published_or_final_version / Education / Master / Master of Science in Information Technology in Education

M.Ed. (Subject Didactics) / Mathematics opens doorways for further studies and careers in the technological and information age. Many students experience problems coping with Mathematics in secondary school due to a multitude of factors. Some factors are connected with the student's innate abilities and the extent to which these have been developed, and others with the teaching practice. Problems include lack of conceptual development, skills in problem solving, computation and poor study methods. These problems can be identified and diagnosed through careful observation, questioning and interpretation of written work. Remedial instruction has to address the individual student's needs. To enhance learning, students have to be actively involved through manipulation of models, discussions, verbal writing assignments, practising his skills and studying. The use of visual proj ections, using colour, graphics and sound by computer, facilitates the recall of previous lessons. Videos of lectures can be used as backup for pupils who were absent. These are but two of the creative ideas suggested as aids for remedial teaching. No instant recipes are prescribed, but, for the teacher who really has the interest of his pupils at heart, many guidelines are provided...

This study investigated the factors related to student retention in a comprehensive community college developmental education mathematics program. The purpose was to identify and describe these factors and to develop strategies for improving retention in the community college developmental education mathematics program. Tinto's 1975 model of institutional departure was employed to examine different factors relating to retention in developmental education mathematics courses. In accordance with established criteria, data were collected using the Institutional Integration Scale (IIS) and Students Existing Records (SER). The IIS survey instrument questionnaire was completed by 41 students from a sample of 56 developmental education students enrolled in college level mathematics, and the data thus collected were used for analysis. Data were analyzed using frequency count, percentage, and the chi-square statistical analysis with a significant level of 0.05. The analysis of the data showed that the responding sample was primarily white, females aged 18 to 45. Most of the respondents had high grade point averages, did not miss any developmental education mathematics classes, and attended extra curricular activities infrequently. More fathers than mothers of the sample population had received a college education. Academic goal commitment, institutional experience, academic involvement, and placement grades were not statistically significant factors influencing retention. Among the major findings were: Development education instructors appeared to make the difference, institutional experience, academic goal commitment, and placement grades did not appear to play a major role; the students' academic involvement beyond classes appeared negligible; age, gender, grade point average, and parental educational levels were not significant factors for student retention in developmental education mathematics courses. Although statistical evidence did not support reversal of the proposed null hypotheses, pertinent issues for further research were raised.

Recent international reports, for example TIMSS (2011 & 2015), point to serious challenges in South African learner performance in Mathematics and Science. Of greatest concern is that research findings (e.g. Graven, Venkat, Westaway and Tshesane 2013) suggest that many South African learners show signs of mathematical knowledge gaps in the lower grades. Hence, there is a need to address challenges of this nature very early in Foundation Phase. This study was undertaken with a view to contribute towards addressing mathematical challenges encountered by learners in Foundation Phase This empirical enquiry was undertaken under the auspices of the South African Numeracy Chair Project (SANCP) at Rhodes University whose mission is to develop sustainable ways of improving quality teaching and learning of Mathematics in South Africa. A relatively new SANCP programme called Pushing for Progression (PfP) run as part of the after-school Maths Clubs to develop the number sense and four Operations in learners was used to achieve the research aims of this study. Research participants were drawn from the Maths Clubs established by the researcher in a small rural town of Ottosdal in the North West Province of South Africa. This Study is grounded on the Vygotskian perspective and uses the interpretivist qualitative research method for data collection and analysis. Sampling was done opportunistically by enlisting participants (12 teachers and 117 learners) on the basis of their availability and willingness to participate. Pre- and post-assessment of learners’ proficiency on the four Basic Operations was conducted at the beginning and at the end of the research project, respectively. This was done to determine the impact of the project on learner performance. Data analysis was done thematically and through the comparison of learner results of the pre- and post-assessment. The findings point to the effectiveness of the PfP Programme in learner performance. This can be deduced from improved scores between pre- and post-assessment and the observations made by participant-teachers on their respective club learners’ mathematical proficiencies. Accordingly, based on the findings, this study recommends, inter alia, that since the PfP programme is still in its early stages, similar research be conducted elsewhere. Additionally, the Department of Basic Education could consider exploring the PfP programme as one of several other strategies to help improve learner proficiency in Mathematics.

It can be argued that the Namibian curriculum is largely influenced by a Western epistemology. However, many studies suggest that learners make powerful meanings of mathematical concepts they are learning if they visualise these and experience them in relation to what they already know from their own cultural backgrounds. According to the Namibian National Curriculum for Basic Education (NNCBE, 2010), it is not only important for learners to acquire mathematical knowledge and skills, but also to develop and grow their identities, cultures and values as individuals. The aim of this study was to explore and investigate how selected mathematics teachers employ visualisation as a teaching approach to re-contextualise indigenous knowledge (IK). The study set out to explore how conceptual understanding is enhanced by participation in an intervention programme. The use of visualisation is considered an important mediating and pedagogical tool in the mathematics classroom to enhance the mathematics learning of learners. The research is informed by a socio-cultural theory of learning and is located within an interpretive paradigm. The study was conducted at four schools in the Oshana region of Namibia and involved four mathematics teachers who were purposefully selected due to their willingness to use visualisation-IK approaches in their teaching, based on their responses to the survey. The methodologies used are qualitative and quantitative case study. To gather data, document analysis, a survey, lesson observations and focus group interviews were used. The study found that most teachers in the Oshana region have an understanding of the effective use of visualisation-IK approaches. However, the study revealed that visualisation- IK approaches are mostly used in grades 4 to 7 mathematics classrooms. It also discovered that most of the visualisation approaches that teachers employed aligned well with the curriculum and promoted conceptual understanding in the teaching of mathematics. The results of the study showed that teachers have experience of the enabling and constraining factors in using a visualisation-IK approach to teaching mathematics.

M.Ed. / The object of this research project is to do an error analysis of standard five pupils' mathematics books and to to create guidelines for a mathematical programme, using direct instruction, learning strategies and problem solving skill ...

M.Ed. (Subject Didactics) / The ideal in education is that the curriculum provided (by the teacher) and the curriculum received (by the pupil), as originally drafted by the designers, should agree. However, there are indications that this ideal is often not achieved in the teaching of Mathematics, the reason being, inter alia, the backlog in the subject arising from inadequate knowledge as a result of misconceptions in regard to certain basic concepts. Misconceptions among pupils indicate that the shaping of understanding and mastering the concepts have been inadequate. It should be kept in mind that frame of reference and world view are peculiar to each pupil and will be utilized by him for interpreting and processing new concepts. It is therefore essential that the world view of the pupil should be investigated as being the factor which is probably basic to the problem of misconception. The point of departure is therefore that pupils have divergent world views, which invariably affect their understanding of Mathematics. Throughout the ages misconceptions were inextricably part of natural science in general and Mathematics in particular. During modern times, since the 1960s, Boyd has paved the way for reflection regarding misconceptions in natural scientific teaching by using the term "unfounded beliefs", and the attention was actively drawn to the problems surrounding misconceptions. Terms now mostly used as synonyms for misconceptions are conceptual framework, alternative frameworks, and alternative conceptions...

Afrikaans: Ontoereikende prestasie in wiskunde is ‘n verskynsel wat besonder algemeen voorkom en navorsers is dit eens dat die probleem veral by swart leerders kritieke afmetings aanneem. In die veranderende Suid-Afrika is een van die onderwysrealiteite dat 'n groot deel van die bevolking, vanweë verskeie faktore, steeds blootgestel word aan opvoedings- en omgewingsituasies wat nie bevorderlik is vir die optimale verwerkliking van die leerders se persoonsmoontlikhede nie, en tewens ook yan hierdie verwerklikingsgeleenthede weerhou. Die Tswanaleerders in die Mafikeng-area bevind hulle in ‘n opvoedingsituasie wat nie altyd vir optimale verwerkliking van hul persoonsmoontlikhede bevorderlik is nie. Een moontlike uitkoms van hierdie situasie is dan ook ontoereikende prestasie in wiskunde. Daar is veral gefokus op die taalaspek, waar die Tswanaleerders eendersyds probleme ondervind met die 'taal' van wiskunde, en andersyds dat hulle nie in hul moedertaal nie, maar wet in Engels onderrig word. Die doeI van hierdie studie is onder meer die verkenning van die Tswanaleerder in die Mafikeng-area se ontoereikende prestasie in wiskunde. Dit is gedoen deur die inskakeling van ‘n Diagnostiese Toets en ‘n Leerdersvraelys. Die kognitiewe en affektiewe fasette van die Tswanaleerder se prestasie in wiskunde is gemeet. Deur middel van assessering en evaluering is die huidige stand van die Tswanaleerder se prestasie in wiskunde onder die vergrootglas geplaas. 'n Remediëringstrategie wat spesifiek gerig is op die Tswanaleerder in die Mafikeng-area is saamgestel. Hierdie remediëringstrategie fokus op assessering en evaluering, deur gebruik te maak van die Diagnostiese Toets (Mafikeng-area) en die Leerdersvraelys. Daar is ook aangetoon in welke mate 'n wiskundeportefeulje in sodanige remedieringstrategie ingeskakel kan word. 'n Kontrolelys aan die hand waarvan wiskundefoute by die Tswanaleerder in die Mafikeng-area moontlik geidentifiseer kan word, is ook verskaf. 'n Bespreking van die diagnostiese ontleding van 'n Graad 4-groep se prestasie in die Diagnostiese Toets (Mafikeng-area) is ter iIIustrasie verskaf. Die voorgestelde remediëringstrategie is 'n potensiele hulpmiddel vir onderwysers/esse van die Tswanasprekende leerders in die Mafikeng-area om probleemareas in wiskunde te identifiseer en te hanteer. English: Inadequate achievement in mathematics frequently occurs especially amongst black learners where the problem is becoming critical. In a changing South Africa one of the realities in education is that a large part of the population, on account of various factors, is still being exposed to educational and environmental situations that do not promote the optimal realisation of the learners' personal potential, and also inhibit actualisation opportunities. The Tswana learners in the Mafikeng area find themselves in an educational situation that does not always promote optimal actualisation of their personal potential. One possible outcome of this situation is inadequate achievement in mathematics. Special attention was given to the language factor according to which learners experience problems with mathematical language on the one hand, and on the other, the problem that the learners are not being taught in their mother-tongue, but in English. The aim of this study is, inter alia, the exploration of the Tswana learner's inadequate achievement in mathemactis in the Mafikeng area. This was done by administering a Diagnostic Test and a Learner's Questionnaire. The cognitive and affective facets of the Tswana learner's achievement in mathematics was measured. The present state of the Tswana learners' achievement in mathematics was determined through assessment and evaluation. A remedial strategy specifically aimed at the Tswana learner in the Mafikeng area was devised. This strategy focused on assessment and evaluation by making use of the Diagnostic Test (Mafikeng area) and the Learner's Questionnaire. The relevant research also indicated to what extent a mathematics portfolio could be incorporated into such a remedial strategy. A check list according to which mathematical errors in the case of the Tswana learners in the Mafikeng area could possibly be identified was also compiled. A discussion of the diagnostic analysis of a Grade 4 group's achievement in the Diagnostic Test (Mafikeng area) is provided by way of illustration. The proposed remedial strategy is a potential aid for teachers of Tswana-speaking learners in the Mafikeng area to identify and deal with problem areas in mathematics. / Dissertation (MEd)--University of Pretoria, 2006. / Curriculum Studies / unrestricted

Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2016. / The purpose of this study was to examine learners’ mathematical word problem solving skills and strategies in Intermediate Phase. The study was prompted by Grade 6 learners’ poor performance in the cognitive area, non-routine mathematical word problems, as revealed in Annual National Assessment reports of 2011, 2012, 2013 and 2014. The study followed action research collaborative method involving 26 Grade 6 learners and their mathematics educator. The school is a rural primary school categorised under quintile two. Problem solving theory by Polya (1957) guided the study in answering three research questions: What are the challenges faced by Grade 6 learners in solving word problems? What are Grade 6 learners’ strategies in solving word problems? How can learners’ problem solving skills and strategies focusing on word problems be improved? Data were collected in a routine structured process: pre-intervention phase, intervention phase and post-intervention phase. Analysis was made through the development of a system of categorisation of learners’ responses. The four principles of problem solving by Polya (1957) namely, the way learners understand the problem, how they devise the plan, how they carry out the plan and the manner in which they look back guided the analysis. The findings of the study revealed that the strategies introduced assisted learners in making sense of the word problems and finally proceeding towards an adequate solution. It was also found out that the learners lacked the ability to read with understanding; the problem being their lack of competence in the language of learning and teaching. The skills which learners also lacked when solving word problems were identified as arithmetic skills and reflective skills.

The purpose of this mixed method study was to determine if there is a relationship between characteristics of supplemental instructors’ personal traits, teaching skills, subject matter, constructive/active, collaborative learning, effective communication, and their practices (as judged by students) and student success in their remedial mathematics course. The college Provost was contacted by email to request an authorization to conduct this study in his college. Once approved, the investigator contacted face to face his colleagues to ask their students to participate in the study because they enrolled in a remedial algebra class where the instructor is assisted by a supplemental instructor (SI leader). Sixteen algebra classes were selected, and each were assisted by supplemental instructors. Students’ scores on the pre-test (at beginning of the semester) and post-test (at the end of the semester) were collected to gauge their achievement on both tests. Students completed a questionnaire that asked about their perceptions about their supplemental instructors’ personal traits, teaching skills, subject matter, constructive/active, collaborative learning, effective communication, and their practices throughout the semester. Students’ mean scores difference on the post-test were higher in 62.5% of the sections than on the pre-test. The evaluation of achievement on both tests, the responses to the questionnaire and comments from students showed that SI leader’s characteristics associated to effective communication/active learning, teaching skills, and personal traits could be contributor to score achievements. The linear regression in the study shows that the three factors did not significantly predict the post-test score. However, the pre-test did significantly predict the post-test score in a remedial Math 20 at the end of the semester (Beta = .47, t (197) = 6.56, p <.05). In addition, the comments in the questionnaire found that students acknowledged their supplemental instructor role in the classroom and during the SI’s weekly sessions.