Thesis (MEd)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This study explored the number sense of 47 final year primary school pre-service teachers in Namibia and was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests. The literature review revealed that learner performance is linked to teacher subject knowledge (Ball, 1990, Ma, 1999) and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics (Ball, 1990; Graven 2004). Number sense studies of pre-service teachers (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) have indicated that the development of number sense should be a focus of primary pre-service teacher education. The data in this mixed method research design were obtained from a Number Sense Questionnaire, a Written Computations Questionnaire and a Mental Calculations Questionnaire. These questionnaires were adapted from instruments developed by Professor Der-Ching Yang for 6th and 8th grade learners in Taiwan. Teacher confidence was measured by the McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Six randomly selected pre-service teachers were interviewed to determine their use of number-sensible strategies. The correlation analysis shows a strong relationship between number sense and mental calculations; between number sense and confidence in both the ability to do and the ability to teach mathematics and between mental and written calculations. The overall results of this study reveal that the final year primary pre-service teachers demonstrate limited number sense and possess very few of the indicators of number sense that were described by Kalchman, Moss and Case (2001). The findings expose a lack of conceptual understanding of the domain numbers and operations, particularly in the domain of rational numbers and the operations of multiplication and division. The pre-service teachers have little or no access to a variety of flexible number-sensible strategies to solve problems and calculate mentally. They lack the fluency in basic facts and procedures to perform written calculations efficiently and correctly. Unexpectedly, the analysis of the confidence survey shows that they are confident in both their ability to do mathematics and their ability to teach mathematics. It is recommended that mental calculations and computational estimation should become a focus of primary school mathematics education. Institutions responsible for teacher training should develop the number sense of pre-service teachers and research effective and long-term professional development programmes. The confidence and willingness of the teachers to learn can be used as an important resource. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die getalbegrip van 47 finale jaar primêre skool voordiens-onderwysers in Namibië en is gemotiveer deur die swak prestasie van die Namibiese primêre skool leerlinge in beide nasionale en internasionale gestandaardiseerde assesseringstoetse. Die literatuurstudie het aan die lig gebring dat leerlinge se prestasie gekoppel is aan onderwyservakkennis (Ball, 1990, Ma, 1999) en dat onderwysers se vertroue in hulle vermoë om wiskunde te doen en te onderrig, die manier waarop hulle onderrig en hul bereidwilligheid om wiskunde te leer beïnvloed (Ball, 1990, Graven 2004 ). Studies van voordiens primêre onderwysers se getalbegrip (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) toon dat die ontwikkeling van getalbegrip 'n fokus van primêre voordiensonderwyseropleiding behoort te wees. Die data in hierdie gemengde metode navorsing is verkry uit 'n Getalbegrip, 'n Skriftelike Berekeninge en 'n Hoofrekene Vraelys. Hierdie vraelyste is gebaseer op die instrumente wat ontwikkel is deur Professor Der-Ching Yang vir graad 6 en 8 leerlinge in Taiwan. Onderwyservertroue is gemeet deur die McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Ses ewekansig geselekteerde voordiens-onderwysers is ondervra om te bepaal watter sinvolle strategieë hulle gebruik om vrae oor getalbegrip te beantwoord. Die korrelasie-analise toon 'n sterk verband tussen getalbegrip en hoofrekene; tussen getalbegrip en vertroue in die vermoë om wiskunde te doen en te leer, en tussen vermoë om hoofrekene en skriftelike bewerkinge te doen. Die algehele resultate van hierdie studie dui daarop dat die finale jaar primêre voordiens-onderwysers oor beperkte getalbegrip en baie min van die aanwysers van getalbegrip wat deur Kalchman, Moss en Case (2001) beskryf is, beskik. Die bevindinge toon ‘n gebrek aan begrip van die domein van getalle en bewerkings, veral in die domein van rasionale getalle en die bewerkings vermenigvuldiging en deling. Die voordiens-onderwysers beskik oor min of geen soepel strategieë om probleme op te los en hoofrekene te doen nie. Hulle beskik nie oor die vlotheit in basiese feite en bewerkings om skriftelike berekeninge doeltreffend en korrek uit te voer nie. Die vertroue wat voordiens-onderwysers uitgespreek het in hulle vermoë om wiskunde te doen en onderrig staan in sterk teenstelling met hierdie bevindige. Dit word aanbeveel dat hoofrekene en skatting 'n fokus van primêre skool wiskunde-onderwys behoort te wees. Instansies gemoeid met onderwyseropleiding behoort die getalbegrip van voordiensonderwysers te onwikkel en navorsing te doen oor effektiewe en lang-termyn programme vir professionele ontwikkeling. Onderwysers se vertroue en bereidwilligheid om te leer kan as 'n belangrike hulpbron gebruik word.

Thesis (MEd) -- Stellenbosch University, 1981. / Bibliography / Theses -- Education / Dissertations -- Curriculum studies / Theses -- Curriculum studies / No abstract available

Thesis (MEd)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: South Africa is in the midst of a mathematics and science education crisis that challenges all key role-players. The Institute for Mathematics and Science Teaching at the University of Stellenbosch (IMSTUS), was involved in several university-school partnership (systemic intervention) projects that sought to provide continuing professional development to mathematics and science teachers and to help them make a greater impact on the learners that they teach. One of these intervention projects was the Sciences and Mathematics Initiative for Learners and EducatorS (SMILES) that targeted mathematics and science teachers and learners in under-resourced schools in the Western Cape. The effects of an intervention aimed at supporting and enhancing teacher professional development will only be seen in the learners once teachers have accepted and mastered the pedagogies proposed. Professional development that does not “enthuse, support, train and renew, and encourage” will probably fail. When considering this, the question that must be asked is whether the SMILES project was in fact enthusing, supporting, training, renewing and encouraging. The purposes and aims of the SMILES project with specific reference to professional development of science teachers were to enhance teachers’ pedagogical content knowledge and address the critical issues confronting science education of which three are: constructivist teaching, understanding the nature of science, and scientific argumentation. The characteristics of effective professional development, the core features of professional development and the theoretical constructs to evaluate professional development of teachers were used in this study to evaluate the effectiveness of the model used in the SMILES project. A concurrent version of the mixed method approach was adopted for the collection and analysis of the data. Although causality is always difficult to prove in a school setting because of the many variables that affect student performance, improved student achievement is the ultimate litmus test for teacher professional development effectiveness. Analysis of the National Senior Certificate results of the project schools compared with the National and Provincial results indicated that the project schools on the whole fared better than the National results. The project schools outperformed the national and provincial results for Life Sciences in 2011, 2012 and 2013 by at least four percentage points. The highest result achieved was 85,5% in 2011. In 2012 and 2013 these results were 82,7% and 83,0% respectively. In Physical Sciences the project schools started with results below that achieved nationally (34,7%) and then ended up with a pass percentage within half a percentage point of the provincial result (72,1%). The Mathematics results were not as positive. The project schools started by achieving a 63,4% pass rate and ended with a percentage pass rate of 63,3% having initially taking a dip down to 51,3%. At the end of the intervention the Mathematics results were better than the national results but were 10% lower than the Provincial average. Although it is difficult to pin down the results solely to the effects of the intervention, the comparison with provincial and national results reasonably controls for most of the extraneous variables including variations in enrolments in these subjects. On the affective side it is almost certain that the attitude of the learners and the teachers toward their respective subjects improved during the tenure of the project. This could have had a positive effect on the National Senior Certificate results achieved by the project schools. / AFRIKAANSE OPSOMMING: Suid-Afrika is midde in 'n wiskunde en wetenskap onderwyskrisis wat alle sleutelrolspelers uitdaag. Die Instituut vir Wiskunde en Wetenskaponderwys aan die Universiteit van Stellenbosch (IWWOUS), was betrokke by verskeie universiteit-skool vennootskapsprojekte (sistemiese intervensie) wat gepoog het om voortgesette professionele ontwikkeling te bied aan wiskunde en wetenskap onderwysers en hulle te help om 'n groter impak op die leerders wat hulle onderrig, te maak. Een van hierdie intervensie-projekte was die Wetenskappe en Wiskunde-inisiatief vir leerders en opvoeders (SMILES) wat wiskunde en wetenskap onderwysers en leerders, in hulpbronarm skole in die Wes-Kaap, geteiken het. Die impak van 'n intervensie wat daarop gemik is om onderwyser professionele ontwikkeling te ondersteun en bevorder, sal eers in die leerders waargeneem kan word, wanneer onderwysers die voorgestelde pedagogieë aanvaar en bemeester. Professionele ontwikkeling wat nie "begeester, ondersteun, oplei en vernuwe asook aanmoedig” nie, sal waarskynlik misluk. Hierdie stelling in ag genome, is die vraag wat gevra moet word, of die SMILES-projek werklik onderwysers begeester, ondersteun, opgelei, vernuwe en aangemoedig het. Die doelstellings en doelwitte van die SMILES projek, met spesifieke verwysing na die professionele ontwikkeling van Wetenskap-onderwysers, was om onderwysers se pedagogiese inhoudelike kennis te versterk en om kritieke kwessies waarmee wetenskap-onderwys gekonfronteer word, aan te spreek. Drie van hierdie kwessies is, konstruktivistiese onderrig, begrip van die aard van wetenskap en wetenskaplike argumentering. Die eienskappe van effektiewe professionele ontwikkeling, die kern kenmerke van die professionele ontwikkeling en die teoretiese konstrukte om professionele ontwikkeling van onderwysers te evalueer, is in hierdie studie gebruik om die doeltreffendheid van die model wat in die SMILES-projek gevolg is, te evalueer. 'n Gelyklopend gemengde-metode benadering is gevolg vir die insameling en ontleding van die data. Hoewel oorsaaklikheid altyd moeilik is om in 'n skoolopset te bewys, as gevolg van die baie veranderlikes wat studente se prestasie beïnvloed, is verbeterde studente prestasie die uiteindelike lakmoestoets vir doeltreffendheid van professionele onderwyser-ontwikkeling. Ontleding van die Nasionale Senior Sertifikaat-uitslae van die projek-skole, in vergelyking met die nasionale en provinsiale resultate, dui daarop dat die projek-skole oor die algemeen beter gevaar het as die nasionale uitslae. Die projek-skole het die nasionale en provinsiale skole se resultate vir Lewenswetenskappe in 2011, 2012 en 2013 met ten minste vier persentasie punte oortref. Die hoogste resultaat behaal was 85,5% in 2011. In 2012 en 2013 was hierdie uitslae onderskeidelik 82,7% en 83,0%. In Fisiese Wetenskappe het die projek-skole met resultate onder wat nasionaal behaal was (34,7%) begin, en geëindig met ʼn uiteindelike slaagpersentasie binne 'n halwe persentasiepunt van die provinsiale resultate (72,1%). Die wiskunde-uitslae was nie so positief nie. Die projek-skole het begin met 'n 63,4% slaagsyfer en geëindig met 'n slaagpersentasie van 63,3% na ʼn aanvanklike insinking na 51,3%. Aan die einde van die intervensie was hul Wiskunde-resultate beter as die nasionale resultate, maar 10% laer as die provinsiale gemiddelde. Alhoewel dit moeilik is om die resultate slegs vas te pen aan die gevolg van die intervensie, dien die vergelyking met provinsiale en nasionale resultate as redelike kontroles vir meeste van die eksterne veranderlikes insluitend variasies in inskrywings in hierdie vakke. Op die affektiewe vlak is dit byna seker dat die gesindheid van die leerders en die onderwysers ten opsigte van hul onderskeie vakke verbeter het tydens die projek. Dit kon moontlik 'n positiewe uitwerking op die projek-skole se Nasionale Senior Sertifikaat resultate gehad het.

The purposes of the study were: to determine the relationship between class size and academic achievement among university students in first-semester calculus classes, and to compare opinions about the instructor, course, and classroom learning environment of university students in small first-semester calculus classes with those in large classes. The sample consisted of 225 university students distributed among two large and two small sections of first-semester calculus classes taught at the University of Texas at Arlington during the fall of 1987. Each of two tenured faculty members taught a large and small section of approximately 85 and 27 students, respectively. During the first week of the semester, scores from the Calculus Readiness Test (CR) were obtained from the sample and used as the covariate in each analysis of covariance of four periodic tests, a comprehensive final examination, and final grade average. The CR scores were also used in a logistic regression analysis of attrition rates between each pair of large and small sections of first-semester calculus. Three semantic differentials were used to test the hypotheses relating to student opinion of the instructor, course, and classroom learning environment. It was found that for both pairs of large and small first-semester calculus classes there was no significant difference in the adjusted means for each of the four periodic tests, the final examination scores, the final grade averages, and the attrition rates. It was also found that the means of the student evaluation of the course by students in small and large classes were not significantly different, and the results of the student evaluations of the instructor and classroom learning environment by students in small and large first—semester calculus classes were mixed.

The purpose of this study was to investigate the relationship among the teachers' use of the individual elements of lesson design, students' mastery of mathematics objectives, the hours of inservice training completed by the teachers and the teachers' years of experience. The individual elements of lesson design are defined by Madeline Hunter and are anticipatory set, objective and purpose, input, modeling, checking for understanding, guided practice, and independent practice.

D.Ed. (Didactics) / Please refer to full text to view abstract

O estudo das Transformações Geométricas do plano, mais particularmente das reflexões por retas, é recomendado em documentos oficiais que direcionam o ensino em nosso no país. Seu estudo é recomendado, dentre outros motivos, pelo seu grande auxílio na resolução de problemas e também pelas possibilidades de associação com outros assuntos de fundamental importância em Matemática como, por exemplo, a congruência de triângulos. Nestes documentos oficiais que balizam a Educação Básica, também é recomendada a implementação de outras metodologias em sala de aula. Na presente pesquisa, associamos essas duas recomendações ao trabalharmos o tópico reflexão por retas por meio de uma sequência de atividades, baseadas na metodologia da Investigação Matemática. Aplicamos essa sequência a dois grupos de professores de Matemática e a um grupo de estudantes de Licenciatura em Matemática. As produções feitas, por eles, nos cadernos de respostas e no software GeoGebra foram analisadas de acordo com a Teoria das Representações Semióticas, de Raymond Duval. Os resultados apontaram que as atividades investigativas em conjunto com o software auxiliaram na resolução dos problemas propostos. Este trabalho indica mais uma alternativa para os professores abordarem o tema reflexão por retas em suas aulas e esperamos estar, também, contribuindo para a formação inicial e continuada de docentes em Matemática. / The study of Geometric Transformations of the plane and, more particularly, reflections in a line, is recommended in official documents of the education in our country. It is recommended, among other reasons, due to its great help in solving problems and also by the possibilities of association with other matters of fundamental importance in mathematics like, as an example, the congruence of triangles. In those official documents that guide the Basic Education, is also recommended the implementation of other methods in classrooms. In this research, we associate these two recommendations in order to work with reflections in a line through a sequence of activities based on the methodology called Mathematics Investigation. We applied the sequence of activities in two groups of mathematics teachers and a group of undergraduate students in Mathematics. The productions made by them in the notebook answers and in the GeoGebra software were analyzed according to the Theory of Semiotic Representations, developed by Raymond Duval. The results showed that the investigative activities, together with the software, helped partially to solve the proposed problems. This work indicates one more alternative for teachers to address the topic reflections in a line in their classes and we hope to be also contributing to the initial and continued education of mathematics teachers.

Submitted by Ricardo Cedraz Duque Moliterno (ricardo.moliterno@uefs.br) on 2018-01-22T21:35:32Z No. of bitstreams: 1 DISSERTA??O MESTRADO - V. FINAL SARA MAMONA.pdf: 1205147 bytes, checksum: 28aac56157850ad49fec25db554eca31 (MD5) / Made available in DSpace on 2018-01-22T21:35:32Z (GMT). No. of bitstreams: 1 DISSERTA??O MESTRADO - V. FINAL SARA MAMONA.pdf: 1205147 bytes, checksum: 28aac56157850ad49fec25db554eca31 (MD5) Previous issue date: 2017-02-10 / This study aimed to investigate the professional knowledge required by the licensed teacher, in the context of the initial training of mathematics teachers for their work in the Education of Young and Adults - EJA, as a modality of Basic Education. To do so, some of the specific objectives defined were: to identify the professional knowledge oriented to the EJA present in the Pedagogical Proposal of the Course of Mathematics from the State University of Feira de Santana - UEFS, Teaching Menus and Plans; Identify the necessary knowledge to be built during the initial training for a graduate in mathematics to work in the EJA; Contribute to the understanding and reflection about the necessary knowledge for the initial formation of mathematics teachers to work in the EJA. Even though the modality represents an important demand to be attended in the Teaching Network, there are still many professionals who work in the modality without training in the area. Considering that the exit profile of the graduates should meet the demands of Basic Education and how the EJA constitutes it, it is necessary to return the look to the initial formation of teachers. Mathematics was chosen because it is one of the areas considered as the most difficult by the students. A qualitative approach was chosen, with the perspective of constructing a sensitive understanding of the studied phenomenon from the perceptions brought by the research subjects - undergraduates and teacher-trainers with some experience in the EJA. The used techniques were document analysis, semi-structured interviews and questionnaires. The locus of the research was the Course of Mathematics from UEFS. This work is structured in five topics, including an introduction; the second topic brings a survey of the researches on the same object of this work and considerations referring to the chosen methodological path; the third topic refers to the theoretical framework with two chapters that deal with initial teacher training, mathematical questions for teaching in the EJA and the specificities of the EJA, listed in three different dimensions that are related to the EJA individuals, the pedagogical and political-administrative dimensions. The fourth topic brings the discussions of the results from the analysis of course documents, the speeches of the research subjects and the reflections established with the theoretical framework. Finally, final considerations demonstrate that the teaching and the subjects of the EJA, their realities and specificities, are the relevant sources to be understood during the initial formation of mathematics teachers to act in EJA. / Este estudo prop?s-se a investigar, no ?mbito da forma??o inicial de professores de matem?tica os conhecimentos profissionais necess?rios ao professor licenciado para a sua atua??o na Educa??o de Jovens e Adultos - EJA, modalidade da Educa??o B?sica. Para tanto, alguns dos objetivos espec?ficos definidos foram identificar os conhecimentos profissionais orientados para a EJA presentes na Proposta Pedag?gica do Curso de Licenciatura em Matem?tica da Universidade Estadual de Feira de Santana - UEFS, Ementas e Planos de Ensino; identificar os conhecimentos necess?rios de serem constru?dos durante a forma??o inicial para um licenciado em matem?tica atuar na EJA; contribuir para a compreens?o e reflex?o acerca dos conhecimentos necess?rios para a forma??o inicial de professores de matem?tica para atua??o na EJA. Apesar de a modalidade representar uma demanda importante para atendimento na Rede de Ensino, ainda h? muitos profissionais que atuam na modalidade sem forma??o na ?rea. Considerando que o perfil de sa?da dos licenciados deveria atender ?s demandas da Educa??o B?sica e como a EJA a constitui, faz-se necess?rio voltar o olhar para a forma??o inicial de professores. A matem?tica foi escolhida por tratar-se de uma das ?reas consideradas pelos alunos como das mais dif?ceis. A abordagem escolhida foi a qualitativa, com a perspectiva de construir uma compreens?o sens?vel do fen?meno estudado a partir das percep??es trazidas pelos sujeitos da pesquisa ? graduandos e professores-formadores com alguma experi?ncia na EJA. As t?cnicas utilizadas foram an?lise de documentos, entrevistas semiestruturadas e question?rios. O l?cus da pesquisa foi o Curso de Licenciatura em Matem?tica da UEFS. Este trabalho est? estruturado em cinco t?picos, sendo uma introdu??o; o segundo t?pico traz um levantamento das pesquisas realizadas que tratam do mesmo objeto deste trabalho e considera??es referentes ao percurso metodol?gico escolhido; o terceiro t?pico consta do quadro te?rico com dois cap?tulos que tratam da forma??o inicial de professores, de quest?es matem?ticas para o ensino na EJA e sobre as especificidades da EJA, elencadas em tr?s distintas dimens?es que est?o relacionadas aos sujeitos da EJA, as dimens?es pedag?gicas e pol?tico-administrativas. O quarto t?pico traz as discuss?es dos resultados a partir da an?lise de documentos do curso, das falas dos sujeitos da pesquisa e das reflex?es estabelecidas com o quadro te?rico. Finalmente, no ?ltimo t?pico, s?o apresentadas as considera??es finais que apontam que o ensino e os sujeitos da EJA, suas realidades e especificidades, s?o as fontes relevantes para serem compreendidas durante a forma??o inicial de professores de matem?tica para a atua??o na Educa??o de Jovens e Adultos.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-07-30T12:25:10Z No. of bitstreams: 1 Marcelo Rivelino Rodrigues.pdf: 4565631 bytes, checksum: 768cc5f53630e3bfa212a133d70cbecf (MD5) / Made available in DSpace on 2018-07-30T12:25:10Z (GMT). No. of bitstreams: 1 Marcelo Rivelino Rodrigues.pdf: 4565631 bytes, checksum: 768cc5f53630e3bfa212a133d70cbecf (MD5) Previous issue date: 2018-04-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Probabilistic knowledge is relevant to life in society, since well-founded decision-making can help provide a competitive edge both in the labor market and daily life. The present study investigated the conceptions of probability and randomness held by basic education teachers when faced with questions that address these topics. Data were collected from 41 sixth- do ninth-grade Brazilian teachers who responded to “Probabilistic Concepts Questionnaire”, applied to reveal the conceptions of probability held by the group. The multidimensional data were interpreted by subjecting the teachers’ responses to implicative and cohesive analysis, using Hierarchical, Implicative, and Cohesive Classification (CHIC) software, which yielded cohesion and implication graphs of the relationships operating among the variables investigated. The categorizations delineated by Azcárate and Cardeñoso for conceptions of probability, as well as the definition of probabilistic literacy formulated by Gal, provided the theoretical framework for the study. Two official educational guidelines—the Brazilian Curricular Guidelines (locally referred to as PCN) and the Brazilian Common Curricular Basis (BNCC)—were compared to detect similarities and pinpoint changes made to these documents with regard to the teaching of probability in basic education. In addition, Chevallard’s Anthropological Theory of the Didactic was employed to identify the types of tasks, techniques, and theories present in a mathematics textbook series approved by the National Textbook Program (PNLD). The analysis evidenced the probabilistic conceptions held by the participants, in the dimensions of randomness and probability. Four groups were identified in each dimension. Dimension randomness: deterministic; causality; multiplicity; uncertainty. Probability dimension: indefinite; causality; deterministic; uncertainty; subjectivity. The analysis evidenced the probabilistic conceptions held by the participants, in the dimensions of randomness and probability. In the randomness dimension, six groups of conceptions were identified: determinism; causality; multiplicity; uncertainty; standard; undefined. The probability dimension comprised five groups: causality; determinism; uncertainty; contingency; personalist. The investigation shed light on the conceptions of probability held by the participants, allowing probabilistic literacy levels to be categorized / Os conhecimentos probabilísticos mostram-se relevantes na vida em sociedade, pois cada vez mais as tomadas de decisão criteriosas apresentam-se como um dos diferenciais no mercado de trabalho, bem como em nosso dia a dia. Por esta razão, esta pesquisa teve como objetivo analisar as concepções de probabilidade e aleatoriedade de professores que atuam no ensino básico, quando estes se defrontam com questões que envolvem tais temas. Para a coleta de dados, aplicou-se o instrumento de pesquisa “Questionário de Concepções Probabilísticas”, a 41 professores do ensino fundamental II (6º ao 9º ano), visando identificar as concepções probabilísticas apresentadas por este grupo. Como metodologia, optou-se pela análise de dados multidimensionais, aplicando-se análise implicativa e coesitiva às respostas dos professores, utilizando software de Classificação Hierárquica, Implicativa e Coesitiva (CHIC), que gerou grafos de coesão e de implicação das relações entre as variáveis observadas. Para fundamentar o estudo, apoiamo-nos nas categorizações de concepções probabilísticas de Azcárate e de Cardeñoso e na definição de letramento probabilístico proposta por Gal. No desenvolvimento da pesquisa, foram analisados documentos oficiais como os Parâmetros Curriculares Nacionais (PCN) e Base Nacional Comum Curricular (BNCC) para observação de semelhanças, e possíveis evoluções na passagem do 1º para o 2º documento, no que tange às orientações para a abordagem do tema probabilidade no ensino básico. Também se analisou uma coleção de livros didáticos aprovada pelo Programa Nacional do Livro Didático (PNLD), com o objetivo de identificar, à luz da Teoria Antropológica do Didático, os tipos de tarefas, técnicas, tecnologias e teorias presentes nas atividades propostas na coleção. As análises permitiram identificar as concepções probabilísticas que emergiram dos participantes, nas dimensões aleatoriedade e probabilidade. Na dimensão aleatoriedade seis grupos foram identificados: determinista; causalidade; multiplicidade; incerteza; padrão; indefinidos. A dimensão probabilidade compreendeu cinco grupos: causalidade; determinista; incerteza; contingência; personalista. Destaca-se, ainda, que as análises possibilitaram categorizar os níveis de letramento probabilístico

Submitted by Mariana Dornelles Vargas (marianadv) on 2015-05-25T13:53:19Z No. of bitstreams: 1 formacao_docente.pdf: 1103895 bytes, checksum: 87eb39709baa4087ec2be94bb70dc471 (MD5) / Made available in DSpace on 2015-05-25T13:53:19Z (GMT). No. of bitstreams: 1 formacao_docente.pdf: 1103895 bytes, checksum: 87eb39709baa4087ec2be94bb70dc471 (MD5) Previous issue date: 2012 / Nenhuma / Constituir-se professor requer um longo processo. Cada sujeito traz consigo conhecimentos, habilidades, saberes e crenças, muitas vezes, tão arraigados que a formação acadêmica não consegue mudá-los. O presente estudo investiga a relação entre a formação do professor e a construção de crenças que são evidenciadas na prática em sala de aula pelos professores de Matemática. Pergunta-se: Como se constroem as crenças dos professores de Matemática sobre seu campo de conhecimento no decorrer da formação e trajetória docente? Como as crenças matemáticas dos professores orientam sua prática pedagógica junto aos alunos de quintas séries do Ensino Fundamental? A pesquisa de abordagem qualitativa utiliza-se das narrativas escritas e entrevistas orais, gravadas e transcritas com seis professores de Matemática. A análise das falas desses professores fundamenta-se teoricamente em Tardif, Nóvoa, Ponte, Ernest, Gómez Chacón, Vila e Callejo, Marcelo Garcia, Cunha e Perrenoud, entre outros e estrutura-se em seis eixos: a opção pela formação docente; saberes adquiridos e disciplinas determinantes na formação acadêmica; saberes docentes advindos do estágio e seus reflexos na prática docente: o campo de conhecimento e seu entendimento na voz das professoras; o ensino aprendizagem; dificuldades, possibilidades; a Matemática segundo as crenças das professoras. O relato das docentes entrevistadas evidencia a importância da formação acadêmica na construção de crenças e concepções, bem como a influência de sua prática junto aos alunos. Embora as marcas pessoais trazidas e a história de vida de cada uma sejam poderosas, a formação acadêmica reforçou concepções e/ou contribuiu com algumas mudanças. A força do campo de conhecimento foi reforçada, mas abriram-se novas possibilidades e questionamentos, que fizeram e fazem os professores continuar buscando mais espaços de formação. / A long process is required to be a teacher. On the first education acquired each student brings knowledge and skills and beliefs, a lot of times so ingrained that the gradation on the bachelors degree can not change them. This case study investigates the relation between the teacher's graduation and the construct of beliefs that are evidenced on the practice in the classrooms by the Mathematics teachers. The question is: How are the Math teacher's beliefs built during the graduation and docent trajectory about its knowledge? How the teachers Mathematics beliefs lead its pedagogic practice with the fifth grade students of the Elementary School? The qualitative approach research uses the written narrative and recorded and transcribed interviews with six Mathematics teachers. The speech analysis of these teachers is theoretically based in Tardif, Nóvoa, Ponte, Ernest, Gómez Chacón, Vila e Callejo, Marcelo Garcia, Cunha e Perrenoud, etc. The speech analysis is structured in six main ideas: the option for the docent graduation; obtained knowledge and determinant subjects on the academic graduation; docent knowledge occurred from the stage and its consequences during the docent practice; the knowledge and it understanding by the teachers; apprenticeship - difficulties and possibilities; the Mathematics according to the teachers beliefs. The interviewed teachers' report clearly proves the academic graduation importance on the beliefs and conceptions' construct, as well its practice influence with the students. Although the personal points brought and the history of life of each one is powerful, the academic formation increased conceptions and contributed with a few changes. The force of the knowledge field was reinforced, but new possibilities and questioning were opened that did and still do the teachers keep looking for more spaces of formation.