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The main objective of this study was to determine the progress made in the development of mathematical proficiency, in the domain of number skills, by learners in the two cohorts (namely: Mathematics and Mathematical Literacy) during Grade ten. The research was conducted at Temple Valley Secondary School, which is situated at Verulam, north of Durban in KwaZulu-Natal. Furthermore, this research study was questionnaire-based employing basic descriptive statistics as well as qualitative analyses. Data was collected through numeracy (number) skill tests, a questionnaire and focus group interview responses of grade ten mathematics learners. A total of two skill tests were administered and 3 focused group interviews were conducted with six grade ten learners each. The first test and first attitudinal questionnaire was administered in May 2006 when learners had branched off into the two paths of mathematics. Thereafter, a second test and second attitudinal questionnaire was administered, during October 2006; when learners had completed most of the school year. The October-test was followed by the focus group interviews. A convenient sample was used in selecting the learners for this research study and a purposeful sampling technique was used for the focus group interviews. All grade ten learners at Temple Valley Secondary School were selected as the sample. The results showed that the mathematics learners slightly outperformed the mathematical literacy learners in the development of mathematical proficiency for number skills. The findings from this research could inform: Teachers of grade ten learners with an interest in improving the mathematical proficiency, in number skills, of learners and; curriculum developers and materials development specialists who prepare mathematical material for grade ten classrooms. The results showed that none of the grade ten learners, from either cohort, were mathematically proficient in May or October. From the study, it was noted that the female grade ten learners generally outperformed their male counterparts. The focus group interviews revealed that learners had a positive attitude to the learning of the subject mathematics, despite the poor test results of this study. / Thesis (M.Ed.)-University of KwaZulu-Natal, 2008.

This study encompasses the use of concept maps to investigate learners' conceptual understanding of mathematics of a grade eight class in the predominantly Indian suburb of Shallcross. The grade eight learners that were the participants of this study were in the secondary school for the first time. They were in the middle of the Senior Phase within the General Education and Training Phase of their schooling career. This study is embedded in an action research methodology and is conducted from an interpretivist paradigm. Operating on a mixed methods theory, concept maps constructed by learners were analysed through the duration of the study. Towards the end of the study learners completed a questionnaire. Based on certain responses in the questionnaire and the analysis of the concept maps, six learners were then selected and interviewed to probe learners' conceptual understanding of concept maps. The results of the study reveal that most learners find concept maps enjoyable, fun and a creative way to learn mathematics. Further analysis of the questionnaire indicates that learners enjoy the social dynamics that group work provides and they found that working together also enhances their understanding. Further analysis of individual and group concept maps reveals that group work is effective in the use of concept mapping. The results of the study suggest that concept maps might be successfully used in assessing learners' declarative knowledge. An important implication of this study is that concept maps can be practically and effectively applied to a variety of outcomes within the constraints of the classroom. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2009.

This study intends to foreground visual literacy within the wider context of visualisation and visual thinking in mathematics teaching and learning. Visualisation in general has been receiving attention in mathematics education research. I distinguish visual literacy from visualisation by referring to visual literacy as the combination of visualisation and logical thought. Visual literacy emphasises construction of meaning through the process of decomposition, comprehension and analysis of visual representations. The section on functional relationships is located in the National Curriculum Statement (NCS) for mathematics in the Further Education and Training (FET) phase for Grades 10-12 (Department of Education, 2003). Graphical functional relationships, which form an integral part of functions and algebra in the FET phase for Grades 10-12, demand visual literacy, which includes graphical interpretation and comprehension skills. Therefore, the conceptual understanding associated with graphs is dependent on the way graphs are presented. This study examines learners‟ and educators‟ procedural and conceptual understanding of the graphs they sketch and interpret in the FET curriculum. The data analysis contributes towards the fast growing body of knowledge on visualisation in mathematics with the significant impact visual literacy has on the conceptual understanding of mathematical graphs. The analysis reveals that the overarching theoretical framework of constructivism embracing the Process-Object, Visualizer-Analyzer and Semiotic models are useful in illustrating and justifying the link between visual literacy and the conceptual understanding of learners. In examining the visual understanding of graphical representations of ten Grade 11 learners and the two mathematics educators that teach them, the data reveals that learners display a somewhat skewed understanding of the nature of the Cartesian plane, the characteristics of graphs, functional notation and graphical terminology. In fact their educators, in some instances, displayed similar understandings. Learners display procedural understanding of graphical representations to a large extent. The educators‟ visual understanding does suggest that learners‟ interpretation of graphs is in some way influenced by the way they teach. The overriding contribution of the research study is that visual literacy plays a significant role in the conceptual understanding of functional graphical relationships. The relationship between graphical representations and logical thought is central to visual literacy. Key concepts: visual literacy, conceptual understanding, graphical representations, visualisation, analytical thinking, constructivism, process-object, Visualizer / Analyzer, semiotics and vehicles of reasoning. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2009.

In this thesis, I describe how interactive journal writing was used to improve the understanding of mathematics, and to foster communication with two groups of remedial grade ten students. Mathematics is a gatekeeper course in high school, and students who are not successful with this subject are at a distinct disadvantage, both in terms of their education and in their future careers. A persistent source of difficulty for these students is related to language; students often struggle both to understand what is being taught, and how to explain concepts or problem solutions in their own words. Interactive journal writing was initiated as a means of addressing this situation, and of meeting the objectives proposed by the Quebec Education Plan, which specifies three closely related competencies: (1) solve situational problems; (2) use mathematical reasoning; (3) and communicate by using mathematical language. There is ample proof in the research literature that communication plays an important role in supporting learners by helping them clarify, refine and consolidate their thinking. / This study demonstrates the importance of allowing and encouraging students to use writing as part of their learning processes. By writing about what they are being taught, students are forced to slow down, examine and reflect on the steps they use to solve problems. Sharing what they write promotes meaningful dialogue and personal engagement, essential ingredients of successful learning.

In recent years much has been said and written concerning the widening gap between the newer developments in mathematics and that which is traditionally taught in secondary schools. Not unnaturally, leading scholars in mathematics have looked at the school programmes and found them wanting in many respects. [...]

This study was designed to explore the patterns and trends in attitudes towards mathematics and attainment in mathematics among Indian pre-matriculants. It also aimed at investigating the relationships between attitudes and attainment and the effects of differences in sex, grade, levels and certain background variables on mathematics attainment and attitudes. A set of 24 multiple-choice mathematics test items, compiled to test cognitive outcomes in mathematics at three taxonomic levels, served as a measure of attainment in mathematics. An attitude scale of 48 Likert-type items comprising six dimensions was developed to measure pupil's attitudes towards mathematics (affective outcomes). In addition, questionnaires were used to collect data on selected background variables and teachers' ratings of the pupils. The test, attitude scale and questionnaires were administered to 680 pupils selected randomly from 17 secondary schools in Durban. The 53 teachers responsible for the 151 mathematics class units (Std 9 and Std 10) at these schools also participated in the research project. The data was subjected to statistical analyses (item analyses, correlational analyses, z-scores and ANOVAS) by computerization. The reliability and validity of both the mathematics test and the attitude scale were demonstrated. The potential value of these instruments as measures of cognitive and affective outcomes in mathematics has been presented and argued. The significances of the relationships in respect of the background variables (including sex, grade and levels) and mathematics attitudes and attainment have been carefully documented (see summary - section 6.4). The relationship between attitudes towards mathematics and attainment in mathematics was found to be positive and significant, with no difference between males and females. It was also demonstrated that attainment in mathematics might be predicted from attitude and ability (IQ) scores, and a regression equation was derived for this purpose. Finally, consideration was given to implications of the major findings and problems for future research. / Thesis (Ph.D.)-University of Durban-Westville, 1981.

The constitution of Republic of South Africa (Act 108 of 1996) provides the basis for curriculum transformation and assessment for development in South Africa. The curriculum aims to develop the full potential of each learner as a citizen of a democratic South Africa. Formative assessment is seen as an assessment that can develop the standard of education in South Africa. Muller (2004) asserts that the C2005 policy document and assessment policy for General Education and Training make much of the need to shift from this "authoritarian" approach, to assessment which is formative, standard-based and continuous. Therefore, formative assessment is important in the process of teaching and learning. This study explores teachers' knowledge of formative assessment and how they translate it into practice within a context of Mathematics. It examines the nature of assessment techniques used by educators at the school and explore its relationship with practice. Furthermore, it aims to determine whether the educators are willing to adapt formative assessment practice to meet the changing demands of South African school education as prescribed by the New Curriculum Statement (NCS) in grade 8. Data collection and observations for the study were conducted at a high school in Hammarsdale, KwaZulu-Natal, South Africa. Four teachers were interviewed to determine their perception of formative assessment. Two of the four teachers were selected on basis of the interviews for further data collection. These two were observed when conducting lessons. At least two lessons for each teacher were observed. The nature of the task that the two teachers designed for formative purpose and the feedback they gave to learners were analyzed. The findings from this study suggest that teachers do not reject or resist change in practicing formative assessment, but they have not been properly assisted to replace the old practices with new ones. The teachers therefore, interpret formative assessment according to their own accumulated understanding, which differ from teacher to teacher. Thus, the study recommends that if the change in assessment practice is to be "efficient", it must be accommodated by "appropriate" professional development of teachers. / Thesis (M.Ed.) - University of KwaZulu-Natal, Durban, 2009.

This research aimed at measuring the extent to which a group of senior secondary pupils were attaining desirable cognitive objectives in mathematics. The summary of the design and procedures adopted in this study and the major findings which emerged is presented here. A scheme of objectives for mathematics learning at the senior secondary level was suggested in accordance with Bloom's Taxonomy of Educational Objectives and recent research relating to the Taxonomy and other classifications used in mathematics education. Multiple choice-type test items were constructed with reference to the above scheme of objectives and to content areas selected from the standard grade senior secondary mathematics syllabus. A pilot test was administered and analysed. The selection of items for the final form of the test was based on a consideration of item analysis data, distractors, reliability, validity, rating of items according to objectives and length of test. The final forms of the test and questionnaire were administered to a selected sample of 769 standard nine pupils from 14 Indian high schools in the Durban and District Area. The test was manually scored and the scores were subjected to statistical analyses by computerization. The findings suggest that: (i) it is possible to devise a reasonably reliable and valid test instrument to test at least two different levels of objectives in mathematics learning at senior secondary school level; (ii) the lower level objectives in mathematics are significantly easier to attain than the higher level objectives, which tends to support - in at least two levels - the assumption of hierarchical structure of a taxonomic classification of objectives; (iii) the performance in mathematics of the higher grade pupils tends to be adversely affected by being taught mathematics in mixed higher and standard grade classes. / Thesis (M.Ed.)-University of Durban-Westville, 1975.

The study examined the relationship between the sexrole stereotyping and the mathematic achievement of academicallytalented tenth grade females. The sample was drawn from two middle schools and one high school in the Lake Central School Corporation, St. John, Indiana. The sample included students in grades six and ten. The sixth grade sample was used forinstruments: the quantitative battery of the Houghton Mifflin Cognitive Abilities Test (CAT), the mathematics computation and mathematics concepts batteries of the CTB/McGraw-Hill Comprehensive Tests of Basic Skills (CTBS), and the Maferr Inventories of Feminine and Masculine Values. There was not a significant decline in the quantitative achievement of scores of academically-talented tenth grade females as determined by achievement scores from the females' seventh, eighth and tenth grade CTBS test. There were no significant differences in the seventh, eighth and tenth grade quantitative achievement scores of academically-talented tenth grade females as compared to male peers. A weak negative correlation was found between the non-significant changes of the tenth comparative purposes only. There werethree data gathering grade females' CTBS score means for seventh, eighth and tenth grade and the females' inclination toward family orientation, self orientation or a balance between the two as perceived the way the females actually were and, then, perceived the way the females' ideal woman would respond. Additional analysis resulted in the following: 1) tenth grade females indicated that the ideal female would be inclined toward self orientation; 2) sixth grade females indicated that the ideal female would be inclined toward a balance between family orientation and self orientation; and 3) sixth grade females were inclined to be self oriented, while sixth grade males were inclined toward an even distribution among the three - family orientation, balanced and self orientation. Recommendations for further research included: choosing an achievement test that would provide more differentiation (an out-of-level test might be considered); conducting a longitudinal study, following the sample through five years of school; finding a better method of gathering sex-role stereotyping data; increasingthe sample size; and locating a more representative geographic location for the study.