Magister Educationis - MEd (Mathematics)

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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 of graphic calculators on the mathematical achievement in quadratic functions of urban Eritrean grade 10 students
(University of the Western Cape, 2003) Mebrahtu, Amare Teclemicael; Julie, Cyril
The purpose of this study was to investigate the effect of graphic calculators on the mathematical achievement of Eritrean grade 10 students related to the concepts of quadratic function. The study adopted a quasi-experimental design that involved two groups of students: the graphic calculator group and paper and pencil group. A total of 41 students from two secondary schools were involved in this study. 20 students were in the graphic calculator group and 21 in the paper and pencil group. A quadratic functions test was used to determine whether there is a significant difference in the mean achievement score between the two groups at the pre-test and post-test stages. The groups were compared by using the student's t test for independent samples.
Eritrean grade eight student understanding of algebraic variables
(University of the Western Cape, 2003) Yosief, Tekie Sium; Julie, Cyril
This study investigated Eritrean grade eight students' understanding of algebraic variables. A complete count survey of all secondary schools of one province was done and the one that took part in the study was Gash-Barka province. The study adopted the test and framework developed by Kuchemann (1980). Children's responses and the items themselves were classified into "levels of understanding". Items of the test were classified into four levels based on the name that can be given to letters in solving a problem and the structural complexity of the item. These items were used to classify the Eritean grade eight students' performances into five "levels of understanding".The present study produced results that showed that 72.6 % of the students dealt with letters in algebraic expressions and equations as objects. Whilst 3.7 % of the students were able to regard letters as specific unknowns, only 0.2 Yo of the students were able to consider letters as generalized numbers or variables. That is, almost all (95.9 %) of the tested Eritrean grade eight students were unable to cope consistently with items that can properly be called algebra, that is, items where the use of letters as unknown numbers cannot be avoided. Comparisons by school and gender were done to see if there were relationships among the levels of understanding and the two variables. The findings showed that there was no significant relationship among the levels of understanding and gender of the students. However, the comparison by school showed that there was significant relationship between schools and levels of understanding. The Pearson chi-square test showed that the relationship between the level of understanding and gender was not significant, whereas the relationship between levels of understanding and school was statistically significant at 0.05 level of significance.
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.
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.
An investigation into the nature of verbal interactions during the practical training of medical technology students
(University of the Western Cape, 1999) Paulsen, Moira Catherina; Julie, Cyril
various ideas have been propagated regarding the way people come to know in apprenticeship situations. The particular set of social practice theory that informs this study is that related to old-timers and newcomers. The newcomer comes to know by constant engagement in the activities of the community of experts. This study shows that being around the old-timer does not necessarily gibe rise to learning if the contact between these two agents does not occur as a shared practice. This shared practice will facilitate the curriculum that must exist between them. This curriculum be it a learning curriculum and/or a teaching curriculum can only be successful if the shared practice is transparent to the newcomer, and the newcomer is accepted as a legitimate peripheral participant. The participation of the newcomer in the activities of the old-timer ensures learning to occur. As long as the old-timer prevents the newcomer from engaging in the authentic tasks of medical technology, the newcomer will fail to develop a sense of the 'whole' of the trade and learning will be impaired. The old- timer provides a bridge between the development of knowledgeable skill and identity, and the production and reproduction of a community of experts. The author's own experience in Medical Technology training and the increasing challengers to empower learners generated questions around the training of medical technology students. It is argued that learners make sense of theoretical ideas by 'doing' that what is learned in the theory. This necessitates the use of the tools of the trade. During this engagement with the tools various phases can be operated in. These phases include the 'way-in' phase and the 'practice phase'. Medical technology practice i.e. the way medical technologist engages in the trade allows for the development of a community of experts. This however also requires the development of certain skills. These skills can be cognitive- and/or practical skills. This study put emphasis on the nature of verbal interactions during the practical training of medical technology students. The study further provides evidence that apprenticeship training of medical technology students takes the form of imitation, i.e. it is unsystematic and unsupported. The emphasis of the training is on service delivery rather than on teaching. There is visible between learning in the formal academic setting (Site A) and learning in the apprenticeship learning situation (Site B).

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