This thesis is primarily concerned with the effects of education for future teachers in the context of the Swedish teacher training (Government Bill 1999/2000:135 2000). It belongs to a theoretical tradition in which the education system is viewed as a key factor in cultural production and reproduction in educational practices through symbolic control (Apple 2009; Ball 2006; Bernstein 2000, 2003). Symbolic control defines how forms of social interaction affect what is possible to think, say and do in different situations. The thesis is focused specifically on student mathematics teachers learning to become teachers of mathematics. It has a particular focus on the materials used in this, the meanings given to these materials and the identities produced through the possible embodiment of these meanings. The use of different educational technologies, including in particular ICT, has been of special interest. It aims therefore to understand both how mathematical discourses are produced and reproduced in teacher education and how this colours student teachers’ views on mathematics and their professional identity (Bernstein 2000, 2003; Valero 2007). The main outcomes of my thesis are that through the way that mathematics is taught and learned, mathematics teacher education in practice reproduces traditional ways of teaching and learning. This in that mathematics instruction is built around a ritualized practice based on the ability to solve exercises related to an examined-textbook-based content. ICT use in this context is not transformative. Rather it seems as if teaching and learning with digital technology operate as a relay in the reproduction of traditional forms of education practice. This is contrary to the intentions to renew and revitalise mathematics education and the thesis thus suggests that there is a need to scrutinize the way new technology is formulated in official discourses and appropriated in educational work. Two other things are also noteworthy in the thesis findings. The first is an increased emphasis on formal subject content through recent policy developments. This re-emphasis reaffirms the value of authoritative subject studies content as the central and most important component in the professional knowledge base. On the basis of the finding from the thesis the logic of the reform may be questioned. Also important is the ICT discourse that is constituted in wider society by selected agents. In this discourse digital technology often in many ways defines (post)modern society and the position it and education have as a driving force toward economic competitiveness. An alternative, more reflexive and critical approach where questions about technology uses in education are emphasized is suggested as necessary. / Disputationen äger rum fredagen den 4 maj 2012, kl. 13.15, Sal Gamma, Hus Svea, IT Fakulteten, Forskningsgången 4, Lindholmen

Thesis (M.ED.) --University of Limpopo, 2008 / The Department of Education language policy states that all official languages may be used in the teaching and learning at South African schools. The department of Education has adopted an Additive Multilingualism as an approach to teaching. English is however, still being used as the language of learning and teaching, even to the learners who are not mother-tongue speakers of the language. This study explores the question of whether code-switching aids or impedes teaching and learning in Mathematics. The problem arises when learners encounter concepts in Mathematics which are written in English and need to be explained in English. Learners often struggled to understand these concepts with the results that educators resort to using their home language to try to explain what these concepts mean. To understand the nature of this problem and how it affects teaching and learning, a qualitative research was undertaken. Two secondary schools in the Sekgosese East Circuit were purposefully sampled for this study. The purpose of the study was to explore the role of code-switching in the teaching and learning of concepts in Mathematics and its effects on the acquisition of Mathematics. The findings revealed that the school were code-switching was applied performed better in Mathematics than the school where code-switching was not employed. The study recommended that educators should use the learners’ home language in instances where their knowledge of English impedes them to convey the meaning clearly.

Thesis (M.A. (Mathematics Education)) --University of Limpopo, 2013 / This study intended to improve Grade 9 learners’ mathematical processes of solving word problems. It was an action research study in my own classroom consisting of 64 Grade 9 learners. Learners were given learning activities on word problems to carry out as part of their normal classroom mathematics’ lessons. Data were collected in two stages: first, through passive observation, that is, without my intervention, and later through participant observation thus provoking their thinking as they attempt the given questions. The learners’ responses were analyzed through checking the mathematical processes they used without my intervention. Learners also submitted their post-intervention responses for analysis of progress after interventions. The scripts were reviewed based on four problem- solving stages adopted from George Polya (1945). Those stages are, namely understanding the problem, devising the plan, carrying out the plan and looking back. It became evident from the findings that learners attempt solving word problems with no understanding. Communication, reasoning and recording processes appear to be key factors in assisting learners to make sense of word problems and, finally, proceeding towards an adequate solution.

This doctoral research was concerned with the role of language and its implications for the learning, teaching and assessment of mathematics for children aged 4-9 years. Earlier research by the author had established language and assessment as bridges enabling learning although they had the potential to increase the divide between teacher and learner. Reflection raised the question on how children achieved in mathematics despite potential difficulties with language and assessment. Review of the literature concluded that resources and sociocultural norms were also bridges between learner and teacher. A model was established of the relationships and processes between all perceived variables that provided an external, theoretical structure to be evaluated against structuralist, pragmatic and integrational linguistic approaches and empirical outcomes. The overarching approaches adopted were institutional ethnography and case study. An appropriate methodology was devised whereby sophisticated ICT equipment captured all visual and speech events during classroom interactions. Frequency analysis at word level, content analysis at utterance level and discourse analysis at total speech level triangulated with content analysis of interviews and evaluation of documentation completed the empirical research. Data analysis revealed five registers of children’s talk. Evidence suggested that the peer-peer ‘conditioned talk’ used in focused group work was the most effective for learning as it enabled them to discern the small steps in the inferential leaps in discourse made by their teachers, work out problems together, inform their peers, share findings and reinforce each others’ learning. Learners’ language showed aspects of structural, pragmatic and integrational linguistics, confirming a conclusion of the literature review that the various linguistic approaches discussed should be used to support and not exclude each other. The contribution made to knowledge is the ethnomethodology provided by the model, ICT resource and the five registers of talk revealed by the linguistic approach to discourse analysis. Teachers would be able to understand nuances of language used by their pupils and acquire essential skills and tools to put into effect the personalised learning agenda. Peer-peer observation of teachers would be an appropriate platform for the observation of the different registers used by learners, the resources that generate those registers, and their most effective use to close the gap between natural language and the subject specific language of mathematics.

Made available in DSpace on 2018-06-27T19:13:12Z (GMT). No. of bitstreams: 2 Stefane Layana Gaffuri.pdf: 3250223 bytes, checksum: 40260452a0ff9143b4f594fc6e6b27d2 (MD5) Stefane Layana Gaffuri.pdf.jpg: 3528 bytes, checksum: 11cc3f59597b71de2e0048f1f80ad421 (MD5) Previous issue date: 2012-11-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work´s aimed to analyze the contributions that the Teaching-Learning-Assessment methodology through Problem Solving provides learning in early Probability concepts. The research subjects were students from one third semester class, from the Administration course, in the Statistics subject, from Centro Universitário Franciscano UNIFRA, in Santa Maria RS. In the theoretical chapter, we address the Probability and its different approaches, the research starts with a historical introduction, followed by an analysis of its applications and concepts, and also for the search of works from other authors who had referred to teaching and learning this content. The research was a qualitative type and the collected dada was based on the participant observation during the development of the activities developed by the students in groups, registered in the researcher and the students ´ field diary. The activities developed in the classroom followed the steps of Problem Solving method, suggested by Onuchic and Allevato (2009): problem preparation, individual reading of the problem, group reading, problem solving, observation and encouraging, solving record on the blackboard, plenary, search of agreement and formalization of the content. The activities developed in the classroom were organized in learning sessions, aiming the concept building of Probability. The research linked the use of manipulative to solve problems, it providing visualization, questioning, reflection and construction of knowledge by students. The results indicated that in front of an unknown math concept, the students tried to mean it by means of their conceptual images which already exist and the new ones built during the activities. It was possible to identify, also, the difficulty to group in creating strategies, argue and formulate mathematical ideas. Also, the results of the research indicate the importance of problem solving as a teaching strategy, which can provide the students the building of their knowledge. / O presente trabalho teve por objetivo analisar as contribuições que a metodologia de Ensino-Aprendizagem-Avaliação através da Resolução de Problemas proporciona à aprendizagem de conceitos iniciais de Probabilidade. Os sujeitos da pesquisa foram alunos de uma turma do terceiro semestre do curso de Administração, na disciplina de Estatística, do Centro Universitário Franciscano - UNIFRA, em Santa Maria RS. Na fundamentação teórica, a Probabilidade e seus diferentes enfoques são abordados, iniciando-se a pesquisa com uma introdução histórica, seguida por uma análise de suas aplicações e seus conceitos, e pela busca de trabalhos de outros autores que se referiam ao ensino e à aprendizagem desse conteúdo. A pesquisa é de natureza qualitativa e teve como instrumentos de coleta de dados, a observação participante, durante o desenvolvimento das atividades realizadas pelos alunos, e registradas no diário de campo da pesquisadora e dos alunos. As atividades em sala de aula seguiram os passos da metodologia de resolução de problemas, sugeridos por Onuchic e Allevato (2009): preparação do problema; leitura individual do problema; leitura em conjunto; resolução do problema; observar e incentivar; registro das resoluções na lousa; plenária; busca do consenso e formalização do conteúdo. Essas atividades foram organizadas em sessões de ensino, e agrupadas visando à construção dos conceitos inicias de Probabilidade. A pesquisa atrelou o uso de materiais concretos com a resolução de problemas, propiciando à visualização, o questionamento, a reflexão e a construção do conhecimento por parte dos alunos. Os resultados indicaram que frente a um conceito matemático desconhecido, os alunos buscaram exprimi-lo por meio dos conceitos já conhecidos e os novos construídos no decorrer das atividades. Verificou-se, também, a dificuldade do grupo em criar estratégias, argumentar e formalizar ideias matemáticas. Os resultados da pesquisa apontam, também, para a importância da inclusão da resolução de problemas como estratégia de ensino, a qual pode proporcionar aos alunos a construção do próprio conhecimento.

ICT, i.e. information and communication technology, is today an important part of the society. ICT tools are used in many different aspects in the everyday life, for example to perform transactions in the bank or to stay in touch with relatives and friends. Not long ago, ICT also became important in the world of school. Many schools have been equipped with ICT tools, like for example a virtual learning environment, laptops for teachers and pupils or smartboards, and many other schools are planning to. Meanwhile, the teachers are trying to catch up with the development and integrate the newly introduced technology in their work. Development in this area is requested in order to not let the teachers’ ICT literacy fall behind. Therefore, the teachers’ ICT literacy in relation to the use of ICT has been studied within the frame of this thesis. The aim of this study is to increase the understanding of what significance teachers’ ICT literacy may have for the organization of teaching in mathematics at three senior high schools in Stockholm during the academic year 2013/2014. The study was carried out by setting up interviews with mathematics teachers, attending one of their mathematics lessons for observation and handing out a questionnaire to the pupils at the lesson. The results obtained were analyzed and interpreted based on previous research in the area of ICT and learning and pedagogy. With the results obtained it appears that ICT tools may work as a support for pupils learning if the teachers know how and when to use the tools in their teaching. It is not enough that the teachers only work with ICT tools, but the use of ICT tools must be adapted to the pupils and with focus on their learning. In addition to that, the teachers’ ICT literacy differs in some extent. Some teachers mastered the use of ICT tools generally, for example by using computer programs, while other teachers also had knowledge of a computers’ functions and they could create programs. The teachers’ also used ICT tools in different extents. Meanwhile, it is clearly shown that their use of ICT tools is similar in the sense that the tools are used as substitutions for other existing tools, but with possible functional improvement. Since the teachers’ ICT literacy did differ while their use of ICT tools were the same, the fact that a teachers’ ICT literacy does not necessarily have significance for the organization of the mathematics teaching has been drawn as a conclusion, even though Skolverket have concluded something else in their evaluation. / IKT, dvs. informations- och kommunikationsteknik, är en viktig del i vårt samhälle idag. IKT-redskap används i många olika avseenden i vardagslivet, t.ex. till att genomföra transaktioner på banken eller hålla kontakten med släkt och vänner. För inte särskilt länge sedan blev IKT en viktig del även i skolans värld. Många skolor har utrustats med IKT-redskap, som t.ex. en lärplattform, bärbara datorer till lärare och elever eller smartboards, och många andra är på väg att göra det. Samtidigt försöker lärarna hänga med i utvecklingen och integrera den nyinförda tekniken i sitt arbete. Kompetensutveckling inom området efterfrågas för att lärarnas IKT-kompetens inte ska halka efter. Inom ramen för detta examensarbete har därför lärarnas IKT-kompetens i relation till användningen av IKT studerats. Syftet med studien är att öka förståelsen för vad lärares IKT-kompetens kan ha för betydelse för organiserandet av undervisningen i matematik i tre gymnasieskolor i Stockholm under läsåret 2013/2014. Undersökningen genomfördes med hjälp av intervjuer med matematiklärare, observationer som utfördes på en av deras matematiklektioner och enkät som besvarades av eleverna på den lektionen. De resultat som erhölls analyserades och tolkades utifrån tidigare forskning inom ämnet IKT och lärande samt pedagogiska teorier. Med de erhållna resultaten visar det sig att IKT-redskap kan fungera som stöd för elevers lärande om lärarna vet hur och när de ska använda redskapen i sin undervisning. Det räcker inte med att lärarna kan arbeta med IKT-redskapen, utan användningen av IKT-redskap måste anpassas efter eleverna och med deras lärande i fokus. Dessutom visar det sig i resultaten att lärarnas IKT-kompetens skiljer sig i någon grad från varandra. En del lärare visade endast på generell behärskning av IKT-användning, som att t.ex. arbeta med datorprogram, medan andra lärare även hade kunskaper om datorers funktioner och kunde programmera. Lärarna använde även IKT i olika stor utsträckning i sin undervisning. Samtidigt framgår det i studien att deras användning av IKT-redskap är likartad i den bemärkelsen att redskapen används som ersättare till andra redan befintliga redskap, fast med eventuell funktionell förbättring. Då lärarnas IKT-kompetens skiljde sig, samtidigt som användningen av IKT var likartad, så har slutsatsen dragits att en lärares IKT-kompetens inte nödvändigtvis har betydelse för organiserandet av matematikundervisningen. Detta trots att Skolverket har i sin utvärdering konstaterat annat.

Made available in DSpace on 2016-06-02T19:35:47Z (GMT). No. of bitstreams: 1 4798.pdf: 2422263 bytes, checksum: 82536db8cae0f223bf6247c55001a288 (MD5) Previous issue date: 2012-12-21 / Financiadora de Estudos e Projetos / This research aimed to investigate the mathematics formative processes of Early Years students-teachers in an online Pedagogy course taking the following question into consideration: What formative processes are evidenced by students-teachers when inserted in specific mathematical disciplines in an online Pedagogy course? Our theoretical framework discusses the concepts of: professional development, knowledge base for teaching, reflection, autonomy, interaction, collaboration, dialogue, among others. To begin the development of the qualitative study, we contacted, via email, the first group of students who had attended the disciplines Languages of Mathematics 1 and 2 and Supervised Practice 1 and 2 and asked them to answer a characterization questionnaire. Nine students, who were already teachers in kindergarten and/or in Early Years, were the subjects of the research due to our assumption that the formative processes they experienced could have contributed to their professional development, promoting the learning of mathematical content, as well as the learning of teaching skills. Because of them being students of the course who already worked as teachers, we described them in the text as students-teachers. For data collection, we used the activities developed during the mentioned subjects and semi-structured interviews which were conducted via Skype or Messenger. Data analysis was conducted based on the theory of content analysis and two themes emerged with subcategories: Relationship with mathematics and its teaching and learning composed of The narratives of the students-teachers and Indications of changes and; Mathematics formative processes included the subcategories Different writing in the disciplines, Interactions and mediations in the virtual environment, Readings and reflective process on practice and Teaching in supervised practices. The results showed that the students-teachers had some small changes in their beliefs about mathematics, its teaching and learning, the classroom practices, their feelings regarding mathematics and the teacher-student relationship. Moreover, the formative processes they experienced promoted the (re)construction and (re)signification of the mathematical content studied and provided the learning of teaching practices. The printed material used in the disciplines, the activities, the interactions that occurred between the students-teachers and their classmates when participants proposed questions, discussed the mathematical concepts and peer feedback and shared classroom practices, as well as the mediations conducted by tutors were fundamental for this to happen. The analysis also indicated that they increased their knowledge base for teaching and mobilized the process of pedagogical reasoning to develop activities concerning mathematical content for the supervised teaching practice, the ways of working it with students and aspects of lesson planning such as unexpected situations that may occur and the timing for completion of activities. / Esta pesquisa teve como objetivo investigar os processos formativos em matemática de alunas-professoras dos Anos Iniciais em um curso a distância de Pedagogia a partir do seguinte questionamento: Quais processos formativos são evidenciados por alunasprofessoras quando inseridas nas disciplinas específicas de matemática em um curso a distância de Pedagogia? No referencial teórico, discutimos os conceitos de: desenvolvimento profissional, base de conhecimento para o ensino, reflexão, autonomia, interação, colaboração, diálogo, entre outros. Para iniciarmos o desenvolvimento do estudo, de natureza qualitativa, entramos em contato, via e-mail, com os estudantes da primeira turma que já haviam cursado as disciplinas de Linguagens Matemática 1 e 2 e Estágio Supervisionado 1 e 2 e solicitamos que respondessem a um questionário de caracterização. Nove alunas já eram professoras na Educação Infantil e/ou nos Anos Iniciais do Ensino Fundamental e foram os sujeitos da pesquisa devido a nossa hipótese de que os processos formativos vivenciados poderiam ter contribuído com o desenvolvimento profissional delas, promovendo aprendizagens dos conteúdos matemáticos e também aprendizagens da docência. Pelo fato delas serem alunas do curso e já atuarem como professoras as identificamos, no texto, como alunas-professoras. Utilizamos para a produção de dados as atividades desenvolvidas nas disciplinas mencionadas e entrevistas semiestruturadas que foram realizadas via Skype ou Messenger. A análise dos dados foi realizada a partir da teoria de análise do conteúdo e emergiram dois eixos temáticos com subcategorias: Relação com a matemática e seu ensino e aprendizagem composto por As narrativas das alunas-professoras e Indícios de mudanças e; Processos formativos em matemática se constituíram das subcategorias Diferentes escritas nas disciplinas, Interações e mediações no ambiente virtual, Leituras e o processo reflexivo sobre a prática e As regências nos estágios. Os resultados evidenciaram que as alunasprofessoras tiveram algumas pequenas mudanças em suas crenças sobre a matemática, seu ensino e aprendizagem, sobre as práticas de sala de aula, sobre os sentimentos com relação à matemática e sobre a relação professor-aluno. Além disso, os processos formativos vivenciados promoveram a (re)construção e a (re)significação dos conteúdos matemáticos estudados e proporcionaram aprendizagens da docência. Para tanto, foram fundamentais o material impresso utilizado nas disciplinas, as atividades propostas, as interações que ocorreram entre as alunas-professoras e os colegas em que as participantes propuseram questionamentos, discutiram os conceitos matemáticos e os comentários dos colegas, argumentaram e trouxeram práticas de sala de aula, além das mediações realizadas pelos tutores. As análises também apontaram que elas ampliaram sua base de conhecimento para o ensino e que mobilizaram o processo de raciocínio pedagógico ao elaborarem as atividades com relação aos conteúdos matemáticos para as regências do estágio, as formas de trabalhálos com os alunos e aspectos do planejamento da aula como os imprevistos que ocorrem e o tempo para realização das atividades.

Submitted by GABRIELA CASTRO SILVA CAVALHEIRO (gcvsilva@gmail.com) on 2017-08-29T21:47:00Z No. of bitstreams: 1 TES_DOUT20170815_CAVALHEIRO_GABRIELA_CASTRO_SILVA.pdf: 4696572 bytes, checksum: ba2b7c84f99f3235ac1d1ab9e2e6ea4c (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-08-30T17:17:23Z (GMT) No. of bitstreams: 1 cavalheiro_gcs_dr_bauru.pdf: 4696572 bytes, checksum: ba2b7c84f99f3235ac1d1ab9e2e6ea4c (MD5) / Made available in DSpace on 2017-08-30T17:17:23Z (GMT). No. of bitstreams: 1 cavalheiro_gcs_dr_bauru.pdf: 4696572 bytes, checksum: ba2b7c84f99f3235ac1d1ab9e2e6ea4c (MD5) Previous issue date: 2017-08-15 / Este trabalho trata da resolução de problemas (RP) e da investigação matemática (IM) na formação inicial de professores de Matemática e objetivou responder às seguintes perguntas de pesquisa: Quais as contribuições, para licenciandos em Matemática, de um processo de intervenção formativa que envolve teoria, prática e análise da RP e da IM como metodologias de ensino e aprendizagem de Matemática? Segundo esses sujeitos, quais as potencialidades e as dificuldades didático-pedagógicas no uso em sala de aula das metodologias em questão? Eles preferem alguma dessas metodologias ao utilizá-las na prática? Por quê? Com o intuito de alcançar tal objetivo, realizou-se uma investigação qualitativa, mediante estudo do caso a seguir: um processo de intervenção formativa, com sete licenciandos em Matemática, de uma instituição pública de Ensino Superior no interior do estado de São Paulo, matriculados na disciplina Prática Pedagógica VI, vinculada ao estágio supervisionado II, que aborda observação e regência nos anos finais do Ensino Fundamental. Tal processo foi constituído por cinco fases: 0. Discussão sobre a RP e a IM como metodologias de ensino e aprendizagem de Matemática; 1. Elaboração de planos de aula de RP e de IM; 2. Simulação das regências de aula na disciplina Prática Pedagógica VI; 3. Aplicação das regências em aulas de Matemática nas escolas onde os licenciandos estagiavam; e 4. Análise do uso da RP e da IM em termos de potencialidades e dificuldades didático-pedagógicas. A coleta/produção dos dados foi realizada durante três meses, por meio de questionários, análise documental, observação participante e entrevista, sendo analisados à luz dos pressupostos teóricos da análise textual discursiva. Concluiu-se que o processo de intervenção formativa permitiu aos futuros professores: a) ampliar seus conhecimentos prévios e construir novos, b) investigar sua própria prática docente, c) contrastar uma metodologia com a outra, d) refletir na e sobre a ação docente, e e) relacionar teoria e prática. Além disso, esses sujeitos apontaram potencialidades e dificuldades didático-pedagógicas próprias do uso da RP ou IM e também comuns à utilização de ambas as metodologias. Entende-se que esta pesquisa contribuiu para as áreas de Educação e Educação Matemática, pois o processo de intervenção formativa deu origem a uma metodologia de formação docente e também trouxe elementos para práticas pedagógicas efetivas na Educação Básica. / This work deals with problem solving (PS) and mathematical investigation (MI) in the initial Mathematics teacher training and aims to answer the following research questions: What contributions, for undergraduate students in Mathematics, of a process of formative intervention that involves theory, practice and analysis of PS and MI as methodologies of teaching and learning of Mathematics? According to these subjects, what are the didactic-pedagogical potentialities and difficulties in classroom use of the methodologies in question? Do they prefer any of these methodologies when using them in practice? Because? In order to achieve this objective, a qualitative investigation was carried out, through a study of the following case: a process of formative intervention with seven undergraduate students in Mathematics of a public university in the interior of the state of São Paulo, enrolled in the discipline Pedagogical Practice VI, linked to the supervised stage II, which addresses observation and regency in the Secondary School. This process was constituted by five phases: 0. Discussion about PS and MI as methodologies of teaching and learning of Mathematics; 1. Preparation of PS and MI lesson plans; 2. Simulation of the classroom regencies in the discipline Pedagogical Practice VI; 3. Application of regencies in mathematics classes in schools where undergraduate students trained; And 4. Analysis of the use of PS and MI in terms of didactic-pedagogical potentialities and difficulties. The collection/production of the data was done during three months, through questionnaires, documentary analysis, participant observation and interview, being analyzed in light of the theoretical assumptions of the discursive textual analysis. It was concluded that the process of formative intervention allowed the future teachers to: a) expand their previous knowledge and build new ones, b) investigate their own teaching practice, c) contrast one methodology with the other, d) reflect on and about the teaching activity, and e) relate theory and practice. In addition, these subjects pointed out the didactic-pedagogical potentialities and difficulties characteristic of the use of PS or MI and also common to the use of both methodologies. It is understood that this research contributed to the areas of Education and Mathematical Education, since the process of formative intervention gave rise to a methodology of teacher training and also brought elements for effective pedagogical practices in Basic Education.

Made available in DSpace on 2018-06-27T19:13:02Z (GMT). No. of bitstreams: 2 Laura Moreira Bordin.pdf: 2775738 bytes, checksum: 12891239889c50b7d801757bc8d26043 (MD5) Laura Moreira Bordin.pdf.jpg: 3569 bytes, checksum: b503812f643369cda67fcc097918310b (MD5) Previous issue date: 2011-08-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work´s aim was to analyze the contributions which the Teaching-Learning-Evaluation methodology through Problem Solving provides to the Equation of Differences concept learning, founded in the Concept Image and Concept Definition theory of Tall and Vinner (1981).The participants of the research were undergraduated students of the third grade of a Mathematics Teaching License, from UNIPAR Universidade Paranaense, Cascavel, PR. The research was a qualitative type and the collected dada was based on the participant observation during the development of the activities developed by the students in groups, registered in the researcher and the students ´ field diary and audio recording. The activities developed in the classroom followed the steps of Problem Solving method, suggested by Onuchic e Allevato (2009): problem preparation, individual reading of the problem, group reading, problem solving, observation and encouraging, solving record on the blackboard, plenary, search of agreement and formalization of the content. The activities developed in the classroom were organized in three learning units, aiming the concept building of Difference Equations. In the first unit problem-situations were studied involving problem situations which allowed the students to build the concept of Linear Equations of Differences of homogeneous first order; in the second unit problem situations involving Linear Equations of Differences of non-homogeneous first order and in the last unit problem situations were proposed related to Linear Equation of Differences of homogeneous of second order. The results indicated that in front of an unknown math concept, the students tried to mean it by means of their conceptual images which already exist and the new ones built during the research. It was possible to identify an active involvement of the participants in the new concept building which allowed their learning. The results of the research indicate the importance of problem solving as a teaching strategy, which can provide the students the building of their own knowledge. / O presente trabalho teve por finalidade analisar as contribuições que a metodologia de Ensino-Aprendizagem-Avaliação através da Resolução de Problemas proporciona à aprendizagem de conceitos de Equações de Diferenças, alicerçada na teoria de imagem de conceito e definição de conceito de Tall e Vinner (1981). Os sujeitos da pesquisa foram alunos de uma turma da terceira série do curso de Licenciatura em Matemática, da Universidade Paranaense-UNIPAR de Cascavel-PR. Para tal, foi realizada uma pesquisa de natureza qualitativa que teve como instrumentos de coleta de dados a observação participante, durante o desenvolvimento das atividades realizadas pelos alunos reunidos em grupos e registradas no diário de campo da pesquisadora e dos alunos, e gravações em áudio. As atividades em sala de aula seguiram os passos da metodologia de resolução de problemas, sugeridos por Onuchic e Allevato (2009): preparação do problema; leitura individual do problema; leitura em conjunto; resolução do problema; observar e incentivar; registro das resoluções na lousa; plenária; busca do consenso e formalização do conteúdo. As atividades de sala de aula foram organizadas em três unidades de ensino, visando à construção dos conceitos de Equações de Diferenças. Na primeira unidade foram trabalhadas situações-problema que permitiram aos alunos a construção do conceito de Equações de Diferenças Lineares de Primeira Ordem Homogênea; na segunda unidade foram trabalhadas situações-problema envolvendo Equações de Diferenças Lineares de Primeira Ordem não Homogênea e na última unidade foram propostas situações-problema relacionadas com Equações de Diferenças Lineares de Segunda Ordem Homogêneas. Os resultados indicaram que frente a um conceito matemático desconhecido, os alunos buscaram significá-lo por meio de suas imagens conceituais já existentes e as novas construídas no decorrer da pesquisa. Verificou-se um envolvimento ativo dos participantes na construção dos novos conceitos, que permitiu a sua aprendizagem. Os resultados da pesquisa apontam para a importância da inserção da resolução de problemas como estratégia de ensino, a qual pode proporcionar aos alunos a construção do seu próprio conhecimento.

Made available in DSpace on 2018-06-27T19:13:04Z (GMT). No. of bitstreams: 2 Lucilene Oenning Saraiva.pdf: 1871833 bytes, checksum: 1d1ab13bc56881ecec548e19f20fe542 (MD5) Lucilene Oenning Saraiva.pdf.jpg: 3610 bytes, checksum: f7234f5fa942fc34645d9e1b2b9188b7 (MD5) Previous issue date: 2012-04-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O presente trabalho teve como objetivo analisar as possibilidades que a metodologia de investigação matemática pode proporcionar ao ensino e aprendizagem dos conceitos e propriedades de sucessões numéricas. O trabalho foi desenvolvido com 28 estudantes do quarto ano de um curso de Licenciatura em Matemática de uma universidade privada do oeste do Paraná. A revisão de literatura baseou-se em livros, artigos, dissertações e teses que tratam dos aspectos teóricos da investigação Matemática, do papel do professor e da investigação no currículo escolar. A pesquisa é de caráter qualitativo e nela empregaram-se, como instrumentos, anotações de observações de sala de aula, os trabalhos realizados pelos alunos e um questionário aplicado ao final da experiência. O questionário forneceu dados das opiniões dos alunos sobre a experiência realizada. Os resultados obtidos permitiram constatar as dificuldades do grupo de formular hipóteses, argumentar e formalizar ideias matemáticas. Além disso, foi possível constatar que atividades investigativas desenvolvidas na etapa de formação inicial podem incentivar seu uso na futura prática docente e permitir uma mudança de concepção sobre o ensino de matemática e da postura do professor no trabalho de sala de aula.