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

The learning of mathematics is a worldwide concern. International studies over the last decade place South African learners amongst the lowest achievers. Although various initiatives have been tried there does not seem to be any improvement. In the USA and UK initiatives include the involvement of parents and these have been implemented with great success. One of the parent involvement programmes from the USA, the Family Maths Programme has been in South Africa since 1996. This programme has been successful in South Africa but is confined to parents of grades 4-7 children. However, there is no programme for parents of high school learners. As grade 8 is usually the first high school year in South Africa, this study focuses on parents of grade 8 children and their involvement in their children’s mathematics learning. It consists of an initial survey of grade 8 parents’ (from an urban school) mathematical backgrounds and experiences and their involvement in their children’s education. Using key points from the survey and elements from the literature review and other sources, the researcher designed a parent assistance programme for mathematics which was conducted with three groups of parents of grade 8 children from the same high school. Each group of parents was exclusive and the same set of procedures was applied to each group, making this study a qualitative multiple case study, within the interpretive research paradigm. The parent-assistance programme consists of a parents’ workshop and completion of journals over a 7-week period. Parents documented their interactions with their children in structured journals, a process known as participant journaling. After this journaling period, parents and children were surveyed on this interaction by means of follow-up questionnaires. This was followed later in interviews with the parents and mathematics teachers, separately. After the completion of all three case studies parents and children participated in focus group discussions to discuss and share experiences of the programme. The interrogation of the data, on two levels, suggests parents’ and children’s perceptions of mathematics were likely to be positively influenced. The data also suggest that children were likely to become more confident and to improve in mathematics.

The aim of this study was to investigate the role Excel could play in influencing Mathematics and Mathematical literacy learners’ interpretation of functions and their attitude towards Mathematics. I used a Mathematical Graphical Diagnostic (MGD) test, an attitude questionnaire, a reflective questionnaire and semi-structured interviews as instruments. The MGD test and the attitude questionnaire were given to 72 volunteer grade 11 learners at a former Model C school in Port Elizabeth, in the Eastern Cape. This group included 50 pure Mathematics learners and 22 Mathematical literacy learners. From this group, a smaller group of 10 learners further took part in the rest of the study were they went through an intervention were Excel was used as a teaching tool, covering concepts concerning functions. This group included 6 pure Mathematics and 4 Mathematical literacy learners. The 10 learners then re-wrote the MDG test and refilled the attitude questionnaire after the intervention. A reflective questionnaire was administered to the 10 learners after the intervention, with 5 learners from the 10 undergoing interviews in order to meet the objectives of the study. The administration of the MDG test and attitude questionnaire, interviews and reflective questionnaire enabled me to explore the relationship between learner performance and their attitude towards Mathematics as a subject, as well as the comparing the attitudes and performances between pure Mathematics and Mathematical Literacy learners. The study followed a qualitative research design, with an element of quantitative research. The qualitative data yielded findings that revealed the effectiveness of using Excel in teaching functions while the quantitative data revealed the difference in attitude and ability between pure Mathematics and Mathematical Literacy leaners. The findings of the study revealed that Excel played a major role in improving pure Mathematics learners’ results but not those of the Mathematical Literacy learners. The study also showed that technology does not necessarily impact on learners’ attitudes positively.

The study examined student perceptions of global issues when introduced through their Logarithms unit in the Principles of Math 12 course and student opinions regarding the suitability of the issues within the course. Through journal books, the students expressed thoughts, ideas, and concerns related to the mathematics and the global issues. With our global environment being threatened in numerous ways, a need to educate through 'responsibility' is essential. In mathematics, students require relevancy when expected to learn increasingly difficult material. The study addresses the questions of: do students concerns for global issues increase when viewed through a mathematical lens and do the students believe that the global issues have a place in the math class? The findings were varied based on individual experiences of students within the study. In summary, the majority of the students gave positive feedback towards the use of the global issues within the math class. However, there were concerns from weak and strong students and from students currently studying similar topics in Geography. As well, several ESL students expressed concerns surrounding their difficulties with the written language, and anxiety regarding their emergent academic standing. The students favoured global exposures in the math class when they were able to actively participate with a solution, and when direct links to the mathematics being studied at the time was relevant to the global issue. Conclusively, more accessible resources are required for instructors, and more time is needed in the classroom to effectively implement, for all learners, global issues in the mathematics course. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

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 explores the ways in which teachers' interventions interact with and occasion the growth of students' mathematical understanding. Two 'cases' were documented, and these form the two strands of my research. The first strand concerns data collected in my own high school classroom at a time when I was a full-time teacher of mathematics in a small, rural secondary school in the United Kingdom. The second strand concerns data collected in a mathematics classroom in a large, urban high school in Vancouver, British Columbia. The data consist of videotaped lessons in each of the two classrooms, videotaped interviews with students from both strands of the data, copies of students' work from both strands, videotaped interviews with the Vancouver teacher, and my own journal entries. Analysis of the data, which is described in six stages, resulted in the generation of fifteen themes to describe the teachers' actions-in-the-moment. Three of these themes are distinguished from the others as teaching styles, as contrasted with the remaining twelve teaching strategies, and a number of the teaching strategies are clustered within the three teaching styles. The notion of a 'continuum of telling' is developed, upon which the three teaching styles lie, and this continuum is explored in order to probe the ways in which teachers' interventions interact with the growth of students' mathematical understanding. The ways in which teachers' interventions occasion the growth of students' mathematical understanding is probed through an integration of detailed traces of the students' growth of understanding with contemporaneous considerations of the teachers' strategies and styles. Implications to be drawn from these analyses, both for the research community and for teaching and learning, are discussed. I also share my reflections on my own growth as a teacher and as a researcher that I have experienced as a result of participating in, and conducting, this study. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

Average students -- 6th, 7th, 8th grades (middle schools) -- Manipulatives and authentic materials -- Administrative responsibilities.

This dissertation presents a study on Grade 10 learners’ understanding of key Mathematics concepts in selected secondary schools in Chibombo District of Zambia. The performance of learners in Mathematics countrywide has not been gratifying. This study therefore sought to investigate the Grade 10 learners’ understanding of key Mathematics concepts. This poor performance in Mathematics by learners in many schools at grade 12 final examination in Chibombo District prompted the researcher to conduct this study. The target population was 250 Grade 10 learners in five secondary schools in Chibombo District. The data were collected by means of questionnaire and focus group discussions. A concurrent triangulation design was adopted for the study in which the researcher simultaneously gathered both quantitative and qualitative data merged it using both quantitative and qualitative data analysis. The study revealed that Grade 10 learners’ understanding of the key Mathematics concepts of zero, equal, function, and variable is unsatisfactory. However, it is surprising how these learners can reach secondary school level with such a weak understanding of mathematical concepts, which are ubiquitous in the subject. It is anticipated that the findings of this study will provide curriculum developers with new insights into this problem so that they come up with a curriculum that focuses on learners’ understanding of basic concepts that serve as building blocks to next levels. The Ministry of General Education should rigorously monitor this process and provide both technical and financial support required. Finally, based on the findings of this study, the researcher gave some recommendations for improving learners’ understanding of mathematical concepts in schools. / Mathematics Education / M. Ed. (Mathematics Education)

Thesis (M. Ed. (Mathematics Education)) --University of Limpopo, 2017 / Sarton (1936) stated that mathematics has grown so large for a single mind to grasp. Mack (1961) attributes that phenomenon by claiming that mathematics differs from science in that it keeps on adding new concepts to existing ones, whereas in science there is reduction of concepts. This continuing growth makes it impossible for an individual to study mathematics as a whole (Krantz, 2010). Van Bendegem (2009, p. 137) calls the mathematics world a “mad world”. Recently, Ellerton (2014) compared mathematics to a growing tree. A number of challenges arise out of the observations made above. Is the mathematics that is taught in secondary schools an appropriate reflection of the mathematics that is out there today? Is an individual an appropriate embodiment of a secondary mathematics teacher? In the mist of these and many other questions, this study locates itself in the second question and investigated the notion of an embodiment of a secondary mathematics teacher. The main research question that was pursued was ‘How adequate is an individual as an embodiment of a secondary mathematics teacher?’ This question should be understood and interrogated in the context of Festinger’s (1962) dissonance cognitive theory that also serves as the theoretical framework for the study. The expectations of a secondary mathematics teacher do not fit in with an individual’s capacity to embody those. Grounded theory (Glaser, Strauss & Beer, 1967) was used to generate and develop what Elliot and Higgins (2012) called a substantive theory. This was a desktop grounded theory study and data was collected from existing literature of published journals and books. Since the use of documents is recommended as one of the qualitative data collection methods in grounded theory (Strauss & Corbin, 1990), the documents served as primary data where only a few that were relevant to the issues discussed were selected (Breckenridge & Jones, 2009). Content and thematic analyses procedures were used. Content analysis assisted to organise data according to various eras, tracing the growth in mathematics education and mathematics content, comparing them to a mathematics teacher of different eras, which assisted in bringing the answer to the research question posed (Bowen, 2009). Thematic analysis was used to identify commonalities and differences with regard to the notion of a teacher in various eras (Fereday & Muir-Cochrane, 2006). The findings revealed that the notion of a secondary mathematics teacher of the current era is completely not a suitable embodiment of a secondary mathematics teacher. The current notion of an embodiment of a secondary mathematics teacher is seriously challenged by this ever growing subject. Secondary mathematics is so large for an individual to acclimatise with (Sarton, 1936), and there seems to be a need for more than an individual to ensure that mathematics is well taught and learned by learners. It is recommended that other studies should be undertaken to determine as to how many individuals can constitute a composite suitable to embody the requirements of an ideal secondary mathematics teacher.

Within the scope of all that is expected to be accomplished in education, what difference does a tardy make? This study was designed to examine the significance of tardiness, as it relates to student achievement, as measured by the results of the state math test. It also investigated the generation of change by the campus administrator to improve punctuality, with a new method of enforcing the tardy policy with the use of an electronic data system. This study used archived data from the one high school in a suburban school district in Texas. From a student population of 2,631, two subject groups of 919 and 1,310 were determined. Spearman rho results confirmed a moderate inverse relationship between student tardiness and results on the state math test. Descriptive discriminant analysis indicated that tardiness contributed to 25% of the variance in the results on the state math test, when considered alone, and had a smaller contribution when considered with other variables. A visual review of the data portrayed an inverse relationship between the occurrences of tardiness and the pass/fail results on the state math test; as tardiness increased, passing rates decreased. Wilcoxon signed rank test results revealed a reduction in the magnitude of tardiness with the implementation of a new method of enforcing the tardy policy. Tardiness does impact academic achievement, as affirmed in this study. Also, the campus administrator can implement changes that improve punctuality. This study signified that the phenomenon of tardiness should be given greater consideration as a factor impacting both cognitive and non-cognitive development and endorsed that minutes do matter.