Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on July 29, 2009) Includes bibliographical references.

Submitted to the Faculty of Education in fulfilment of the requirements for the degree of MASTER OF SCIENCE EDUCATION in the Department of Mathematics, Science and Technology (MSTE) at the University of Zululand, 2015. / This study set out to investigate beliefs held by pre service Bachelor of Education (B.Ed) students about the nature of science and science teaching and learning. The research sample comprised one hundred and eighty four (184) third and fourth year (B.Ed) students majoring in mathematics and physical sciences. Data on students’ epistemological beliefs about the nature of science and science teaching and Learning were collected using two questionnaires: The Nature of Science as Argument Questionnaire (NSAAQ) and Beliefs About Reformed Science Teaching and Learning (BARSTL). Furthermore the study sought to find out if those beliefs cohered with the beliefs espoused by the National Curriculum Statement (NCS) for Physical Sciences grades 10-12. The conceptual framework of this study was framed upon the preponderance of literature that carried the view that a teacher’s classroom practices are a consequence of two main dialectic influences: (a) the teacher’s epistemological beliefs about the nature of science, which may be either naïve or sophisticated; and (b) the teacher’s beliefs about teaching and learning, which may be either traditional or reformed. Accordingly, the conceptual framework guiding the study opined that teachers holding naïve beliefs about the nature of science, and those holding traditional notions of teaching and learning will be characterized by teacher-centred instructional approaches, while those holding sophisticated beliefs of the nature of science and a reformed view of teaching and learning will be associated with learner-centred instructional approaches. This study was a case study conducted at a South African university, and involved one hundred and eighty-four third and fourth year students registered for a four-year Bachelor of Education (B.Ed) degree for the Senior and Further Education and Training phase. During these two final years of the programme students are engaged in science enquiry practices in their Methods modules. The participants were registered in physical science and mathematics education. Intact groups were used, so there was no sampling undertaken to select participants. Data were collected by the use of (a) the Nature of Science as Argument Questionnaire (NSAAQ), to determine epistemological beliefs held by the participants about the nature of science, as well as the concurrence of those beliefs with the views about science teaching and learning espoused by the NCS; and (b) the Beliefs about Reformed Science Teaching and Learning (BARSTL) questionnaire, to determine the beliefs held by preservice education students about science teaching and learning. Data analysis involved the use of both descriptive statistical methods to decipher patterns and general trends regarding the epistemological beliefs about science held by participants, and their beliefs about science teaching and learning, as well as inferential statistics to test both a priori and a posteriori hypotheses. Similarly, statistical analysis was carried out to determine whether or not third- and fourth-year pre-service science education students held beliefs about science teaching and learning that were in agreement with the pedagogical content beliefs about science teaching and learning espoused by the NCS. The study found that pre service students held significantly more sophisticated epistemological beliefs about the nature of science at fourth year than at third year level. The results also showed that fourth year students demonstrated a significantly higher level of ‘reformed oriented teaching and learning beliefs’ about science than did the third year students. The results however showed that third and fourth year students held beliefs that were not in line with the beliefs espoused by the National Curriculum Statement (NCS). These results support studies which have found that student teachers become more sophisticated in their epistemological beliefs towards graduation. The findings also showed that the B.Ed programme is succeeding in developing both epistemological beliefs about the nature of science and teaching and learning. The degree to which the programme succeeded in developing these beliefs was however quite small. This study recommends that further investigations be done to determine whether students who hold sophisticated epistemological beliefs about the nature of science and ‘reformed beliefs about science teaching and learning’ also demonstrate superior science teaching skills

The purpose of this study is to present arguments concerning a zestful learning for children ages 6-9 in mathematics. Four books in mathematics has specifically been analyzed to investigate what is written concerning a zestful learning. By means of an argumentation analysis within a qualitative text analysis the arguments are put forth. The didactic choices of the chosen literature are analyzed in a subject-matter didactic context. The result implicates a multitude of arguments and didactic choices supporting a zestful learning. The most prominent one is that teaching should presuppose the every-day life of the students, be varied concerning both education and environment and promote communication. Education should relate to joint experiences and clarify the already gained knowledge in math’s of the students, thus enhancing the students’ self-esteem within mathematical contexts: in addition, if students experience the usability of math’s and are given the opportunity to apply their body and senses in gaining this knowledge this is beneficial for zestful learning. To feel a desire to learn engages the students and motivates them to learn. As a conclusion there are many opportunities in creating zestful learning possibilities, prior research shows the importance of making the experience of learning enjoyable to promote a lifelong lust to learn, which is one of the assignments of school according to Läroplan för grundskolan, förskoleklass och fritidshemmet 2011 (Skolverket 2011).

The purpose of this study is to present arguments concerning a zestful learning for children ages 6-9 in mathematics. Four books in mathematics has specifically been analyzed to investigate what is written concerning a zestful learning. By means of an argumentation analysis within a qualitative text analysis the arguments are put forth. The didactic choices of the chosen literature are analyzed in a subject-matter didactic context. The result implicates a multitude of arguments and didactic choices supporting a zestful learning. The most prominent one is that teaching should presuppose the every-day life of the students, be varied concerning both education and environment and promote communication. Education should relate to joint experiences and clarify the already gained knowledge in math’s of the students, thus enhancing the students’ self-esteem within mathematical contexts: in addition, if students experience the usability of math’s and are given the opportunity to apply their body and senses in gaining this knowledge this is beneficial for zestful learning. To feel a desire to learn engages the students and motivates them to learn. As a conclusion there are many opportunities in creating zestful learning possibilities, prior research shows the importance of making the experience of learning enjoyable to promote a lifelong lust to learn, which is one of the assignments of school according to Läroplan för grundskolan, förskoleklass och fritidshemmet 2011 (Skolverket 2011).

The present research aims to evaluate the extent of deaf children’s delay in mathematics, identifying the moderators of this delay and determine the longitudinal predictors of their mathematical achievement. For five decades, studies have reported that deaf children lag behind their hearing peers in mathematics (Gottardis, Nunes and Lunt, 2011). Background factors such as age, degree of hearing loss, presence of cochlear implant and types of educational provision were previously hypothesised to be moderators of the extent of this delay but, up to now, they have not been tested. Pagliaro (2010) argued that number knowledge, working memory and degree of hearing loss could be possible causes of deaf children’s difficulties in mathematics but no clear conclusions were reached. The present investigation aims to provide insight into the causes of deaf children’s delay in mathematics. The survey study addressed the first aim of the present study. The maths test of the Performance Indicators for Primary School (PIPS) was used as outcome measure. Factors related to deaf children (degree of hearing loss, age, years in education, presence of cochlear implant, gender, causes of deafness) and background factors (highest maternal education, language used at home, type of educational provision) were assessed as possible predictors and moderators of the extent of deaf children’s delay in mathematics. The overall extent of deaf children’s delay in mathematics was of -1.76 SDs. The older the children get and the more years they spend in special schools for the deaf or in units for hearing impaired, the wider is their gap in mathematics achievement compared with their hearing peers. It is, therefore, necessary to intervene in their mathematical learning in the early years of schooling in order to create pathways for improvement. The second aim of the present study was addressed through a longitudinal design. Logical-mathematical reasoning, working memory and counting ability were chosen as predictors of deaf children’s mathematical attainment on the basis of theoretical framework, evidence from longitudinal studies and from the analysis of the difficulties that deaf children have in these factors compared with hearing peers. Hierarchical regression analyses were used to assess the independence of the contributions of logical-mathematical reasoning, working memory and counting ability to the prediction of deaf children’s mathematical achievement measured through the PIPS. Age, years in education, type of educational provision and non-verbal intelligence were used as controls. Counting ability and working memory did make independent contributions to the prediction of deaf children’s mathematical success but logical mathematical reasoning was by far the strongest predictor. When the predictors were entered in the model, none of the control variables predicted significantly deaf children’s mathematical achievement. This study makes several empirical contributions. First, it established age, years in education and types of educational provision as moderators of the extent of deaf children’s delay in mathematics. Second, it determined the plausibility of a causal link between logical-mathematical reasoning, counting ability, working memory and deaf children’s mathematical achievement. The implication is that schools must explicitly plan to improve deaf children’s mathematical reasoning, counting ability and working memory when they are in kindergarten and in the first years of school in order to help the children’s mathematical development.

Not often do mathematics teachers instruct to improve students' attitudes toward mathematics. The pressures to cover the state-mandated curriculum drive teachers to instruct for procedural understanding with few connections. The lack of real-life connections results in students with low motivation toward mathematics and results in poor mathematics attitude (Ma andamp; Kishor, 1997). The purpose of this mixed-methods research is to examine self-regulated learning as an instructional technique aimed at increasing mathematical attitudes while also increasing achievement and to reveal barriers to its implementation in the classroom.The research study involved an intervention in a Mid-South urban high school at the 9th grade level. All students who participated were enrolled in the middle track at the school, thus taking an Algebra I course. The intervention took place with four teachers in seven separate classes. Students were given the opportunity to regulate their own learning based on objectives for district and state requirements. In this pre/post design, students were surveyed for their mathematics attitude and achievement using the Attitude Toward Mathematics Inventory (Tapia, 1996) and a polynomial survey designed by the researcher. Teachers were surveyed and interviewed prior to the study to develop a sense of their teaching preferences. During the experiment classroom observations were conducted to assist in developing themes in the intervention. Following the study, extensive interviews took place with each participating teacher.Data analyses revealed no statistically significant difference between the control and experimental group in regards to mathematics attitude and achievement. Qualitative analysis using constant comparative strategies (Denzin andamp; Lincoln, 2000) revealed many teacher barriers and misconceptions. Teachers felt uncomfortable with the technique and were unable to allow the students to fully regulate their learning. The teachers imposed a timeline, quizzes, written tests, and direct instruction techniques on the students during the study. All of these created barriers to the students fully regulating their learning. Also, teachers' perceptions of learning and attitude were not valid. Teachers believed the students achieved at a lower level than with a traditional approach and viewed their attitudes as worse than normal. This was in direct contrast to the quantitative results.

The study took the form of action research situated in a case study. The participants consisted of sixteen Grade 11 learners who attend a non-profit tutoring organisation called Ikamva Youth on Saturday mornings and who volunteered to learn mathematics with mathematical software. Data were collected from the learners using a structured questionnaire, journals in which learners were encouraged to record their daily experiences and by studying the learners’ own written work during the research period. Moreover, the research closed with a focus group session. The study primarily described three aspects, viz. the degree to which learners are able to work with the strands of strategic competence and adaptive reasoning with particular emphasis on interpretation and application, knowledge production and justification and social collaboration; barriers in terms of working with these strands in a digital environment that may interfere with the learning process; and, the personal (affective) response of the students to the availability of technology. Findings suggest that the participants experienced difficulties in accessing these particular strands of mathematical knowledge, and subsequently expressed the desire to revert back to a place where the teacher assumes a more direct teaching style and where the focus of mathematical learning is on technique. In other words, learners preferred routine expertise, whilst appearing to lack in adaptive expertise. With respect to the second aspect of the research, it is suggested that one of the most prominent barriers to integrating technology into mathematics does not necessarily relate to adjustments in terms of the instrumental use of software and the computer environment, but seems to stem from the learners’ own epistemologies and beliefs about the nature of what constitutes effective mathematical teaching and learning. In paying attention to the voice of the learners it surfaced that the learners tend to associate computers more strongly with a cultural tool for entertainment than with mathematical learning. Although the study points out that implementing an interactive curriculum integrated with technology into a classroom with learners from low socio-economic backgrounds is not necessarily straightforward, it does suggest that with more frequent exposure certain learners can develop a propensity for working within a cognitively rich problem-solving context and effectively employ the mathematical software as an extension of their own thinking. This study adds to broader research on the role of technology in learning by reporting that the learners felt that the contextualisation of mathematics, followed by the ability to manipulate the graph themselves were the main contributors to their mathematical learning. The learners disregarded the visualisation effect of the computer as they felt that it had very little impact on their mathematical learning.

Student Number : 0215974F - MSc Dissertation - School of Mathematics Education - Faculty of Science / The report presents an investigation on how learners’ home language can be used as a support for learning mathematics. This qualitative case study was conducted in Phelindaba Primary School wherein learners use English as the language of learning and teaching which is not their home language. This school worked in collaboration with the Home Language Project to facilitate the learning of mathematics using the learners’ home language as a resource. The study revealed that when learners use their home languages they interact better with their peers, the teachers and their tasks. Learners used home languages to achieve conceptual understanding, procedural fluency, adaptive reasoning and strategic competence, which would in turn develop their productive disposition

Made available in DSpace on 2016-12-23T14:01:51Z (GMT). No. of bitstreams: 1 Christiane Milagre da Silva Rodrigues.pdf: 6089005 bytes, checksum: 1377ec6994c6ea24a428e2dd77610eb4 (MD5) Previous issue date: 2013-12-19 / The goal of this research was the enlarge of the teaching and learning process of mathematics to Down syndrome students enrolled at the last years of Fundamental Education, assuming the characteristics of a collaborative case study. The man subjects were two finalist Fundamental students from a public school at Serra - ES. Alice, 16 years old, coursing 7th grade and Barbara 13 years old cursing 6th grade. Each one of them were accompanied by a Pedagogy intern. The research sought to identify and evaluate their logic-mathematics knowledge, analyzed the teaching and learning process of Mathematics, the students limitations and their potentials. Sought for strategies to bring them this subject learning, and established relationships for mathematics knowledgeable constructions that allowed the comprehension and transform daily life. The data collection was performed through observation, field diaries, analytics memories, documental analyses and audio recording. We supported our theoretical foundation mainly based on Vigotski and D Ambrosio. We performed an exploratory period in which some students were observed in class and at school facilities. Semi-structured interviews were performed with professionals who worked with these students, their responsible and with the students themselves. The survey showed that the students did not have elemental numerical knowledge worked on initial grades, they were not literate and had few interactions with teachers and classmates in class. They were observed during four months, in the four weekly classes which activities that had as an objective develop their mathematic knowledge, were explored regardless the subject given by each grade. Development were seen although steel shy. The paper revealed forms to perform a more effective teaching of Mathematics in Inclusive Education, providing a (re) building a pedagogical practice by the school on the benefit of the development of essential skills to a student competence with Down syndrome / Esta pesquisa teve como objetivo ampliar a compreensão do processo de ensino e aprendizagem da Matemática para alunos com síndrome de Down inscritos nos últimos anos do Ensino Fundamental, assumindo as características de um estudo de caso colaborativo. Os sujeitos centrais foram duas alunas dos últimos anos do Ensino Fundamental de uma escola pública municipal de Serra - ES. Alice, de 16 anos, cursava a 7ª série, e Bárbara com 13 anos o 6º ano. Cada uma delas era acompanhada por uma estagiária que cursava Pedagogia. A pesquisa procurou identificar e avaliar seus conhecimentos lógico-matemáticos, analisou o processo de ensino e aprendizagem de Matemática empregado, as limitações das alunas e suas potencialidades. Buscou estratégias para levá-las à aprendizagem desta disciplina, e estabeleceu relações para a construção de conhecimentos matemáticos que lhes permitisse compreender e transformar o seu dia a dia. A coleta de dados foi realizada através da observação participante, diário de campo, memórias analíticas, análise documental e áudio gravação. Para o embasamento teórico nos apoiamos principalmente em Vigotski e D Ambrósio. Realizamos um período exploratório em que as alunas foram observadas em suas aulas e nos demais espaços escolares. Foram realizadas entrevistas semiestruturadas com profissionais que trabalhavam com essas alunas, com seus responsáveis e com elas mesmas. A sondagem mostrou que as alunas não possuíam conhecimentos numéricos elementares trabalhados nas séries iniciais, não eram alfabetizadas e interagiam pouco com professores e colegas na sala de aula. Elas foram acompanhadas durante quatro meses, nas quatro aulas semanais de Matemática, quando foram exploradas atividades que visavam melhorar seu desempenho matemático, independentemente do conteúdo relativo à série cursada. Houve avanços, ainda que tímidos. O trabalho apontou para formas de realizar um ensino mais efetivo da Matemática na Educação Inclusiva, proporcionando à Escola (re)construir uma prática pedagógica que favoreça o desenvolvimento de habilidades imprescindíveis à competência do aluno com síndrome de Down

This study was designed to evaluate the effectiveness of a computer-based outreach programme that addresses one aspect of a national strategic recommendation in South Africa. This outreach programme, which started in 1982, was in its twentieth year of existence in 2001 and provided support in mathematics and physical science to Grade 12 students and teachers from historically disadvantaged schools. This study examined the role that the outreach programmes played at two schools during 2001 and endeavoured to provide an analysis of the intended, implemented, perceived and achieved programmes for this year. Therefore, the purpose of this study was to investigate the effectiveness of this outreach programme in providing support to both teachers and students in the teaching and learning of mathematics and physical science. The goals and objectives of the outreach programme (the intended programme) were identified from documentation of the Outreach Project and interviews with Outreach Project managers. In addressing the implementation of the outreach programme (the implemented programme), lessons at each of the two, Mini-Computer Supported Education Centres (MICSECs) were observed over a period of four months. At one centre (Centre A), the lessons consisted of a formal (talk-and-chalk) presentation followed by an informal part when students worked on the computer in the same period. At the second centre (Centre B), the MICSEC was used as an adjunct to the normal classroom lesson, that is, students were taught in their normal classrooms and then, at least once a week, taken by their teacher to the MICSEC to do problem-solving on the computers. The perceptions of students (the perceived programme) were examined by an actual and preferred version of the Computer-Assisted Learning Environment Questionnaire and by interviews conducted with both individual students and groups. / At Centre A, the students preferred more involvement, more open-endedness, more organisation and more learning assessment opportunities in their computer-assisted classes but also less integration of computers in their every day classes whilst desiring investigation procedures in their classes to remain the same. At Centre B, students preferred to be more involved, to have more open-ended activities in their classes, have more learning assessment opportunities and a greater level of integration of computers but a reduction in investigative activities. Findings from student interviews were summarised as reflecting three viewpoints with regard to the inclusion of computer-assistance in classes. Students holding one viewpoint considered the inclusion of computer-assisted learning as important to their learning and were convinced that their interaction with the computer, fellow-students and teacher, led to an improvement in their learning. Students holding the second viewpoint conveyed a message of insecurity in the use of computers for they were not sure whether their working with computers made any difference to their learning. Many students' views were somewhere between the first and the second viewpoints which left the impression that these students were not convinced that using the computers would guarantee them success in the final examination. The third viewpoint was strongly articulated by a group of three students at Centre A and to a lesser degree at Centre B (one student), who considered that the new computer-assisted classes played no role in their learning and that teacher-centred classes would produce better results. The extent to which the outreach programme met its objectives (the achieved programme) included improved student performance on the matriculation examinations. / Teachers and students were generally positive of the support that they received but indicated that more computer terminals were required to address students' individual needs. The mean achievement of students at both schools improved in both mathematics and physical science, but more so in physical science. The MICSECs mainly served as a resource to students at the school where the centres were based and provided limited computer skills to students from historically disadvantaged backgrounds. The findings of this study provided insight into the implementation of computer-assisted classes in two disadvantaged schools and the results can serve as baseline data for conducting research into computer-assisted learning environments in other secondary school grades in South Africa. However, it should be noted that students at the Grade 12 level also wanted a continuation of, indeed more of, teacher-centred teaching, in addition to the computer-assisted classes because of the perceived competency of teachers in helping them perform well in the matriculation examination.