O presente trabalho tem por objetivo divulgar e explorar as Provas sem Palavras no âmbito do Ensino Fundamental e Médio para, posteriormente, servir de possível material de consulta por parte de professores, na busca de melhores métodos de explicação sobre importantes assuntos desenvolvidos em sala. Dessa forma, imagina-se que a compreensão dos alunos através da visualização fortalecerá de maneira significativa a aquisição do conhecimento. Para tanto, são sugeridos diversos temas onde a visualização é desenvolvida e explicada, seja através de relato, seja através de demonstrações matemáticas. / The aim of the present work is to disseminate and explore the Proof Without Words in the scope of elementary and high school to be used later as a possible reference material for teachers in the search for better methods of explanation on important subjects developed in the classroom. In this way, it is imagined that students’ comprehension through visualization will significantly strengthen the acquisition of knowledge. In order to do so, several themes are suggested where the visualization is developed and explained, either through storytelling or through mathematical demonstrations.

The purpose of the study was to explore the relationship between mathematics teachers’ subject matter knowledge and their teaching effectiveness. A convenient sample of 19 grade 11 mathematics teachers and 418 students were initially selected for the study and took part in some stages of the study. Of this lot, only 11 teachers and 246 students participated in all the stages of the study. Explanatory Mixed methods research design which entails the use of a co-relational study and a descriptive survey design were employed in the study. Data was collected from the teachers using a self report questionnaire, Teacher Subject Matter Knowledge of Trigonometric Functions Scale (TSMKTFS) and peer evaluation questionnaire, and from students using teacher evaluation questionnaire and Student Trigonometric Functions Performance Scale (STFPS). All the instruments had their validity and reliability accordingly determined. Quantitative data gathered was analysed using descriptive and inferential statistics while qualitative data gathered from teachers’ and students’ tests were analysed using task performance analysis. It was found that a positive, statistically significant relationship existed between teachers’ subject matter knowledge and the composite measure of their teaching effectiveness. The relationships between teachers’ subject matter knowledge and students’ achievement and also between teachers’ subject matter knowledge and students’ rating of the teachers’ teaching effectiveness were found to be positive and statistically significant. However, the relationships between teachers’ subject matter knowledge and teachers’ self rating as well as teachers’ subject matter knowledge and peers’ rating of teachers’ teaching effectiveness were not found to be statistically significant though they were positive. Further data analysis showed that there was a difference between the subject matter knowledge of effective and ineffective teachers and also between the students taught by effective teachers and the students taught by the ineffective teachers. / Institute of Science and Technology Education / PhD (Mathematics Education)

Constructivist teaching strategies are undeniably accepted as effective in achieving the desired educational goals of constructing knowledge through active and creative inquiry. Inasmuch as teachers would love to adopt these strategies in their teaching, mathematics teachers find themselves in a situation where they are forced not to use them. This study investigated the factors that impacted on the selection and adoption of constructivist teaching strategies in selected Gauteng’s urban schools. Four (4) public schools and sixteen (16) mathematics teachers participated in the study. The parallel mixed methods design was employed in the study to produce both quantitative and qualitative data. The data were therefore analysed both quantitatively and qualitatively. It was found that the participating mathematics teachers had an understanding of constructivist theories of teaching and that they perceived their classroom environments to be constructivist in character. The study also found that the adoption of constructivist teaching strategies was hindered by teachers’ lack of skills and competencies to handle a curriculum that they felt was handed down to them without their full involvement at all the stages of its development. Learners’ family backgrounds were also identified as a major social factor that impacted negatively against selection of constructivist strategies. Based on these findings, recommendations were made on how constructivist views can be realised in the teaching of mathematics in South African schools. / Mathematics Education / M. Ed. (Mathematics Education)

Text in Afrikaans, abstract in Afrikaans and English / Hierdie studie is daarop gemik om te bepaal tot welke mate wiskundeleerlinge op skool en onderwysstudente in wiskunde, onderrig in logika ontvang as agtergrond vir strenge bewysvoering. Die formele aspek van wiskunde op hoerskool en tersiere vlak is besonder belangrik. Leerlinge en studente kom onvermydelik met hipotetiese argumente in aanraking. Hulle leer ook om die kontrapositief te gebruik in bewysvoering. Hulle maak onder andere gebruik van bewyse uit die ongerymde. Verder word nodige en voldoende voorwaardes met stellings en hulle omgekeerdes in verband gebring. Dit is dus duidelik dat 'n studie van logika reeds op hoerskool nodig is om aanvaarbare wiskunde te beoefen. Om seker te maak dat aanvaarbare wiskunde beoefen word, is dit nodig om te let op die gebrek aan beheer in die ontwikkeling van 'n taal, waar woorde meer as een betekenis het. 'n Kunsmatige taal moet gebruik word om interpretasies van uitdrukkings eenduidig te maak. In so 'n kunsmatige taal word die moontlikheid van foutiewe redenering uitgeskakel. Die eersteordepredikaatlogika, is so 'n taal, wat ryk genoeg is om die wiskunde te akkommodeer. Binne die konteks van hierdie kunsmatige taal, kan wiskundige toeriee geformaliseer word. Verskillende bewystegnieke uit die eersteordepredikaatlogika word geidentifiseer, gekategoriseer en op 'n redelik eenvoudige wyse verduidelik. Uit 'n ontleding van die wiskundesillabusse van die Departement van Onderwys, en 'n onderwysersopleidingsinstansie, volg dit dat leerlinge en studente hierdie bewystegnieke moet gebruik. Volgens hierdie sillabusse moet die leerlinge en studente vertroud wees met logiese argumente. Uit die gevolgtrekkings waartoe gekom word, blyk dit dat die leerlinge en studente se agtergrond in logika geheel en al gebrekkig en ontoereikend is. Dit het tot gevolg dat hulle nie 'n volledige begrip oor bewysvoering het nie, en 'n gebrekkige insig ontwikkel oor wat wiskunde presies behels. Die aanbevelings om hierdie ernstige leemtes in die onderrig van wiskunde aan te spreek, asook verdere navorsingsprojekte word in die laaste hoofstuk verwoord. / The aim of this study is to determine to which extent pupils taking Mathematics at school level and student teachers of Mathematics receive instruction in logic as a grounding for rigorous proof. The formal aspect of Mathematics at secondary school and tertiary levels is extremely important. It is inevitable that pupils and students become involved with hypothetical arguments. They also learn to use the contrapositive in proof. They use, among others, proofs by contradiction. Futhermore, necessary and sufficient conditions are related to theorems and their converses. It is therefore apparent that the study of logic is necessary already at secondary school level in order to practice Mathematics satisfactorily. To ensure that acceptable Mathematics is practised, it is necessary to take cognizance of the lack of control over language development, where words can have more than one meaning. For this reason an artificial language must be used so that interpretations can have one meaning. Faulty interpretations are ruled out in such an artificial language. A language which is rich enough to accommodate Mathematics is the first-order predicate logic. Mathematical theories can be formalised within the context of this artificial language. Different techniques of proof from the first-order logic are identified, categorized and explained in fairly simple terms. An analysis of Mathematics syllabuses of the Department of Education and an institution for teacher training has indicated that pupils should use these techniques of proof. According to these syllabuses pupils should be familiar with logical arguments. The conclusion which is reached, gives evidence that pupils' and students' background in logic is completely lacking and inadequate. As a result they cannot cope adequately with argumentation and this causes a poor perception of what Mathematics exactly entails. Recommendations to bridge these serious problems in the instruction of Mathematics, as well as further research projects are discussed in the final chapter. / Curriculum and Institutional Studies / D. Phil. (Wiskundeonderwys)

Although South African teachers have ample opportunities for professional development (PD), weak results of learners show that these opportunities have had a limited effect on the development of the Mathematics teachers’ instructional skills. The improvement of the teaching of Mathematics is regarded as a solution to learners’ poor performance, because teachers play a key role in the improvement of pupils’ learning. In the light of this, a Mathematics PD programme implemented in a province of South Africa was evaluated and served as a case study. The aim of this evaluation was to probe the quality of the programme since it had been suggested that improving the quality of teaching can be achieved by offering effective PD programmes. Thus, the evaluation was done in an attempt to establish the academic value of the intervention. The investigated programme – which was implemented in a rural and under-resourced setting – focused on FET Mathematics teachers and used mentoring and workshops as its key intervention implementers. Five teachers were involved in this programme. Data collection methods included semi-structured interviews, lesson observations, mentoring and workshop reports, the results of learners, and pre- and post-test results of the participants. The evaluation of the PD programme revealed the following: that the workshops addressed the participants’ content knowledge gap to a limited degree; that mentoring was able to assist with the individual classroom-related needs of the participants, and that the community of practice formed in the workshops helped the participants to develop by means of working together on lesson preparation, micro-teaching, and content knowledge exercises. Other findings revealed that the duration of the workshops were adequate, however their intensity was insufficient to effectively address the participants’ needs, and that the workshops were carefully planned, given that the same topics were repeated. The mentor teachers and other facilitators encountered challenges relating to the long intervals between the mentoring sessions, the limited post-lesson-observation discussion time, the significant distances between the involved schools and the heavy teaching load of the participants. Nevertheless, recommendations on improving the effectiveness of future PD programmes included careful selection of the dosage of interventions, site-based mentoring, to incentivise participants of PD programmes, alleviating the teaching load of overburdened participants and the creation of conducive environments in rural areas for the formation of communities of practice. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education (Mathematics Education))

The study seeks to examine the role of mentoring and how it could be used in the process of professional development of mathematical literacy teachers in the Greater Taung area. The study attempts to flag the importance of mentoring in professional development, especially for mathematical literacy teachers. To obtain data for the study sixteen mathematical literacy teachers from Taung area (within Ruth Mompati District) were purposively selected. Questionnaires and interviews were used to collect relevant data. Literature review, based on previous studies on mentoring also provided data for the study. The following findings emerged from the study: a) that mentoring has over the years has been an effective process for developing early-career teachers’ practices b) that there are no formal mentoring programmes to assist mathematical literacy teachers in the Greater Taung area c) there is a need for effective communication between the mentor and the mentee, since the learning that takes place in a mentoring relationship is usually through regular interaction.From the findings, a collaborative form of mentoring is recommended.Both parties in this relationship are considered as a source of knowledge that can contribute to the learning that occurs within the context of mentoring. / Mathematics Education / Ph. D. (Mathematics Education)

The quality of education in South Africa has come increasingly under scrutiny for various reasons and learners ‘performance in mathematics is one of the main areas of concern. Learners in secondary schools in Nzhelele East Circuit in Limpopo Province, South Africa, are not performing well in mathematics. Learners who want to pursue careers such as civil engineering, medicine and other qualifications where mathematics is a prerequisite find it difficult to follow these careers. The study used focus group discussions with 20 Grade 12 learners, face-to-face semi-structured interviews with six teachers and four SMT to investigate factors affecting grade 12 learners performance in mathematics in two secondary schools. The study highlighted socio-cultural and psychological factors that are seen to be barriers in mathematics performance. The purpose of this study was to explore factors that affect Grade 12 learners’ performance in mathematics. As there are many factors, this study's main emphasis was on the influence of the home environment, teachers’ competence and attitudes in teaching mathematics, learners’ attitudes towards mathematics and strategies that can be used to improve learners’ performance in mathematics. The afore-said were named themes each of which related to questions contained in the semi-structured interview schedule. The study included literature review from Kenya, Ghana and South Africa. Qualitative research method was used. Interviews were conducted with SMT, teachers and learners. The researcher set out to answer the following question What are the dominant and most profound socio-cultural and psychological factors of the Grade 12 mathematics learners affecting performance in the Nzhelele East Circuit, Vhembe District of Limpopo Province? The following points will also be taken into consideration during this research. How do learner performance trends in mathematics education look like among Grade 12 mathematics learners in the Nzhelele East Circuit, Vhembe District of Limpopo Province, and South Africa? What are the teacher-based factors established to have been contributory to the state of learner performance in mathematics in the selected participant schools? What are the School Management Team (SMTs) factors established to have been contributory to the state of learner performance in mathematics in the selected participant schools? THE AIMS AND OBJECTIVES Aim This study investigates the dominant and most profound socio-cultural and psychological factors affecting learner performance in mathematics among Grade 12 learners in the Nzhelele East Circuit, Vhembe District of Limpopo Province, and South Africa. Objectives The objective of this study was to explore the socio-cultural and psychological factors in the home and school environment that affect Grade 12 learners performance in mathematics at Nzhelele East Circuit, Vhembe District of Limpopo Province. Based on the above question the following were findings of the research. • Mathematics is believed to be a critical school subject in most regions of the world in general, and Sub-Saharan Africa in particular. • A plethora of governments – especially those in developing economies where governments are targeting industrialization and technological development believe mathematics is crucial for facilitating development and advancement of the general populace of their regions. • Mathematics is a compulsory subject in most education systems around the world. • There are a variety of complexities and constraints affecting the teaching and learning of mathematics in most regions of the world. • There is poor learner performance in mathematics. This is indicated by high failure rate in mathematics during end-of-year learner assessments. • The reasons for the poor performance of learners in mathematics in the selected schools were vast and intertwined. • Efforts have been made at international level to intervene with regard finding solutions to complexities and constraints affecting teaching-learning environment in mathematics. • The complexities and constraints affecting the teaching-learning environment of mathematics in South Africa stem from South Africa's past era of apartheid education. • Mathematics has been a major target of improvement and transformation by the post-apartheid government in South Africa. • Regardless of the efforts made by the post-apartheid government in South Africa to improve and transform teaching-learning environment in mathematics, there are perpetual complexities and constraints still hindering progress, and this affects learner output in mathematics. • Mathematics is one of the poorly performing subjects in the post-apartheid education system in South African schools – especially those schools which are based in formerly disadvantaged areas such as homelands and townships. • There is a growing body of literature investigating the complexities and constraints affecting the teaching-learning of mathematics in South Africa. Apart from the conclusions based on general observations, the study furthermore concluded that critical learner-based factors, teacher-based factors and SMT-base factors contributed to the state of affairs in the selected participant schools. This study therefore concluded thus: • Learner-based factors Mathematics learners were poorly prepared in the lower grades for senior grades. In other words, learners lacked proper foundation and background in mathematics. Learners were not well taught the basics of mathematics in previous grades. Furthermore, mathematics learners lacked assistance with homework for example because the majority of parents were illiterate and therefore not involved in supervision of learners beyond school environment. Learners showed negative attitude towards their teachers and the subject. Learners were not self-motivated in mathematics. • Teacher-based factors Teachers did not have enough workshops on how to teach mathematics, and also on content knowledge improvement. Less creative teachers were teaching mathematics. Teachers lacked support from their principals. The majority of teachers lacked passion in mathematics. • School Management Teams (SMTs) factors This study concludes that mathematics teachers were not receiving adequate support from the School management Teams (SMTs). Lack of teacher support by SMTs stems from poor organisation of supervisory roles expected from SMTs. Teachers' work is not being properly monitored and supervised. RECOMMENDATIONS Based on the conclusions drawn from the study, the following recommendations are crucial, and they have to be implemented: • Recommendations to the Department of Education This study recommends that the Department of Education should monitor or revisit the methods of teaching and learning of mathematics. Assessment should also be revisited to ensure that the mathematics paper is not too long for the learners during examinations. Enlisted service providers who facilitate teacher workshops for mathematics must be conversant with content requirements of mathematics. Considerations should be made to simplify the mathematics question paper. The Department of Education should also provide necessary resources such as textbooks timeously. Knowledgeable mathematics specialists and advisers could be enlisted to visit regular visits to schools to assist teachers and learners throughout the year. • Recommendations to the School Management Teams (SMTs) The SMT should ensure that their educators are adequately qualified to teach mathematics. as a subject as well as being able to teach their learners in a way that they understand the subject. In addition, teachers who are knowledgeable in teaching mathematics should be appointed to teach mathematics. The SMTs should also ensure that compulsory workshops are provided for mathematics teachers at school level. Furthermore, the SMTs should ensure that educators are able to identify learners that are under-performing, monitor the utilisation of study time and assist in resolving problems regarding the poor performance of such individual learners. School Management Teams shall facilitate additional after-hours lessons and sessions to assist learners identified as lacking in home environment assistance for example. Moreover, SMTs should also encourage all Grade 12 mathematics learners to participate in supervised extra mathematics lessons and extra-mural activities in order to develop and build their self-confidence and positive self-esteem. In addition, the SMT members should be more supportive to their mathematics teachers. Continuous moderation of teachers' work should be encouraged. School Management Teams (SMTs) should also develop motivational programmes and instruments to encourage and motivate learners in their respective schools. For example, performing learners could be awarded with prizes in public – especially during school organised functions which might include learners, teachers and parents. • Recommendations to the teachers The teachers should make it a point that they attended mathematics workshops as organised by various stakeholders. Teachers' interest in mathematics could be improved by improving their knowledge of subject content in mathematics, and personal recognition by authorities. Performing teachers could also be recognised and awarded with prizes publicly at school gatherings and meetings. Teachers should also be encouraged to obtain further qualifications and skills in mathematics. • Recommendations to the learners Efforts should be made to improve learners’ attitudes towards mathematics, and in addition to their mathematics teachers. Learners should be made aware of national target for mathematics education and the implications thereof. This could be achieved by utilizing educators – especially those who teach Guidance as a subject to learners to provide more convincing evidence of the spin-offs of obtaining good passes in mathematics in South Africa. SUGGESTION FOR AREAS NEEDING FURTHER STUDY There is a need to conduct follow-up research on: • applied strategies and instrument to improve learner attitude towards mathematics. • Establishing whether the complexities and constraints affecting learner performance in mathematics affect both girl and boy learners the same considering that their circumstances and conditions might materially differ. / Curriculum and Instructional Studies / M. Ed. (Curriculum Studies)

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-07-11T12:30:59Z No. of bitstreams: 1 Adriano de Morais Martins.pdf: 1050611 bytes, checksum: f9d015c33a34637340247d0cbd439217 (MD5) / Made available in DSpace on 2018-07-11T12:30:59Z (GMT). No. of bitstreams: 1 Adriano de Morais Martins.pdf: 1050611 bytes, checksum: f9d015c33a34637340247d0cbd439217 (MD5) Previous issue date: 2018-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The purpose of this thesis is to bring the debate about the affective domain in Mathematics Education to the national scene and as specific objectives: to understand the affective domain, to select and present a synthesis of texts related to the theme and to identify the theoretical references used. For that, we developed a theoretical study of a qualitative nature, built from the study of international researches that deal with the affective domain and its dimensions, supported by content analysis. The study is justified by the lack of debate in Mathematics Education of this topic in the national scope and the absence of theoretical and theoretical-methodological studies. Throughout our study, we define the affective domain as a set of dimensions formed by beliefs, attitudes, values and emotions. Initially, we sought to understand the historical process that led to the studies that were focused on the beliefs for the studies focused and other dimensions of the affective domain. The construction of the research was based on contemporary studies by international authors, all of 2015. Thus, the studies selected for our research were: the study entitled "Toward a participatory approach to" beliefs "in Mathematics Education" by Jeppe Skott, which dealt with a contemporary vision for the study of beliefs; the study "From Love, Frustration and Mathematics: A Historical-Cultural Approach to Emotions in Teaching and Learning Mathematics" by Luis Radford, who studied the construction of emotions and how they fit into teaching mathematics in a classroom; "The Attitude Construct in Mathematical Education" written by Pietro Di Martino and Rosetta Zan, which dealt with issues related to attitude building; the study by Katrin Rolka and Bettina Roesken-Winter entitled "Network between theories to understand beliefs and their fundamental role in Mathematical Education", which proposed studies from the intercession of different theories about beliefs; and the study written by George N. Philippou and Marilena Pantziara, "Developments of Effective Beliefs in Mathematics Teachers," who advocated studies on effective teacher beliefs that correspond to beliefs about the teacher's ability to organize and execute directed actions to accomplish a task specific. The studies show that when looking at teacher training and student achievement through theoretical lenses aimed at the affective domain, we can obtain better results in the research that addresses teacher training, better understand the difficulties of the students and propose continuing education course more effective. In this way we hope that this study will contribute to Brazilian researchers who intend to study this subject / A presente tese tem como objetivo geral trazer o debate sobre o domínio afetivo na Educação Matemática para o cenário nacional e como objetivos específicos: compreender o domínio afetivo, selecionar e apresentar uma síntese de textos relacionados ao tema e identificar os referenciais teóricos utilizados. Para tanto, desenvolvemos um estudo teórico de caráter qualitativo, construído a partir do estudo de pesquisas internacionais que tratam do domínio afetivo e suas dimensões, apoiados na análise de conteúdo. O estudo se justifica pela carência de debate na Educação Matemática desse tema em âmbito nacional e a ausência de estudos teóricos e teóricos-metodológicos. Ao longo de nosso estudo, definimos o domínio afetivo como um conjunto de dimensões formados pelas crenças, atitudes, valores e emoções. Inicialmente, buscamos compreender o processo histórico que conduziu os estudos que estavam voltados às crenças para os estudos voltados às demais dimensões do domínio afetivo. A construção da pesquisa ocorreu a partir de pesquisas contemporâneas de autores internacionais, publicados em 2015. Dessa forma, os estudos selecionados para nossa pesquisa foram: o estudo intitulado “Rumo a uma abordagem participativa para “crenças” em Educação Matemática” de Jeppe Skott, que tratou de uma visão contemporânea para o estudo das crenças; o estudo “Do Amor, frustração e Matemática: uma abordagem histórico-cultural de Emoções no Ensino e Aprendizagem de Matemática” de Luis Radford, que estudou a construção das emoções e como elas se inserem no ensino de matemática em uma sala de aula; “O constructo de atitude em Educação Matemática” escrito por Pietro Di Martino e Rosetta Zan, que trataram de questões relativas à construção de atitude; o estudo de Katrin Rolka e Bettina Roesken-Winter intitulado “Rede entre teorias para compreender crenças e seu papel fundamental na Educação Matemática”, que propuseram estudos a partir da intercessão de diferentes teorias sobre crenças; e o estudo escrito por George N. Philippou e Marilena Pantziara, “Desenvolvimentos de crenças eficazes nos professores de Matemática”, que defenderam estudos sobre crenças eficazes de professores que corresponde as crenças sobre a capacidade do professor organizar e executar ações direcionadas para realizar uma tarefa específica. Os estudos apontam que ao olhar para a formação do professor e rendimento escolar dos alunos por meio de lentes teóricas voltadas ao domínio afetivo, podemos obter melhores resultados nas pesquisas que abordam formação de professores, compreender melhor as dificuldades dos alunos e propor curso de formação continuada mais eficazes. Desse modo esperamos que esse estudo contribua para pesquisadores brasileiros que se propuserem a estudar esse tema

Made available in DSpace on 2016-04-27T16:57:35Z (GMT). No. of bitstreams: 1 Agnaldo Da Conceicao Esquincalha.pdf: 2760765 bytes, checksum: 4b98025a110f8c095d5e0d5b8d626829 (MD5) Previous issue date: 2015-03-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims at investigating the knowledge revealed by tutors of a distance continuing education course for mathematics teachers. The context of the research was the tutoring system of the Improvement Course in Mathematics, offered by the State Government of Rio de Janeiro from 2011 onwards. Initially we follow the work of 32 tutors over a year between 2011 and 2012 in order to list and classify the types of interventions in discussion forums among the course participants. After considering the results, we offer initial training to freshman tutors in 2012, to promote an improvement in the actions that we consider to be below expectations. Between August 2012 and July 2013 six tutors, the subjects of this research, were followed and participated in a training program in service. For the training of tutors, beyond the specifics of the Improvement Course in Mathematics, we grounded our work on the TPACK (Technological Pedagogical Content Knowledge) theoretical framework, assuming that technological, pedagogical and mathematical knowledge skills are fundamental for the exercise of their functions. The research, qualitative in nature, made use of questionnaires and conducting focus groups to collect data, which were interpreted under the light of thematic content analysis. For the triangulation of data, we used the discursive types found in interventions by tutors in the course s discussion forums. Our analysis indicated that affective and attitudinal components play a key role in the exercise of mentoring in this context and, therefore, we concluded the research by proposing the expansion of TPACK theoretical framework, including these components in a fourth type of knowledge, featuring TPACK-OTE (Technological Pedagogical Content Knowledge-Online Teacher Education) / Neste trabalho, teve-se o intuito de investigar os conhecimentos revelados por tutores de um curso de formação continuada para professores de Matemática, oferecido na modalidade a distância. O contexto da investigação foi o sistema de tutoria do Curso de Aperfeiçoamento em Matemática, oferecido pela Rede Estadual do Rio de Janeiro a partir de 2011. Inicialmente, acompanhou-se o trabalho de 32 tutores ao longo de um ano, entre 2011 e 2012, a fim de elencar e tipificar suas intervenções realizadas em fóruns de discussão junto aos cursistas. A partir dos resultados, foi oferecida uma formação inicial aos tutores ingressantes em 2012, a fim de promover melhoria nas ações consideradas aquém do esperado. Entre agosto de 2012 e julho de 2013, foram acompanhados, e participaram de um programa de formação em serviço, seis tutores, que constituem os sujeitos desta pesquisa. Para a formação desses tutores, além das especificidades do Curso de Aperfeiçoamento, houve inspiração no quadro teórico TPACK (Technological Pedagogical Content Knowledge), assumindo que os conhecimentos tecnológicos, pedagógicos e de conhecimento matemático são fundamentais para o exercício de suas funções. A pesquisa, de natureza qualitativa, utilizou-se de questionários e de grupos focais para coleta de dados, que foram interpretados à luz da análise temática de conteúdo. As tipologias discursivas encontradas nas intervenções realizadas pelos tutores nos fóruns de discussão permitiram a triangulação dos dados. As análises indicaram que componentes afetivo-atitudinais têm papel fundamental no exercício da tutoria no contexto da formação continuada de professores a distância e, por isso, a pesquisa é concluída com uma proposta de expansão do quadro teórico TPACK, incluindo esses componentes em um quarto tipo de conhecimento, caracterizando o TPACK-OTE (Technological Pedagogical Content Knowledge-Online Teacher Education)

Made available in DSpace on 2016-04-27T16:57:37Z (GMT). No. of bitstreams: 1 Rubens Vilhena Fonseca.pdf: 1601945 bytes, checksum: 9bd5a69dcacb920b758afcd188c86010 (MD5) Previous issue date: 2015-04-22 / This work aims to analyze a didactic sequence directly linked to the research question, which sought to provide students an investigative route in order to find solutions to the problems raised, which are in the field of number theory, and are related to prime numbers and Fundamental Theorem of Arithmetic, objects of this research, developed with students of the degree course in mathematics of the Pará State University. There were theoretical studies and a literature review for the formulation of the research question and identification of conceptual tools for analyzing protocols. Six questions were applied to ten students, involving prime numbers and the fundamental theorem of arithmetic. Based primarily on studies that considered the number representations and their transparent or opaque characteristics, in a qualitative study, the answers given by the students were analyzed. Preliminary studies allowed the development of a problematic around the following research question: What knowledge and difficulties about the concepts / properties of prime numbers and the fundamental theorem of arithmetic are evidenced by undergraduate students in Mathematics of the Pará State University when subjected to a didactic sequence that intended to involve them in investigative routes formatted from theoretical assumptions related to numerical representations and their transparent / opaque features? The work is justified by the scarcity of research related to number theory in mathematics education in Brazil. The results revealed the need for mastery of undergraduates with regard to issues related to understanding research themes; specifically, difficulties relating to work with certain numerical representations were highlighted, especially in relation to the concepts of primes and the fundamental theorem of arithmetic / Este trabalho tem como objetivo analisar uma sequência didática diretamente ligada à questão de pesquisa, que pretendeu proporcionar aos estudantes um percurso investigativo em busca de soluções para os problemas levantados, que estão no domínio da Teoria dos Números, e são relativos aos Números Primos e ao Teorema Fundamental da Aritmética, objetos desta pesquisa, desenvolvida com alunos do curso de licenciatura em matemática da Universidade do Estado do Pará. Realizaram-se estudos preliminares, de ordem teórica, e uma revisão bibliográfica para a formulação da questão de pesquisa e identificação de ferramentas conceituais para a análise dos protocolos. Foram aplicadas seis questões envolvendo números primos e o teorema fundamental da aritmética a dez estudantes. Com base, principalmente, em estudos que consideravam as representações numéricas e suas características transparentes ou opacas, em uma abordagem qualitativa de pesquisa, analisaram-se as respostas dadas pelos alunos. Os estudos preliminares permitiram a elaboração de uma problematização em torno da seguinte questão de pesquisa: quais saberes e dificuldades acerca dos conceitos/propriedades dos números primos e do teorema fundamental da aritmética são evidenciados por licenciandos em Matemática da Universidade do Estado do Pará quando submetidos a uma sequência didática que pretendeu inserir os mesmos em percursos investigativos, formatados a partir de pressupostos teóricos ligados a representações numéricas e suas características transparentes/opacas? O trabalho justifica-se pela escassez de pesquisas relacionadas com a Teoria dos Números na área da Educação Matemática. Os resultados revelaram a necessidade de um domínio mais amplo dos licenciandos no que se refere às questões relacionadas à compreensão dos temas em tela; especificamente, ficaram evidenciadas dificuldades atinentes ao trabalho com certas representações numéricas, e, principalmente, em relação aos conceitos de números primos e do teorema fundamental da aritmética