Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-12-04T11:55:04Z No. of bitstreams: 1 César Augusto Pimentel de Souza.pdf: 2249653 bytes, checksum: a5e594086976fe654bfb207a8782b87e (MD5) / Made available in DSpace on 2017-12-04T11:55:04Z (GMT). No. of bitstreams: 1 César Augusto Pimentel de Souza.pdf: 2249653 bytes, checksum: a5e594086976fe654bfb207a8782b87e (MD5) Previous issue date: 2017-09-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present study deals with the concepts of Literacy and Mathematical Literacy under the aegis of solving problems from a qualitative, documentary and bibliographical approach. The purpose of this paper is to analyze the convergences and divergences between the guidelines of the PNAIC/2014 Book 4 "Operations in Problem Solving" and a collection of mathematical textbooks for the first years of elementary school (1st, 2nd and 3rd years), focusing on the problems of Additive and Multiplicative Structure. The following French theories were used in the theoretical reference: Gérard Vergnaud's Theory of Conceptual Fields (TCC) and Yves Chevallard's Anthropological Theory of Didactics (TAD). TCC was useful for classifying the types of problems of the Additive and Multiplicative Structure present in Book 4 of the PNAIC/2014 and in the three volumes of textbooks entitled Mathematical Literacy. The TAD, in turn, provided the analysis of the praxeological organizations that are articulated around the types of tasks, techniques, technologies and theories of the problems selected in the textbooks. The results obtained are based on elements and findings that support the idea that there is a partial consonance between the PNAIC’s teacher training book and the textbook. It has been found that some types of TCC problems have not been addressed in Book 4 of the PNAIC and in the Textbooks Collection, and it has also been found, on the basis of the TAD, that although textbook problems are presented with a diversity of contexts and forms, usually demand the same action of the subject in relation to mathematical knowledge. The conceptual and methodological choices identified in the quoted materials are addressed in this research / O presente estudo versa sobre os conceitos de Alfabetização e Letramento Matemático sob a égide da resolução de problemas a partir de uma abordagem qualitativa e de caráter documental e bibliográfico. O objetivo deste trabalho é analisar as convergências e divergências entre as orientações do Caderno 4 do PNAIC/2014 “Operações na Resolução de Problemas” e uma coleção de livros didáticos de matemática destinados ao ciclo de alfabetização (1º, 2º e 3º anos), com foco nos problemas de Estrutura Aditiva e Multiplicativa. Foram utilizadas no referencial teórico as seguintes teorias francesas: A Teoria dos Campos Conceituais (TCC) de Gérard Vergnaud e a Teoria Antropológica do Didático (TAD) de Yves Chevallard. A TCC foi útil para a classificação dos tipos de problemas de Estrutura Aditiva e Multiplicativa presentes no Caderno 4 do PNAIC/2014 e nos três volumes de livros didáticos intitulados como Alfabetização Matemática. A TAD, por sua vez, propiciou a análise das organizações praxeológicas que se articulam em torno dos tipos de tarefas, técnicas, tecnologias e teorias dos problemas selecionados nos livros didáticos. Os resultados obtidos baseiam-se em elementos e constatações que permitem defender a ideia de que existe uma consonância parcial entre o Caderno de formação de professores do PNAIC e o livro didático. Verificou-se que alguns tipos de problemas identificados pela TCC não foram contemplados no Caderno 4 do PNAIC ou na Coleção analisada, e verificou-se também, com base na TAD, que embora os problemas propostos nos livros didáticos se apresentem com uma diversidade de contextos e formas, geralmente demandam a mesma ação do sujeito em relação ao conhecimento matemático. As escolhas conceituais e metodológicas, identificadas nos materiais citados também foram analisadas e pudemos identificar convergências e opções distintas que caracterizam esses materiais

The thesis deals with the issues that are tied with reading and mathematical literacy. The literacy is being considered by solved exrcises at the second grade of elementary school. The purpose of this work is to bring nearer the connectedness between reading literacy and other subjects - in this case mainly math. The work is divided into two parts. The first part deals with the theory, in which there is outline of the description of reading and mathematical literacy, verbal exercises and what is the function of working sheets. The second part is practical. There are put created working sheets with chosen topics from math, which were given to the pupils at the elementary school. The cooperation with pupils wihtin filling the working sheets can be also found in this thesis. The analysis of this literacy and processes of solving are attached in the end.

The purpose of this study was to compare Turkey and the European Union (EU) regarding aspects (use, self-confidence and attitude) of students&rsquo / information and communication technologies (ICT), the relationships between ICT aspects and mathematical and problem solving literacy performances, and to understand education policy makers&rsquo / perceptions on ICT in Turkey. A multimethod (quantitative and qualitative) research design was used in this study. Country groups &ndash / an EU member group, a new EU member group and Turkey- were formed on the basis of the status of a country in the EU, and that of having ICT data in the Programme for International Student Assessment (PISA) 2003. This study has three focuses. The first focus of the present study was to examine similarities and differences in ICT use, self-confidence in ICT and attitudes toward computers in students from Turkey and the EU. The sample of this focus was those students from the EU member group (N=56,610), the new EU member group (N=24,834) and Turkey (N=3,231) who participated in the PISA 2003. Multivariate analysis of covariance - controlling students&rsquo / economic, social and cultural status (ESCS) and attitudes toward computers- and univariate analysis of covariance -controlling ESCS- were conducted to see whether students&rsquo / ICT aspects differ across country groups. The first focus of the present study indicated that Turkish students have lower self-confidence in using computer and the Internet and they use the Internet less frequently than students in the EU. Contrary to this, the findings of this focus revealed that Turkish students have relatively more positive attitudes toward computers and they use program/software more frequently than do students in the EU. The second focus of the present study was to model the relationships among ICT factors and mathematical and problem solving literacy performances of Turkish and the EU students. The sample of this focus was those students from the EU member group (N=57,787), the new EU member group (N=25,359) and Turkey (N=3,590) who participated in the PISA 2003. The proposed path analytic models were separately tested for each country group. The second focus revealed that students&rsquo / socioeconomic and cultural status and selfconfidence in routine computer tasks have positive and medium level relationships with their mathematical and problem solving literacy performances, for all country groups. Furthermore, students&rsquo / self-confidence in Internet tasks had a positive and low level relationship with these performances for all country groups. On the other hand, it was found that students&rsquo / frequency of computer and Internet use and their self-confidence in high-level computer tasks have generally negative and small relationships with these literacy performances in all country groups. The third focus aimed to investigate education policy makers&rsquo / perceptions of the ICT policy making and implementation process in Turkey, and their evaluations of the findings of the quantitative phase of this study. The participants of this focus consisted of seven education policy makers from the Ministry of National Education and universities in Turkey. The data, collected with interviews, were content-analyzed by coding data, identifying, and relating the categories and sub-categories, that is, open, axial and selective coding were conducted respectively. In the third focus of the present study, participants specified the primary issues of ICT policy making and the implementing process in Turkey and made suggestions on these issues. Participants frequently related the findings of the quantitative phase of this study to the economic, social and cultural status of students.

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2010.

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2010.

The purpose of the present study is to investigate the factors affecting mathematical literacy of 15-year-old students in Programme for International Student Assessment (PISA) across different cultural settings. The present study was conducted across three countries. These countries are Brazil, Japan and Norway. The countries were selected on the basis of their rankings in PISA 2000 study. Japan represented a high performing country with an average score of 557, Norway represented an average performing country with an average score of 499, and Brazil represented a low performing country with an average score of 334. The study explored how mathematical literacy is stimulated by predictors related to the students, the families and the school. A separate factor analysis was carried out for each questionnaire such as student questionnaire and cross curricular competencies questionnaire within the data of each country. Since the results of factor analyses of three countries were parallel, the observed variables representing the latent variables were selected from the student questionnaire and cross curricular competencies questionnaire administered in PISA 2000 in order to be used in the structural equation modeling. The included factors affecting mathematical literacy in PISA 2000 are attitudes towards reading, student-teacher relations, climate, communication with parents, usage of technology and facilities, attitudes towards mathematics and reading literacy. The proposed model was tested using structural equation modeling across three different cultures with different performance levels in PISA 2000. The findings of the study show that the latent independent variable having the strongest effect on mathematical literacy is the usage of technology and facilities in Brazil, communication with parents in Japan and attitudes towards reading in Norway. Moreover, the results were as follows: (1) Reading literacy significantly and positively influences mathematical literacy in all three countries. (2) There is a reciprocal relationship between the attitudes towards mathematics and mathematical literacy. In Brazil, the influence of attitudes towards mathematics on mathematical literacy is higher. However, the influence of mathematical literacy on attitudes towards mathematics is higher in Norway. (3) The attitudes towards reading have a negative direct effect and a positive indirect effect on mathematical literacy. (4) The student-teacher relations have a positive effect on mathematical literacy in Japan and Norway. But, in Brazil, this effect is negative. (5) The student-related factors affecting school climate are significantly and positively related to mathematical literacy in Brazil. On the other hand, the effect of climate on mathematical literacy is negative in Japan and non-significant in Norway. (6) Communication with parents significantly and positively influences the mathematical literacy in all three countries. (7) The usage of technology and facilities significantly and positively affects mathematical literacy in Brazil. However, this effect is negative in Japan and non-significant in Norway.

Orientador: Prof. Dr. André Ricardo Oliveira da Fonseca / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2014. / Este trabalho busca chamar a atenção para a necessidade do uso da formalização matemática como etapa a se cumprir na aprendizagem do conceito de função para o Ensino Médio, sendo este o principal objetivo. O problema da pesquisa constitui-se em: qual a necessidade do ensino ser contextualizado e a relevância da evolução histórica de conceitos, culminando na necessidade do uso da formalização matemática para o ensino de funções. Este estudo fundamenta-se em BOYER (1974), FIORENTIN (1994), SCHREINER (2004), MACIEL (2011), CARAÇA (1951), LOBEIRO (2000), LIMA (2005, 2006, 2012), FERREIRA (2013), COSTA (1971), DAVIS (1986). Esta pesquisa tem caráter qualitativo e utiliza como instrumentos: questionários para seis voluntários, sendo metade deles oriundos de escola pública ainda cursando o 2 o ano do Ensino Médio e os demais, de escola privada e já cursando o 1 o semestre do Ensino Superior. Aula direcionada baseada nos dados colhidos a partir dos questionários e como última etapa do processo, enquete sobre o reconhecimento da importância da formalização matemática. Os resultados apontam para uma preocupação com a qualidade das aulas ministradas sobre funções, de maneira que a formalização deva ser trabalhada de modo consistente, equilibrada, e principalmente, provida de significado ao educando. Em síntese o ponto inicial para o sucesso é uma alfabetização matemática de qualidade, promovendo situações de desafios e estímulos que facilitem o uso de abstrações. Sendo fundamental a qualificação e aperfeiçoamento dos professores de todos os níveis de ensino. / This work seeks to call attention to the need of the use of the mathematical formalization as a phase to go through the learning of the concept of function for secondary school (High School), being this its main goal. The problem of the research lies in: what the need of the contextualized teaching is and the relevance of the historical evolution of concepts, culminating on the need of the use of the mathematical formalization for the teaching of functions. This study is based on BOYER (1974), FIORENTINI (1974), SCHREINER (2004), MACIEL ( 2011), CARAÇA (1951), LOBEIRO (2000), LIMA (2005, 2006, 2012), FERREIRA (2013), COSTA (1971), DAVIS (1986). This research has a qualitative character and utilizes as instruments: questions for six volunteers, being half of them public school still coursing the 2nd year of High School and the others, from private school and already in the first semester of college or university. Directed class based on the data picked from the questions and as the last phase in the process, a survey about the acknowledgement of the importance of the mathematical formalization. The results point to a concern with the quality of the classes ministrated on functions, so that the formalization should be worked in a consistent, balanced way, and mainly provided with the meaning to the learner. Summing up, the start to success is a qualified mathematical literacy, promoting situations of challenges and stimuli which facilitate the use of abstractions. Being fundamental the qualificaon and perfectioning of teachers in all levels of teaching.

What happens when teachers are required to implement a mandatory mathematics literacy curriculum whose purposes and pedagogy is distinctly different from that of mathematics curricula of the past? More specifically: How do teachers beliefs and understandings of the curriculum affect the implementation pathway of a mathematics reform intended for ALL? In 2006 the national Department of Education of South Africa introduced a new curriculum into the mathematics landscape, namely Mathematical Literacy. This curriculum, which is markedly dissimilar in pedagogy, politics and purposes from past mathematics curricula, was introduced as a mandatory alternative to mathematics in the senior secondary phase of schooling; not as an integral component of mathematics curricula but as a unique subject of its own. It recognizes that every adult and therefore every child can and should do some form of mathematics. This research focuses on the implementation of this new curriculum in a context were mathematical literacy levels are not only unacceptably low among pupils leaving secondary schooling but also among many teachers charged with delivering mathematics education to the learners in South Africa. The three research questions guiding this study are: 1) What do teachers understand to be the purposes, problems and possibilities contained in the mathematical literacy curriculum? 2) How do teachers proceed to implement the mathematical literacy curriculum in their classrooms? 3) Why do teachers implement this curriculum in the ways they do? In other words, what explains the implementation pathways followed by the mathematical literacy curriculum in real classroom contexts? A review of the literature on curriculum and policy implementation revealed broad encapsulating themes that provide lenses for reform failure. It also provided a perspective that calls for domain specific research. Following on this, the study articulated a broader conceptual framework premised on the perception that a deep understanding of a curriculum is required, for contemporary reforms in mathematical literacy, especially if the goal is to pursue deep change in instructional practices and beliefs. Within this framework, three propositions were generated and then later tested against the emerging data: Proposition one: Teachers may not have a deep understanding of the purposes, problems and possibilities contained in the Mathematical Literacy curriculum. Proposition two: Teachers implement the Mathematical Literacy curriculum in their classroom using beliefs and pedagogies that are already entrenched in their practice. Proposition three: Teachers implement mathematical literacy only because it is a mandatory subject and not because of any strong conviction of the inherent value of this curriculum. A qualitative research design was used which included two in-depth case studies against the backdrop of a snapshot survey of fifty-four mathematical literacy teachers as an embedded unit of analysis. Using evidence from an array of data collection instruments, the study found that the two educators had a superficial understanding of the intentions of the curriculum both in terms of required pedagogy and purpose of the reform. For both educators the teaching of mathematics in context was outside their paradigm of understanding as was their limited grasp of the 'spirit' of this new reform. What was further revealed was that educators teaching mathematical literacy felt and expressed an overwhelming threat to the status of their professional teaching identity. The explorative study concludes with implications for future studies and professional teacher development. It also further expands on why a strong theory of action is mandatory if the challenges of complex curriculum change are to be met. / Thesis (PhD (Education Policy Studies))--University of Pretoria, 2008. / Education Management and Policy Studies / unrestricted

The main aim of the study was (1) to identify errors committed by learners in financial mathematics and (2) to understand why learners continue to make such errors so that mechanisms to avoid such errors could be devised. The following has been hypothesised; (1) errors committed by learners are not impact upon by language difficulties, (2) errors committed by learners in financial mathematics are not due to prerequisite skills, facts and concepts, (3) errors committed by learners in financial mathematics are not due to the application of irrelevant rules and strategies. Having used Polya’s problem-solving techniques, Threshold Concept and Newman’s Error Analysis as the theoretical frameworks for the study, a four-point Likert scale and three content-based structured-interview questionnaires were developed to address the research questions. The study was conducted by means of a case study guided by the positivists’ paradigm where the research sample comprised of 105 Grade-10 Mathematics Literacy learners as respondents. Four sets of structured-interview questionnaires were used for collecting data, aimed at addressing the main objective of the study. In order to test the reliability and consistency of the questionnaires for this study, Cronbach’s Alpha was calculated for standardised items (α = 0.705). Content analysis and correlation analysis were employed to analyse the data. The three hypotheses of this study were tested using the ANOVA test and hence revealed that, (1) errors committed by learners in financial mathematics are not due to language difficulties, as all the variables illustrated a statistical non-significance (2) errors committed by learners in financial mathematics are not due to prerequisite skills, facts and concepts, as the majority of the variables showed non-significance and (3) errors committed by learners in financial mathematics were due to the application of irrelevant rules and strategies, as 66.7% of the variables illustrated a statistical significance to the related research question.

Philosophiae Doctor - PhD / In this study the construct of personal theories is used to represent the teacher's conceptions, which are interpreted as the consciously held beliefs. The teacher's personal theories encompass beliefs, images, values and attitudes as well as understanding about teaching and learning. This study investigates the influence of the teacher's conceptions of mathematics, of the teaching and learning of mathematics and of the context before and after a structured learning experience. The interest in the teacher's conceptions is derived from the assumption that these serve as a primary component that influence how teachers think about their professional responsibilities and how they act in their classrooms. Furthermore, the extent of implementation of a new curriculum has been linked to the scope of congruence between the teachers' conceptions and the underpinning philosophy of the intended curriculum. The study of the teacher's conceptions is especially relevant during a time of educational reform, such as the current transition to an Outcomes Based Education curriculum in South Africa. The participants in this study consist of four primary school mathematics teachers with various educational backgrounds, who teach at schools situated in different physical environments. The conceptions that these teachers have of mathematics, of the teaching and learning of mathematics and the influence of the context are investigated using a variety of instruments. Data collection was done with a questionnaire, a repertory grid, a semi-structured interview and lesson observations. The teachers participated in the Teaching Intervention and Support Programme (TISP), as a structured teacher learning experience. The programme is centred on the integration of the developmental and socio-cultural perspectives on teacher learning. With the developmental perspective the focus is on the acquisition of intellectual skills, while the socio-cultural perspective emphasizes participation in social practice. Both are directed at effecting conceptual change. With the developmental approach the process of conceptual change involves the development of new conceptions from existing conceptions. From the socio-cultural perspective the context is paramount and conceptual change is seen as new ways of being and acting within a particular context. The teachers were invited to attend a two-week intervention session, followed by a six months support programme that was aimed at establishing a teacher learning community. The learning experiences provided during the intervention session were drawn mainly from Realistic Mathematics Education. On completion of the programme, the teachers' conceptions of mathematics, of the teaching and learning of mathematics and the influence of the context were again investigated. The results of this study show that two of the participants had highly mechanistic conceptions of mathematics, and the teaching and learning of mathematics. The remaining two had a more empiristic approach with its high focus on environmental activities. After the programme, the teachers with the mechanistic views adopted a mixed. conception with some of the mechanistic conceptions retained, but now interspersed with some empiristic and realistic conceptions. The participants with the empiristic conceptions adopted a more realistic conception, but again to varying degrees. Thompson's (1991) hierarchical structure for the development of conceptions was also used to describe the extent of conceptual change. However, it was found that a concentric, rather than a hierarchical representation is a more appropriate to describe these changes. With regards to the socio-cultural view of conceptual change, all the participants perceived the context differently. The teachers' actions were also more commensurate with the practices associated with teachers that encourage learner autonomy, mathematical investigations and a facilitative role for the teacher.