context must be provided in order to provide more efficient mathematics education. It is imperative that the Korean school system must develop a particular program for nurturing learners‘ mathematical power. Furthermore, mathematics education policy makers must reconsider whether the current education system is appropriate, and also listen to learners‘ preferences when designing appropriate mathematics curriculum and textbooks.
Problem-solving in geometry in collaborative small group settings: how learners appropriate mathematical tools while working in small groups
(University of the Western Cape, 2011) Cooper, Phadiela; Mbekwa, Monde; Julie, C
Problem-solving in Mathematics is an important skill. The poor performance of South African learners in international tests such as the Trends in International Mathematics and Science Study (TIMSS) and in schools in general indicates that emphasis should be placed on problem-solving in the teaching and learning of Mathematics. The new national senior certificate curriculum in South Africa encourages group work amongst learners. The thesis proposes that learning is enhanced in a small-group setting, since learners actively engage with the problems. Furthermore, Euclidean Geometry is perceived by learners to be a „difficult‟ section of Mathematics. However, Geometry is important since the skills acquired while doing Geometry can be applied to various fields of study. This research focused on Geometry problem-solving in collaborative small-group settings. An inductive approach was taken that focused on what learners were doing while they were doing problem-solving in geometry in collaborative groups. Problem-solving is viewed as a situated and contextually-determined activity. The research focused on how learners appropriated tools (physical as well as intellectual) and how they interacted with one other and the subject matter. The socio-cultural perspective was the theoretical framework underpinning the study. In this perspective, learning is seen as a social process in which learners actively participate and contribute with ideas and arguments. In addition, learning is seen as a situated activity. The research was carried out in the form of a case study that focused on three groups of three learners each, from a secondary school in Khayelitsha, a township approximately 30 km outside Cape Town, South Africa. The small groups were monitored and observed in a school setting and special attention was given to their interaction within their group, given their social and cultural context. The ethnographic approach to data gathering, which allows for the routine, everyday, taken-for-granted aspects of school and classroom life, was used. Data were collected by means of audio and video recordings, interviews with learners and teacher observations. The data analysis included analysis of field notes, audio and video transcripts and learners‟ written work. The data were analysed in terms of Pickering‟s theory that all scientific practice is a “dialectic of resistance and accommodation” and that this constitutes a “mangle of practice” (Pickering, 1995).

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