Submitted by Jean Coutinho (jeanlbiko@hotmail.com) on 2015-12-16T19:31:10Z No. of bitstreams: 1 MatematicaparaoEnsinoAC.pdf: 2609857 bytes, checksum: aae033891c7c90a4c130cf4f93a30ae3 (MD5) / Approved for entry into archive by Maria Auxiliadora da Silva Lopes (silopes@ufba.br) on 2015-12-17T18:56:16Z (GMT) No. of bitstreams: 1 MatematicaparaoEnsinoAC.pdf: 2609857 bytes, checksum: aae033891c7c90a4c130cf4f93a30ae3 (MD5) / Made available in DSpace on 2015-12-17T18:56:16Z (GMT). No. of bitstreams: 1 MatematicaparaoEnsinoAC.pdf: 2609857 bytes, checksum: aae033891c7c90a4c130cf4f93a30ae3 (MD5) / O objetivo deste estudo foi modelar uma Matemática para o Ensino do conceito de combinação simples em Análise Combinatória. Os materiais de análise utilizados nesta pesquisa foram observados em duas fontes: produções científicas a partir de uma Revisão Sistemática e um estudo com professores. A estrutura de análise proposta foi o Estudo do Conceito e suas ênfases: realizações, panoramas e vinculações. Para tal propósito, foi analisado um corpus de dez artigos publicados em periódicos brasileiros, nas áreas de Educação e Ensino, avaliados pelo sistema WebQualis da CAPES como A1, A2, B1 e B2. Além disso, foi organizado um estudo coletivo cujos integrantes foram seis professores atuantes nos níveis fundamental, médio e/ou superior que possuíam experiência no ensino de Análise Combinatória. Como resultado, foi apresentado um modelo de Matemática para o Ensino de combinação simples, estruturado em quatro panoramas: formalista, instrumental, ilustrativo e comparativo, que sugerem implicações para o fazer do professor que ensina combinação simples e desdobramentos da pesquisa. / ABSTRACT The aim of this study was to model a Mathematics for Teaching the concept of simple combination in Combinatory Analysis. Materials observed in this investigation came from two sources: a systematic review of scientific production and a study with teachers. The proposed structure for the analysis was a Concept Study in its emphases: realizations, landscapes and entailments. In favor of that, a corpus of ten articles published in Brazilian journals in the areas of Education and Teaching was analyzed, all of them evaluated by CAPES’ system WebQualis as A1, A2, B1 and B2. In addition, there was a collective study with six teachers acting in primary, secondary and/or higher education who had experience in teaching Combinatory Analysis. As a result, presented a model of Mathematics for Teaching the concept of simple combination, structured in four landscapes: formalist, instrumental, illustrative, and comparative, which suggest implications for the actions of the teacher that teaches simple combination, and for possible outspread of research.

Made available in DSpace on 2014-12-17T15:05:03Z (GMT). No. of bitstreams: 1 PauloGFG_DISSERT.pdf: 1837404 bytes, checksum: 19812711d911e7553726f109f602c45f (MD5) Previous issue date: 2013-11-22 / It is still common among contemporary educational proposals an overemphasis abstraction, to the formalism and symbolism of mathematical knowledge at the expense of the sociocultural aspects of Mathematics. Coming up by questioning some academic mathematical tenets and valuing knowledge developed in different sociocultural contexts within Mathematical Education, the Ethnomatematics is consolidating itself as a research field. Despite its contributions to the educational context, because its philosophical character and the paucity of debates about the subject, the implementation of educational proposals for basic education are scarce. Given this situation, this dissertation comes up with a view to develop an educational intervention in the light of Ethnomathematics in a class of 6th grade of an elementary school from a red ceramic industries workers community, located in a countryside from Russas-CE and from this intervention, to develop a set of pedagogical recommendations aiming basic education teachers. Adopting a perspective of qualitative research, particularly guided by action research, this study used observation, field diary, interviews and activities with students as tools for data collection. It was found that the use of field research as part of teaching and learning favored the placement of students as critical subjects of their own reality . Furthermore, the educational experience culminated in the development of a method of teaching based on a relationship between protocooperational Ethnomatematics and the Resolution of Problems. It is necessary to broaden the debate about the ways in which the Ethnomatematics can contribute to the school context, bringing proposals closer to the reality of basic education teachers in order to help the promotion of an education which values cultural diversity without taking away the students from the access of the academic knowledge / Ainda ? comum entre as propostas educacionais contempor?neas uma ?nfase excessiva a abstra??o, ao formalismo e ao simbolismo do conhecimento matem?tico, em detrimento dos aspectos socioculturais da Matem?tica. Surgindo por questionar alguns dogmas da matem?tica acad?mica e por valorizar e reconhecer conhecimentos desenvolvidos em diversos contextos socioculturais no ?mbito da Educa??o Matem?tica, a Etnomatem?tica vem se consolidando como um campo de pesquisa. Apesar de suas contribui??es para o contexto escolar, devido seu car?ter mais filos?fico e pela incipi?ncia de debates sobre o tema, a implementa??o de propostas educacionais para o ensino b?sico s?o escassas. Diante deste quadro, a presente disserta??o surge com intuito de desenvolver uma interven??o educacional ? luz da Etnomatem?tica em uma turma de 6? ano do ensino fundamental proveniente de uma comunidade de trabalhadores de ind?strias de cer?mica vermelha, localizada na zona rural do munic?pio de Russas-CE e a partir desta interven??o, elaborar um conjunto de recomenda??es pedag?gicas voltado para professores da educa??o b?sica. Adotando uma perspectiva de investiga??o qualitativa, e em particular pautada na pesquisa-a??o, o presente estudo utilizou-se da observa??o, di?rio de campo, entrevista e atividades desenvolvidas com os alunos como instrumentos para coleta de dados. Verificou-se que a utiliza??o da pesquisa de campo como parte do processo de ensino e aprendizagem favoreceu na coloca??o dos estudantes como sujeitos cr?ticos de sua pr?pria realidade. Al?m disso, a experi?ncia educacional culminou na elabora??o de um m?todo de ensino pautado numa rela??o protocooperativa entre a Etnomatem?tica e a Resolu??o de Problemas. Torna-se necess?rio ampliar o debate acerca das formas pelas quais a Etnomatem?tica possa contribuir para o contexto escolar, trazendo propostas mais pr?ximas ? realidade dos professores da educa??o b?sica, de modo a auxiliar na promo??o de uma educa??o que valorize a diversidade cultural sem amputar os estudantes do acesso ao conhecimento acad?mico

Made available in DSpace on 2014-12-17T15:05:03Z (GMT). No. of bitstreams: 1 JulianaMP_DISSERT.pdf: 638536 bytes, checksum: 4cf895f245fff8f9c3c9b64a5ffe6409 (MD5) Previous issue date: 2013-07-22 / This work is the result of a study that aimed to start scoring difficulties that the math teacher is trying to get a historical formation. Considering that the textbook is the material with which the teacher has more contact, start with reading historical texts present in these books. Choose a theme and choose from that we observed limitations ranging from the search for sources of research in relation to the actual historical content. There are many studies that show the importance of the history of mathematics in teacher education and also in the teaching and learning of mathematics. These works , in particular the work of Feliciano (2008 ) entitled : " The use of history of mathematics in the classroom " , along with the information , experiences and opinions given by Professor Anderson Lu?s de Azevedo Paulo , in some meetings , point to need for materials for teaching , since they show that recognizes the importance of this knowledge and the ability to use it in the classroom , but several factors have pushed aside , even the texts present in textbooks. From the analysis of some of the work and contributions of Professor Anderson Paulo we pointed out some of the factors that make historical texts being ignored by teachers and among them are characteristics in appearance and content in the text. To assist in the preparation of materials that meet the expectations of the teacher, we present a manual with suggestions and / or features to choose or produce a good text. These suggestions can make the history books more enjoyable and thus approach the teacher of historical knowledge and later encouraged to seek, in fact, a historical formation / Este trabalho ? resultado de um estudo que teve como objetivo inicial pontuar dificuldades que o professor de matem?tica encontra ao tentar buscar uma forma??o hist?rica. Tendo em vista que o livro did?tico ? o material com o qual o professor tem mais contato, come?amos com a leitura de textos hist?ricos presentes nesses livros. Escolhemos um tema e a partir dessa escolha pudemos verificar limita??es que v?o desde a busca por fontes de pesquisa at? em rela??o ao pr?prio conte?do hist?rico. Muitos s?o os trabalhos que mostram a import?ncia da Hist?ria da Matem?tica na forma??o do professor e tamb?m no processo de ensinoaprendizagem de Matem?tica. Esses trabalhos, em especial o trabalho de Feliciano (2008) intitulado: O uso da Hist?ria da matem?tica em sala de aula , juntamente com as informa??es, experi?ncias e opini?es dadas pelo professor Anderson Lu?s de Azevedo Paulo, em alguns encontros, apontam a necessidade de materiais para o docente, pois mostram que reconhece a import?ncia desse conhecimento e a possibilidade de us?-lo em sala de aula, mas por diversos fatores tem deixado de lado, at? mesmo os textos presentes nos livros did?ticos. A partir da an?lise de alguns trabalhos e das contribui??es do professor Anderson Paulo pontuamos alguns dos fatores que fazem os textos hist?ricos serem ignorados pelos professores e entre eles est?o caracter?sticas na apar?ncia e no conte?do presente no texto. Para ajudar na elabora??o de materiais que atendam ?s expectativas do professor, apresentamos um manual com sugest?es e/ou caracter?sticas para escolha ou produ??o de um bom texto. Essas sugest?es podem deixar os textos de hist?ria mais agrad?veis e assim aproximar o professor do conhecimento hist?rico e posteriormente incentivado a buscar, de fato, uma forma??o hist?rica

This study aims to identify public schools teacher’s perceptions of the Good Teaching Practices, especially the use of technology in the classroom. Additionally, the study identify teacher’s perception concerning the use of a mobile app to teach mathematics. The study begins with a theoretical review that delimit the concept.From this review, an interview guide was designed to identify teacher’s perceptions of good teaching practices and the use of technologies in the classroom. The results suggests that teachers identify Good Teaching Practices in a conceptual approach, but not in a practical approach. In addition, they acknowledge the benefits of technologies for their teaching practices, recognizing the importance for teaching mathematics. / Este estudio busca identificar las nociones que los profesores de instituciones educativas públicas tienen sobre el concepto de buenas prácticas docentes, especialmente, respecto al uso de la tecnología en el salón de clase. Asimismo, se explora las percepciones sobre la utilidad del uso de un aplicativo móvil para enseñar matemáticas. Se inicia con una revisión teórica que delimita el concepto. A partir de esta, se diseñó una guía de entrevista para conocer la percepción de los profesores, sobre las buenas prácticas docentes y el uso de tecnologías. Los resultados apuntan a que los docentes identifican el concepto de buenas prácticas, pero no reconocen casos concretos donde estas se utilicen. Por otro lado, identifican las ventajas de las tecnologías y su uso en el aula, reconociendo aspectos importantes para la enseñanza. / Este estudo busca identificar as noções que os professores das instituições educacionais públicas têm sobre o conceito de boas práticas de ensino, especialmente com o uso da tecnologia na sala de aula. Também explora as percepções sobre a utilidade de usar uma aplicação móvel para ensinar matemática. Começa com uma revisão teórica que delimita o conceito. A partir disso, um guia de entrevista foi projetado para conhecer a percepção dos professores sobre boas práticas de ensino e o uso de tecnologias. Os resultados sugerem que os professores identifiquem o conceito de boas práticas, mas eles não reconhecem casos concretos em que são usados. Por outro lado, eles identificam as vantagens das tecnologias e seu uso na sala de aula, reconhecendo aspectos importantes para o ensino.

M.Ed. (Curriculum Studies) / Please refer to full text to view abstract

The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors.

No description available.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The purpose of the study was to investigate The effect of the Problem-Based Learning Problem Based Learning (PBL) approach in the teaching of composition and inverse functions in a foundation programme. PBL is a philosophical approach to teaching and learning where problems drive the learning. The study was important because it was trying to find out if PBL can improve students’ performance in compositions and inverses of functions at the bridging course for undergraduate mathematics at Oshakati Campus. The study intended to come up with a PBL model suitable for FP mathematics in the teaching of compositions and inverses of functions. The study was done on Science Foundation students who are registered for FP. Eighty students were randomly selected from the foundation students registered for the 2013 academic year. The students were randomly assigned into the experimental and the comparison groups of 40 each. In this study the comparison group of the Foundation students was predominantly taught through the traditional lecture approach while the experimental group was predominantly taught using a hybrid PBL approach. The study also attempted to establish the students’ perceptions with regard to the relevance of inverses and compositions of functions as a concept in a topic that determines their academic destination. It also attempted to ascertain how the PBL approach could best be implemented in order to improve FP students’ understanding of inverses and composition of functions; how Bridging course for undergraduate mathematics (FP) students experience the PBL approach in the teaching and learning of inverses and composition of functions compared to those who are taught using the lecture method and how FP students’ performance on inverses and composition of functions as a result of their PBL experience compare to those who are taught using the lecture method. This study used the concurrent nested mixed methods (qualitative and quantitative) research designs. A quasi experimental design was adopted through the administration of a pre-post-test on experimental and comparison groups. The other designs or methods included a questionnaire survey, focus group interviews, non-participant lesson observation and a group research project on compositions and inverses of functions. The experimental group was then mainly taught through a hybrid PBL approach while the comparison group mainly through the lecture approach for a period of three months. The findings of this research study showed that experimental group students performed significantly better in the overall results analysis but there were no significant differences in performance between the two groups for some Hypothetical Learning Trajectory (HLT) domains on compositions and inverses of functions. It is recommended that PBL should be implemented in the other foundation programme subjects. However, the role of the conventional teaching approaches cannot be undermined in the teaching and learning of compositions and inverses of functions since the students who were taught using this method also improved their performances, and as such these conventional teaching approaches should be used together with PBL in order to get the best results on FP students’ mathematics performance. This study recommends further research on how PBL can be implemented in other FP subjects. This study also recommended that PBL should be implemented right at the beginning of the year when the FP students start their classes in the foundation programme. / AFRIKAANSE OPSOMMING: Die doel van die studie was om die effek van die probleemgebaseerde leer (PBL) benadering in die onderrig van die samestelling en inverse funksies in 'n Stigting program te ondersoek. PBL is 'n filosofiese benadering tot onderrig en leer waar probleme ry die leer. Die studie is belangrik omdat dit probeer het om uit te vind of PBL kan studente se prestasie in komposisies en inverses van funksies te verbeter by die Stigting Program op Oshakati-kampus. Die studie bedoel om vorendag te kom met 'n PBL model wat geskik is vir fondament in die onderrig van komposisies en inverses van funksies. Die studie is gedoen op Science Foundation studente by Oshakati-kampus van die Universiteit van Namibië. Tagtig studente is lukraak gekies uit die fondament studente wat geregistreer is vir die 2013 akademiese jaar. Die studente is ewekansig toegewys in die eksperimentele en die vergelyking groepe van 40 elk. In hierdie studie is die vergelyking groep van die Stigting studente is hoofsaaklik geleer word deur die tradisionele lesing benadering terwyl die eksperimentele groep was hoofsaaklik geleer met behulp van 'n hibriede PBL benadering. Die studie het ook probeer om vas te stel uit wat die studente se persepsies met betrekking tot die toepaslikheid van inverses en komposisies van funksies is soos 'n konsep in 'n onderwerp wat bepaal hul akademiese bestemming. Dit het ook probeer om vas te stel hoe die PBL benadering kan die beste om FP studente se begrip van inverses en samestelling van funksies te verbeter geïmplementeer word; hoe FP studente die PBL benadering in die onderrig en leer van inverses en samestelling van funksies in vergelyking met diegene wat geleer is met behulp van die lesing metode en hoe FP studente se prestasie op inverses en samestelling van funksies as 'n gevolg van hul PBL ervaring vergelyk met dié wat geleer is met behulp van die lesing-metode. Hierdie studie gebruik om die konkurrente geneste gemengde metodes (kwalitatiewe en kwantitatiewe) navorsing ontwerpe. 'N quasi eksperimentele ontwerp is aangeneem deur die administrasie van 'n pre-na-toets op eksperimentele en vergelyking groepe. Die ander ontwerpe of metodes het 'n vraelys opname, fokusgroeponderhoude, nie-deelnemer leswaarneming, en 'n groep navorsingsprojek oor komposisies en inverses van funksies. Die eksperimentele groep is dan hoofsaaklik geleer deur middel van 'n kruising PBL benadering terwyl die vergelyking groep hoofsaaklik deur die lesing benadering vir 'n tydperk van drie maande. Die bevindinge van hierdie navorsing het getoon dat die eksperimentele groep studente uitgevoer aansienlik beter in die algehele resultate analise, maar daar was geen betekenisvolle verskille in prestasie tussen die twee groepe vir 'n paar MTT gebiede op komposisies en inverses van funksies. Die studie het ook bevind dat PBL aan die begin van die jaar reg geïmplementeer moet word wanneer die FP studente begin hul klasse in die fondament program. Dit word aanbeveel dat PBL in al die ander fondament program vakke moet geïmplementeer word. Tog kan die rol van die konvensionele onderrig benaderings nie ondermyn word in die onderrig en leer van komposisies en inverses van funksies, en as sodanig die konvensionele onderrig benaderings moet saam met PBL word gebruik om die beste resultate op FP studente se wiskunde prestasie te kry . Hierdie studie beveel aan verdere navorsing oor hoe PBL in 'n ander fondament program vakke geïmplementeer kan word.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The special needs community is in the midst of a philosophical and physical shift from a segregated system to an integrated system, not only in placement, but more importantly, in terms of learning and affording learners with special needs access to mainstream curricular materials. Mathematical modelling, or challenging mathematics problems solved in small groups, is part of the Australian mainstream curriculum. The purpose of the study was to investigate the way special needs learners learn mathematics from a modelling learning environment. To do this, it was necessary to identify the critical characteristics of the best practice in teaching and learning for learners with special needs, and the critical features of modelling. One theory of learning that has the capacity to promote special needs learners' interaction with mathematical modelling is Feuerstein’s theory of Structural Cognitive Modifiability. A hypothetical learning trajectory was designed for special needs learners at middle school according to general design principles from theory, which was adapted to the learning characteristics of the class. The learning environment comprised of three challenging modelling tasks, together with recommended implementation and support conditions in the classroom. Specifically, the research sought to investigate the ways in which special needs educators can support the higher reasoning processes of special needs students during modelling through design in general, and through mediation specific to each learner. The research took the form of a qualitative study, combining the phases of design-based research with a multiple case study approach. Three cases were analysed in depth. Empirical data were collected through a range of qualitative methods, which included data from student files, field observations, video and audio recordings, focus group interviews with students, and the input of various collaborators across the different phases of planning, design, implementation, and revision. Data were coded and analysed inductively according to emerging patterns and themes. Findings suggest that the use of modelling was successful when implemented with certain characteristics defined in the literature, and that it enabled learners to learn mathematics and also to develop additional outcomes such as social skills and language. During this study, learners' higher-order reasoning was supported through dynamic assessment and subsequent mediation. / AFRIKAANSE OPSOMMING: Die onderwysgemeenskap vir leerders met spesiale behoeftes bevind hulle in die middel van filosofiese en fisiese verskuiwings van 'n geskeide sisteem na 'n geïntegreerde sisteem. Dit omvat die plasing van leerders, maar meer belangrik ook die bemoontliking van toegang van hierdie leerders tot hoofstroom kurrikulêre materiale. Wiskundige modellering, en uitdagende wiskundeprobleme wat deur leerders in klein groepies opgelos word, is deel van die Australiese hoofstroomkurrikulum. Die doel van die studie was om die wyse te ondersoek waarvolgens leerders met spesiale behoeftes wiskunde in 'n modelleringsomgewing leer. Dit is gedoen deur die belangrike kenmerke van beste praktyk vir onderrig en leer in spesiale onderwys, asook die kritiese kenmerke van modellering, te vind. Een leerteorie wat die interaksie van leerders met spesiale behoeftes met wiskunde bevorder, is Feuerstein se teorie van Strukturele Kognitiewe Modifieerbaarheid. 'n Hipotetiese leertrajek was ontwerp vir leerders met spesiale behoeftes op middelskoolvlak. Empiriese data is deur 'n reeks kwalitatiewe aksies: data van studentelêers, veldwaar-nemings, video en klankopnames, fokusgroeponderhoude met studente, asook die insette van verskeie medewerkers oor die verskillende fases van beplanning, ontwerp, implementering en hersiening gegenereer. Die spesifieke leerkenmerke van hierdie leerders volgens algemeen-teoretiese en lokaalgekontekstualiseerde ontwerpbeginsels is nagekom. Die leertrajek het bestaan uit drie uitdagende modelleringsprobleme met aanbevole implementering en ondersteuningsriglyne in die klaskamer. Die navorsing het spesifiek gesoek na wyses waarop hierdie leerders se hoër beredeneringsvaardighede deur hul onderwysers, volgens elkeen se eie behoefte gedurende modellering, deur ontwerp in die algemeen en mediasie in die besonder, ondersteun kan word. Die navorsing, 'n kwalitatiewe studie, was gekombineer met fases van ontwikkelingsgebaseerde ontwerp wat uitgespeel het in 'n veelvuldige gevallestudiebenadering. Drie gevalle is in diepte ondersoek. Data was induktief gekodeer en geanaliseer volgens ontluikende patrone en temas. Bevindinge wys uit dat die gebruik van modellering suksesvol was wanneer die implementering volgens spesifieke kenmerke in die literatuur was. Dit het leerders instaat gestel om wiskunde te leer asook om addisionele uitkomste soos sosiale vaardighede en taal te ontwikkel. In hierdie studie is hoër-orde denke ondersteun deur dinamiese assessering en voortspruitende mediasie.

Although reasons for avoiding help, goal orientation, and social efficacy have been examined in the context of social adaptive help seeking, researchers have not pursued how these constructs influence computer adaptive help seeking. The three studies in this dissertation addressed both social and computer adaptive help seeking. The purpose of this dissertation was to determine if reasons for avoiding help seeking, personal goal orientation, or social efficacy predict social and computer adaptive help seeking for students enrolled in computer-based, developmental mathematics courses in community college settings. The purpose of the first study was to determine if students differentiate among three help-seeking sources: (a) formal, (b) informal, and (c) computer. Study 1 revealed that this population considered two different sources of help: social and computer help. These results were used to formulate the following questions for Study 2 and Study 3: 1. Do reasons for avoidance of help predict social or computer adaptive help seeking? 2. Does personal goal orientation predict social or computer adaptive help seeking? 3. Does social efficacy predict social or computer adaptive help seeking? Study 2 revealed that ability concerns negatively predict social adaptive help seeking and that mastery goal orientations positively predict both social and computer adaptive help seeking. Study 3 revealed that ability concerns negatively predict social adaptive help seeking and that mastery goal orientations and social efficacy for peers positively predict social adaptive help seeking. Additionally, ability concerns negatively predict computer adaptive help seeking, and mastery goal orientations positively predict computer adaptive help seeking. The finding that students who adopt a mastery-goal orientation use both social and computer means to adaptive help seek was not surprising. The finding that students who have ability concerns do not tend to social adaptive help seek is also consistent with previous research. However, the most important conclusion from Study 3 is that students who have ability concerns do not computer adaptive help seek, regardless of the anonymity provided by the computer. More research is needed in this field to examine why students with ability concerns tend to avoid help seeking altogether. / text