Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-10-20T14:04:27Z No. of bitstreams: 1 Simone de Oliveira Andrade Silva.pdf: 2491360 bytes, checksum: 076e3d9c3f47be0c573b1d2a44f767da (MD5) / Made available in DSpace on 2017-10-20T14:04:27Z (GMT). No. of bitstreams: 1 Simone de Oliveira Andrade Silva.pdf: 2491360 bytes, checksum: 076e3d9c3f47be0c573b1d2a44f767da (MD5) Previous issue date: 2017-09-15 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The aim was to identify possible relationship between logical reasoning and mathematical reasoning in children between 9 and 10 years old. Twenty-six children were recruited from an elementary school. They were distributed in two different groups: high and low performance in arithmetic mathematics. An instrument was applied to collecting data. It was composed of five set of problems: two to assess mathematical reasoning and three to assess logical reasoning. Three descriptions for analyses: participants performance outcomes; categorization of participants explanation about their reasoning to solving those problems and; instrument. The results evidenced strong correlation between logical reasoning and mathematical reasoning. The categorization of participants explanation indicated strong incorrect control by presence/absence of number in the mathematics problems and strong incorrect control by statement in problems that involve logic. The instrument was useful to register and analyze difficulties of the participants in solving the items. It is suggested insert qualitative analysis in the teacher assessment to understand student performance. It is advised to add to elementary school education and to teacher training the teaching of logic / O objetivo dessa pesquisa foi de identificar as possíveis relações entre o desempenho em problemas que envolvem raciocínio lógico e raciocínio matemático (de aritmética) em crianças entre 9 e 10 anos. O campo da pesquisa foi uma escola municipal de ensino fundamental de São Paulo, alunos do 5.º ano do ciclo I. Os 26 participantes foram distribuídos em dois grupos (fortes e fracos, com relação ao seu desempenho em matemática – aritmética). Para a coleta de dados, aplicou-se um instrumento composto de cinco conjuntos de problemas (dois avaliaram o raciocínio matemático e três avaliaram o raciocínio lógico). A análise dos dados contou com três etapas: análise quantitativa dos resultados do desempenho dos participantes; a análise e categorização das justificativas dadas pelas ao inquérito e; análise do instrumento. Os resultados sugerem que há correlação entre o raciocínio lógico (sentenças verbais – lógica não formal) e o raciocínio matemático (atividades de aritmética). A categorização das justificativas indicou forte controle incorreto da presença/ausência de número nos problemas matemáticos, forte controle incorreto do enunciado nos problemas que envolvem lógica. A análise do instrumento indicou que, apesar de alguns ajustes necessários, ele serviu para registrar e analisar dificuldades dos participantes na solução dos itens. Diante dos resultados, indica-se que a análise qualitativa seja inserida na avaliação que os professores realizam sobre o desempenho dos alunos em matemática. Recomenda-se, ainda, que o estudo de lógica verbal não formal seja inserido nos currículos da educação básica e na formação inicial de professores

Science, technology, engineering, and mathematics (STEM) educational achievement is vital to economic competitiveness in the United States and abroad. Despite a concerted effort, the US lags well behind many similarly developed nations. Research suggests that the integration of fine arts education into traditional STEM curriculum (STEAM) boosts academic achievement in STEM subjects and closes gaps between low- and high-socioeconomic status students. Justifications for STEAM programs are based, however, on the unexamined assumption, for one, that fine arts courses instill creative and critical thinking skills that can be transferred to STEM subjects. The present study explores the impact of taking fine arts courses on mathematics achievement in high school. Using the High School Longitudinal Study of 2009 and multi-level regression modeling, this study provides evidence that credit accumulation in fine arts courses relates positively to advancing past Algebra II in high school. Additionally, this estimated impact is much greater in magnitude for low-SES students than for their high-SES peers.

This study identified factors related to solving mathematical word problems and then examined the differences in characteristics between students with low achievement in mathematics who were likely to have a learning disability and students with low achievement in mathematics who were unlikely to have a learning disability. Factoral analysis identified two significant factors: abstract thinking and long term retrieval from memory. Results indicated qualitative differences between sixth grade students with achievement in mathematics at or below the 25th percentile with indications of learning disabilities (MLD) and students with achievement in mathematics at or below the 25th percentile without an indication of a learning disability (Low Math/NLD). The Learning Disabilities Diagnostic Inventory, which measures intrinsic processing disorders indicative of learning disabilities, was used to differentiate between students with MLD (n = 13) and students with Low Math/NLD (n = 16). The Woodcock-Johnson III Tests of Achievement, Clinical Evaluation of Language Fundamentals-Fourth Edition, and the Informal Mathematics Assessment (IFA) were used to compare the two groups. In contrast to students with MLD, students with Low Math/NLD had a higher mathematical performance and had more difficulties with math fluency. When solving mathematics word problems on the IFA, a test composed of word problems, student interview, and error analysis, students with Low Math/NLD had more correct answers, more computational errors, and fewer translation errors than students with MLD did. Students with MLD had conceptual difficulties in the areas of analyzing, reasoning, and abstract thinking.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Includes bibliographical references (leaves 83-98). Issued in print and online. Available via ProQuest Digital Dissertations.

The research presented in this thesis is a case study located in the interpretive paradigm of qualitative research. The focus is on the use of van Hiele's theory to explore problems encountered in circle geometry by grade 11 learners and making some policy recommendations concerning the curriculum structure and teaching of the geometry at all grades. The interpretation is based to the learners' background in geometry i.e. their prior knowledge and experience of learning geometry. The study was carried out over a period of three years. The data collection process took a period of two months (April and May 2003) with a group of 21 grade 11 mathematics learners in a rural senior secondary school in the Eastern Cape. The researcher used document analysis, worksheets, participants' observation, van Hiele tests, a questionnaire and semi-structured interviews to collect data. The study showed that the structure of the South African geometry syllabus consists of a some what disorganized mixture of concepts. It is not sequential and hierarchical and it sequences concepts in a seemingly unrelated manner. The study revealed that the South African high school geometry curriculum is presented at a higher van Hiele level than what the learners can attain. The findings of the study showed that many of the grade 11 learners were under-prepared for the study of more sophisticated geometry concepts and proofs. Three categories of reasons could be ascribed to this: Firstly, there was insufficient preparation of learners during the primary and senior phases. Secondly the study indicated that there is overload of geometry at the high school level in the South African mathematics curriculum. Thirdly, the over-reliance on the traditional approach to teaching geometry, poor presentation of mathematical technical concepts and language problems, were identified as possible additional reasons for the poor learner understanding of geometry in general and circle geometry in particular. The study recommends that the structure of the South African geometry curriculum should be revisited and redesigned. Teachers should be empowered and developed to be more effective in teaching geometry through further studies in mathematics and in-service workshops. They should also be engaged in the process of implementing the van Hiele's theory in the teaching of geometry in their classrooms.

M.Ed. (Mathematics Education) / This dissertation was on mathematical proficiencies that learners displayed in their response to final examination questions on sequences and series, differential calculus, analytical geometry and trigonometry. The main focus was on four mathematical proficiencies, procedural fluency, conceptual understanding, strategic competence and adaptive reasoning. The initial goal was to review examination questions to identify mathematical proficiencies that the examination questions demanded and then an analysis of learners’ scripts to identify the mathematical proficiencies that the learners displayed in their response to examination questions. Review of literature first focused on the theoretical framework of the study, constructivism, its guiding principles and how it contributes towards mathematics learning. The framework for mathematical proficiency was shown with an aim of viewing other underlying issues on mathematical proficiency. The four mathematical proficiencies; conceptual understanding and procedural fluency constitute mathematical knowledge and strategic competence and adaptive reasoning are mathematical skills. Mathematical tasks are reviewed as properties of well-structured mathematical tasks in which examination questions were also mathematical tasks. The taxonomy of learning was discussed with an aim of finding properties of the taxonomy that inform the structure of the examination questions. Examination questions on sequences and series, differential calculus, analytical geometry and trigonometry were reviewed, to find mathematical proficiencies that the examination questions demanded and those that learners display in their responses.

This case study centres round an afterschool intervention programme aimed at enhancing mental computation skills of Grade 8 learners at a secondary school in the Erongo educational region of Namibia. Nine research participants took part in the study, and the mental computational strategies exhibited by these participants constitutes the unit of analysis. The study is anchored within an interpretive paradigm and is theoretically underpinned by constructivist epistemology. Kilpatrick, Swafford and Findell’s (2001) model of mathematical proficiency provides the conceptual framework supporting the study. The research was carried out in four sequential phases – an initial pre-test, the intervention itself, a follow-up post-test, and a focus group discussion. The study highlights the underdevelopment of mental computation skills and the associated lack of appropriate mental computational strategies in secondary school learners. It is recommended that appropriate time within the school curriculum be allocated for the development of learners’ mental computation skills.

This study is devoted primarily to a consideration of socio-economic status in relation to achievement in mathematics. However, a review of socio-economic status in relation to intelligence (as revealed in studies in the field) is first made because of the wide use of intelligence tests in an attempt to determine the child’s ability to succeed in school.

The study was undertaken to identify the factors that influence standard seven pupils when they choose whether to continue with mathematics at senior secondary level or not. The relative importance of the factors was also determined. The literature study identified the following factors: attitude towards mathematics, utility of mathematics, family members' influence, mathematics teacher's influence, peer group influence, achievement and gender. The empirical study dealt with the following: * A 77 item questionnaire was completed by 201 standard seven pupils. * The statistical analysis revealed significant differences between pupils who chose mathematics and those who did not, with regard to all variables except gender. * A regression analysis identified the most influential factors as achievement, family members' influence, attitude and the mathematics teacher. * The overall implications were: - Pupils be made to experience success so that their attitudes may change. - Parents must be involved in their children's education. / Psychology of Education / M. Ed. (Psychology of Education)

Thesis (MBA)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: Gender inequity in mathematics performance is a global phenomenon. In both the developed and the developing world, females perform more poorly in mathematics than males at senior secondary school level. In Namibia, the situation is no exception. Examination results for the past few years have shown that males outperform females in mathematics at senior secondary school level. This has resulted in more males taking mathematics as a major subject at tertiary level, with the consequence that they subsequently find better jobs than females. For the purpose of this study, a literature research was done to investigate the factors that might influence the mathematics performance of females and males. The search did not show any significant biological differences between males and females that could explain the differences in performance. Several other factors were, however, identified to playa role in how females perform in mathematics. The factors identified were: interest in mathematics, a person's self-concept, mathematics anxiety, attitude towards mathematics, gender stereotyping, and the roles of the family and teachers. These factors were tested in the Namibian situation by means of a questionnaire that was given to Grade 12 students who do mathematics and it was found that: 1. males and females' attitudes towards mathematics differ significantly. Males seem to have a much more positive attitude towards mathematics; 2. Females experience mathematics anxiety at a higher level than males; 3. Gender stereotyping influences the mathematics performance of females more negatively than males' performance; Family members' influence contributes significantly to the poorer performance of females; 5. Interest in mathematics seems to be higher in males than in females; 6. Teacher influence does not seem to play a significant role in the mathematics performance of males and females. (This is in contrast with the results of the literature review.); and 7. There is no difference in the self-concept of Namibian males and females. To help make mathematics more appealing to girls, the first step is to recognise the disparities. Each person in a girl's circle of family, teachers, community and friends can begin, even before she reaches primary school, to hold high expectations of her and praise her performance. Sophisticated technology is increasingly significant to our nation's economic, political and social health. Almost every element of society - in fields as diverse as music, sports and agriculture - is being touched by technology. To prepare them for.these jobs, we must present science, engineering and mathematics as non-intimidating subjects to every student, so that they will feel encouraged to gain the skills and knowledge necessary for technical careers. As we increasingly become part of the global economy, we must engage the intellectual potential of all our young people. / AFRIKAANSE OPSOMMING: Geslagsongelykheid in wiskunde prestasies is a globale verskynsel. Daar is bevind dat meisies swakker doen as seuns in wiskunde in die senior sekondere skoolfase in beide die ontwikkelende sowel as die ontwikkelde lande. Namibia is geen uitsondering nie. Eksamenuitslae van die afgelope paar jare het gewys dat seuns baie beter vaar as meisies in wiskunde, spesifiek in die senior sekondere skoolfase. Dit het tot gevolg gehad dat meer seuns wiskunde neem as hoofvak na skool en dat hulle gevolglik beter werksgeleenthede as meisies kry. Vir die doel van hierdie studie is 'n Literatuurstudie gedoen om uit te vind watter faktore beinvloed die wiskunde prestasies van studente. Die literatuurstudie het geen noemenswaardige biologiese verskille tussen seuns en meisies uitgewys wat moontlik die verskil in prestasies kan verklaar nie. Verskeie ander faktore is egter geidentifiseer wat beslis 'n rol speel in wiskunde prestasies van meisies. Die faktore wat geidentifiseer was, is: belangstelling in wiskunde, 'n persoon se selfbeeld, wiskunde angs, 'n persoon se houding teenoor wiskunde, geslags stereotipes, die rol van die familie en onderwysers. Bogenoemde faktore is getoets in die Namibiese situasie by wyse van 'n vraelys wat uitgegee is vir graad 12 leerlinge wat wiskunde doen. Die resultate wat verkry is, is as volg: 1. Daar is 'n groot verskil tussen seuns en meisies se houding teenoor wiskunde. Dit wil voorkom as seuns se houding meer positief is as die van meisies; 2. Meisies ondervind wiskunde angs in 'n groter mate as seuns; 3. Geslagstereotipes het 'n negatiewe invloed op die wiskunde prestasies van meisies; 4. Familielede se invloed speel 'n groot rol in die swakker prestasies van meisies; 5. Seuns stel meer belang in wiskunde as meisies; 6. Dit blyk asof die invloed van onderwysers nie 'n noemenswaardige rol speel in die wiskunde prestasies van studente nie; Dit is teenstrydig met die bevindinge in die literatuurstudie. 7. Daar is geen verskil in die selfbeeld van meisies en seuns nie. Die eerste stap om wiskunde meer aantreklik vir meisies te maak, is om die dispariteit tussen seuns en meisies te erken. Elke persoon wat op enige manier met meisies in aanraking kom, hetsy familie, onderwysers, gemeenskap of vriende kan, selfs voorskool al, begin om hoë verwagtinge van hulle te koester en hulle te prys vir goeie prestasies. Gesofistikeerde tegnologie raak al hoe meer belangrik vir ons nasie se ekonomiese, politiese en sosiale welslae. Bykans elke sektor in ons gemeenskap, so divers soos musiek, sport en landbou, word geraak deur tegnologie. Die wetenskappe, ingenieurswese en wiskunde moet dus, sonder intimidasie, aan elke student aangebied word, om hulle sodoende aan te moedig om die nodige vaardighede te ontwikkel vir tegnies beroepe. Ons moet al ons jongmense se intellektuele potensiaal ten volle benut om in lyn te kom met die wereld ekonomie.