In this paper, students' bilingualism and multicultural experiences are examined as cognitive resources for mathematization. Capitalizing on the view of language as action, and on students' familiarity with certain experiences through direct participation, the study includes a conceptual framework, never used with bilingual mathematics learners, to investigate how bilingual students organize and coordinate actions to solve mathematical problems about familiar and unfamiliar experiences in English and Spanish. The study used a research methodology to investigate two questions: (a) How do bilingual students' mathematize familiar experience problems and unfamiliar experience problems in Spanish and English? (b) What do differences and similarities in bilingual students' mathematization across problems and languages reveal about experience and bilingualism as cognitive resources? Findings show important differences. In problems about familiar experiences, students generated more productive actions, more reflective actions, and less unproductive actions than in problems about unfamiliar experience. As for the bilingualism, students used Spanish and English differently. When solving problems in Spanish, they framed actions more socially by including partners or sharing the action with partners, whereas in English they framed actions more individually, more depersonalized, excluding partners and instead relying on words in problems to justify their individual actions. This suggests that reinventing mathematics and themselves as mathematical thinkers is part of using their bilingualism and experiences as cognitive tools, and attention to how they use each language for each type of problem can reveal substantial knowledge about how bilinguals learn mathematics. / text

The primary purpose of this study was to determine the manner in which assessment in mathematics is carried out in the Middle Schools. The study further identified problems educators encountered in assessing learners in mathematics and suggested possible solutions to problems encountered by educators in assessing learners in mathematics. Data was collected through questionnaires responded to by Middle Schools' mathematics educators and through the structured interview. Senior Phase mathematics educators responded to the questionnaire, which contained a blend of both dosed and open-ended questions. Educators took part in the structured interview in which a tape recorder was used. The study established that educators find it challenging to assess learners' mathematics work within the context of Outcomes Based Education and Curriculum 2005, even though the research was able to establish that in-service workshops on assessment in mathematics were conducted. Perhaps this calls for a new approach in conduction in-service workshops. Central to the recommendations of this research is a suggestion that there is a need for in-service workshops, which should focus on areas such as skills to be assessed in homework, class work, tests, examinations, projects, investigative activities and assignments. It was further recommended that educators should be trained on how to prepare rubrics for assessment of learners' mathematics work. / (M.Ed.) North-West University, Mafikeng Campus, 2005

The purpose of this study was to gain insight into observed discrepancies between continuous assessment and final examination average marks in Grade 10 Mathematics in the Oshikoto region of Namibia. The study is framed as a case study and is grounded within the interpretive paradigm. A mixed methods approach was applied, eliciting both quantitative as well as qualitative data. The study took place in two phases. In Phase 1, continuous assessment and Grade 10 final examination average marks for 62 Junior Secondary Schools for the period 2008-2010 were gathered and analyzed. Schools were characterized in terms of the relationship between their continuous assessment and final examination average marks for each of the three years. Phase 2, which was informed by Phase 1, took the form of structured interviews with a sample of three Mathematics teachers and three principals along with a focus-group interview of twelve teachers in order to investigate more deeply the perceptions of teachers and principals toward assessment policy and practice. The study shows that Grade 10 assessment practice in Namibian schools is far from ideal. Many teachers are not fully conversant with the various continuous assessment components as outlined by policy, and teachers are not confident about setting appropriate continuous assessment tasks. There is a strong perception that continuous assessment marks can easily be inflated and those teachers who gave high continuous assessment marks to their learners were generally perceived as being either incompetent or dishonest. While continuous assessment was seen as an important component of teaching and learning, it is evident that teachers and principals would welcome greater clarity, along with standardization and moderation, with respect to continuous assessment practice.

Thesis (MTech (Education))--Cape Peninsula University of Technology, 2009 / Huidiglik is die uitslae van wiskunde in Suid-Afrika baie swak in vergelyking met ander lande. Selfs die meeste Afrika-Iande presteer beter, Die doel van hierdie studie is om die redes en gevolge vir hierdie swak prestasies vas te stel. Dit is ook die navorser se poging om 'n bydrae te lewer tot beter wiskundige ontwikkeling ten opsigte van getalbegrip in die Grondslagfase deur aanbevelings vir opvoeders daar te stel wat benut kan word om hierdie doel te verwesenlik. In die literatuurstudie is Konstruktivisme, soos gesien deur Piaget en Vygotsky, breedvoerig bespreek. Die Realistiese benadering tot wiskundige ontwikkeling in getalbegrip is ook bestudeer. Verder is gefokus op.verskeie aspekte wat wiskundige ontwikkeling beinvloed, Die rede vir graad een en twee leerders se swak getalbegrip van 1 tot 99 en 'n moontlike oplossing vir hierdie probleem gee aanleiding tot die volgende navorsingsvrae: Dien die Plannemakerprogram as 'n doeltreffende hulpmiddel vir grade een en twee opvoeders om leerders se getalbegrip 1 tot 99 te verbeter? en Verbeter die Realistiese benadering, 5005 gevolg in die Plannemakerprogram, leerders se getalbegrip 1 tot 99? 'n Kwalitatiewe navorsingsontwerp is gebruik om die empiriese studie te voltooi. Vier skole in die Overberg-distrik, twee relatief groot en twee multi-graadskole, is gebruik. Gestruktureerde onderhoude is gevoer met ses graad een- en twee opvoeders en getalbegriptoetse is met hul leerders afgele, Die navorsingsresultate het getoon dat opvoeders wei riglyne benodig vir suksesvol!e ontwikkeling van getalbegrip in die Grondslagfase. Dit bevestig ook dat die grondlegging van goeie getalbegrip in graad een gele word en indien leemtes in hierdie belangrike aanvangsjaar ontstaan, leerders vorentoe probleme ondervind. Leerders by skole een en drie, waar die Plannemakerprogram gevolg is, se uitslae is heelwat hoer as skole twee en vier waar opvoeders ander benaderings gevolg het. Die uitslae van skool een se graad twee leerders, waar die Plannemakerprogram reeds vanaf graad een gevolg is, is ook beduidend hoer as skool drie waar die Plannemakerprogram slegs vanaf graad twee gevolg is. Hierdie navorsingstudie ondersoek, analiseer en bespreek die resultate met aanbevelings.

D.Ed. / The study focused on the placement of Grade 10 learners in either Mathematics or Mathematical Literacy. The purpose was to develop guidelines to assist Grade 10 learners to make a proper choice, which would render their placement more justifiable and objective and, in turn, enhance their results. A central theme of the National Curriculum Statement (NCS) is the importance that secondary schools will shape learners to become responsible citizens in a fast-developing, scientific and technological society. South Africa has an urgent need for more scientists, engineers, high-level economists and technicians, which can only be satisfied if learners with potential for science-related studies are identified. Due to the fact that learners need skills to interact critically with the world outside the school environment, more learners should be encouraged to take Mathematics. A good foundation of Mathematics and Mathematical Literacy necessitates the development of guidelines to add value to assessment. Therefore, this study examined the nature of Mathematics and Mathematical Literacy, the historical background of Mathematics education in South Africa, constructivism and its approaches to learning and teaching, as well as cognitive and non-cognitive factors associated with achievement and general test evaluations. A pragmatic philosophy was followed. National Curriculum Statement (NCS) documents were analysed to distinguish between Mathematics and Mathematical Literacy in terms of subject content. Qualitative and quantitative information was collected by means of interviews and questionnaires respectively.The analyses of the NCS documents showed content similarities and differences between Mathematics and Mathematical Literacy and identified the gaps in learners’ learning experiences that could contribute to non-achievement in either subject.

M.Ed. / The method used in the classroom is thought to have an effect on the learners learning the purpose/use of mathematics in their environment. Many see mathematics as a set of signs and symbols that are meaningless in their lives. The manner, in which mathematics is taught in the classroom, extends the thought of learners in believing that mathematics is a compulsory learning area that is required to be passed in order for them to proceed to the next grade. Meanwhile, the learners may be oblivious to the contribution mathematics can make in their lives. One of the major contributory factors for this kind of thought is that mathematics is not taught in a way that helps learners understand its purpose/use in society. Thus, meaningless learning is perpetuated because of the approach in the classroom. If educators could alter their methodology in the classroom, then learners would be able to make sense of the subject and so apply the knowledge in their environment when the need arises. One of the ways to do this is to ensure that educators engage in meaningful and relative teaching. The research for this study was based on the questionnaire and observation instruments. The target was primary school learners from grades five, six and seven, who were required to answer a closed questionnaire based on their understanding of the relevance of mathematics to their environment. The aim was to see how the educators’ methodology affected the learners’ understanding of mathematics. Educators were also given questions along the same lines, with their lessons observed and observations recorded, according to an observation protocol. The conclusion that the researcher reached was that learners were not taught in a purposeful manner that might assist them in understanding and applying mathematics to their environment. Whatever they learnt or were taught in the classroom was in isolation, that is, there was minimal, if any, integration into other learning areas. One possible solution to this problem can be that the educators need to change their teaching strategies. Some of the possible strategies that they could use are cooperative learning, problem solving, the constructivist approach to teaching or an amalgamation of more than one strategy to obtain the outcomes. In effect, if learners are made to realize the relevance of mathematics consciously; their mindset towards learning it will be more welcoming and accepting of it. Understanding forms the foundation for application, and therefore if the problems in the classroom relate to the learners’ experiences in their environment, then mathematics becomes meaningful to them and in turn becomes usable.

Over the past decade, a sizeable body of research has addressed issues in metacognition, the way in which the learner plans, implements and monitors cognitive behavior (Garofalo and Lester, 1985). This type of consideration is of interest to studies which try to build models of human cognitive process for such applications as artificial intelligence and/or curriculum development. To form one's own mental map of a body of knowledge is to discover a structure of, or to impose a structure on, that body of knowledge. In the case of secondary school mathematics curricula, the student is typically discovering structure which is to some degree made explicit in the presentation of the material. However, when the language of instruction is not the student's first language, when the student is unaccustomed to many of the communication conventions of the language of instruction and of the subject register as well, fewer assumptions can be made about how the student is navigating around the body of knowledge. In this study, the relatively scarce questions asked by ESL (English as a Second Language) students in a secondary school English-speaking mathematics classroom were observed over time. The data provide some evidence of the natural manner in which the students attempt to form a mental map of the body of knowledge under exploration. The body of research on classroom questions (e.g. Sinclair and Coulthard, 1975) has focused almost entirely on questions asked by the teacher. Questions asked by students differ in both form and intention from questions asked by teachers, however; as a result the methods of analysis employed in studies of teacher questions are inappropriate for the analysis of student questions. A more appropriate method of analysis for this study's examination of student questions about a body of knowledge was found to be an ethnographic one which regarded questions as a means of eliciting aspects of a structured knowledge domain. Mohan's (1986) knowledge framework, which embodies a structured taxonomy of topics and tasks, is used here to categorize the data according to the type of knowledge sought through each student question. Observed differences between the surface content of student questions and the context-apparent intention of these questions provide some insight into how students may be assisted to better ask the questions which they use to seek help in their navigation of bodies of knowledge. Published teaching materials intended for ESL students of secondary mathematics are examined here for relevance to the students' need to develop help-seeking strategies; suggestions for more effective accommodation of this need are made. Computer software developed by the researcher for exploration of possibilities in computer aided instruction in question formation is described. / Education, Faculty of / Language and Literacy Education (LLED), Department of / Graduate

The purpose of this investigation was to examine, through the use of survey data, relationships between inputs of schooling and outcomes, as measured by student achievement in mathematics. The inputs of schooling were comprised of a number of variables grouped under each of the following categories: students' and teachers' backgrounds; students' and teachers' perceptions of mathematics; classroom organization and problem-solving processes. Outcome measures included student achievement on test total, problem solving and applications. A related question involved exploration of the appropriateness of using cross-sectional survey data to make decisions based on the relationships found among the input and output variables. To address this question, results from a subsequent longitudinal study, which utilized the same instruments, were examined first with post-test data and second with the inclusion of pre-test data as covariates. Data collected from teachers and students of Grade 7 in the 1985 British Columbia Assessment of Mathematics were re-analysed in order to link responses to Teacher Questionnaires with the students' results in teachers' respective classrooms. Responses were received from students in 1816 classrooms across the province and from 1073 teachers of Grade 7 mathematics. The data underwent several stages of analysis. Following the numerical coding of variables and the aggregation of student data to class level, Pearson product-moment correlations were calculated between pairs of variables. Factor analysis and multiple regression techniques were utilized at subsequent stages of the analysis. A number of significant relationships were found between teacher and student behaviors, and student achievement. Among the variables found to be most strongly related to achievement were teachers' attitudes toward problem solving, the number and variety of approaches and methods used by teachers, student perceptions of mathematics, and socio-economic status. Results also show that student background, students' and teachers' perceptions of mathematics, classroom organization and problem-solving processes all account for measurable variances in student achievement. The amount of variance accounted for, however, was higher for achievement on application items, measuring lower cognitive levels of behavior, than on problem-solving items which measured cognitive behavior at the critical thinking level. Through examination of the standardized beta weights from the cross-sectional and longitudinal models, it was found that prediction of change in achievement based on corresponding change in classroom process variables was similar for both models. Differences, however, were found for variables in the other categories. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

M.Ed. (Subject Didactics) / Each child has his own personality and individuality. Children are learning in different ways, at different tempo's and achieve different heights of success with.their efforts. The degree to which the learner is able to master new concepts, is closely related to the reference framework and given pre-knowledge. However, the learning process is not always successful. Various reasons for this phenomena can be identified. This study focuses on the role which misconceptions play in this regard. In general, misconceptions can be defined as a distortion or misinterpretation of the learned concepts. synonyms used to describe this phenomena includes words. like "previous knowledge", "preconceptions" and "alternative frameworks" Misconceptions in Mathematics are numerous. In various studies conducted, misconceptions were identified in almost all areas of Mathematics. Likewise a great deal of misconceptions were found existing among students concerning the handling of fractions. It is an impossible task to research all misconceptions in Mathematics in one study. For this reason it was decided to do research on only one aspect, namely fractions where possible misconceptions can occur. With the empirical research which was conducted, certain misconceptions in the area of fractions were identified. These misconceptions include, amongst other, the following: 1. The sum of and difference between two fractions. There is very little or no notion of the smallest denominator. 2. Multiplying and division of fractions. The student is uncertain about the role which the numerator and the denominator play in the solution. As fractions play such an important role in Mathematical success, it is suggested that a plan of action will be set as soon as possible in order to prevent misconceptions influencing the student learning process.

Please read the abstract in the section 00front of this document / Thesis (PhD)--University of Pretoria, 2006. / Humanities Education / PhD / Unrestricted