Orientador: Dario Fiorentini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-23T20:37:25Z (GMT). No. of bitstreams: 1 Santos_SuelidosPrazeres_M.pdf: 3248639 bytes, checksum: df5758dccce33b51eb115fa7a654d241 (MD5) Previous issue date: 2013 / Resumo: Este estudo tem como hipótese de trabalho que os erros e dificuldades evidenciados pelos alunos na aprendizagem da matemática estão diretamente relacionados com os modos de conceber e realizar o ensino da álgebra em sala de aula. O objetivo principal deste trabalho é identificar e analisar, em investigações que têm como foco de estudo erros no ensino e aprendizagem da álgebra elementar, as relações que se estabelecem entre as concepções de ensino de álgebra, os tipos de erros cometidos pelos alunos e os modos de os pesquisadores lidarem com eles. Para alcançar tal objetivo, foi realizada uma metanálise qualitativa de nove dissertações brasileiras de mestrado que investigaram erros e dificuldades dos alunos em álgebra elementar. Esse corpus de análise foi constituído de acordo com critérios definidos previamente. A metanálise desse corpus foi desenvolvida com base nas seguintes perspectivas de investigação: identificação dos tipos de erros em álgebra presentes nas pesquisas; os modos de conceber a educação algébrica em cada pesquisa, tendo por base Fiorentini, Miorim e Miguel (1993); e as concepções e os modos de lidar com erros evidenciados nesses estudos. Foram identificadas quatro concepções distintas de erro nessas pesquisas: o erro que deve ser corrigido e identificado; o erro considerado como um obstáculo; o erro como parte integrante do processo de ensino e aprendizagem; e o erro considerado como indicador para avaliar/reavaliar a prática pedagógica. Em relação aos erros identificados, foi possível discutir sobre alguns erros que tiveram um caráter mais procedimental, considerados como erros de sintaxe, e outros erros mais relacionados com a interpretação de significados e de conceitos, considerados como erros de natureza semântica. Percebeu-se, ao final da metanálise, que as pesquisas que apresentaram mais erros de procedimentos, alinhavam-se às concepções de educação algébrica fundamentalista estrutural, fundamentalista analógica e linguístico-pragmática. Entretanto as pesquisas alinhadas à concepção exploratória e de desenvolvimento do pensamento e da linguagem algébricos, e que enfatizavam a produção e negociação de significados e a compreensão dos conceitos algébricos, evidenciaram erros de natureza semântica, mesmo na exploração de situações de natureza sintática. Em síntese, os resultados obtidos reforçaram nossa hipótese inicial de que os tipos de erros cometidos ou destacados em álgebra estão diretamente relacionados à concepção que professores e pesquisadores têm do ensino da álgebra. / Abstract: The hypothesis of this research is that the errors and difficulties of students during mathematical learning are related directly to ways of thinking and teaching algebra in classes. Its main goal is to identify and analyze, in study that have as focus the study errors in the teaching and learning of elementary algebra, relations established among the algebra teaching conceptions, the kinds of errors made by students and the researchers' ways of managing them. To get the goal, it was realized a qualitative meta-analysis of nine master's degree Brazilian theses that studied students' errors and difficulties in elementary algebra. The corpus of analysis was established according to criteria defined previously. The meta-analysis was developed based on the following investigation perspectives: identifying of errors kinds in algebra from researches; the ways of thinking the algebra teaching in each research, based on Fiorentini, Miorim and Miguel (1993); and the conceptions and the ways of managing the errors evidenced in the studies. It was identified four concepts of errors: error that must be identified and corrected; error regarded as an obstacle; error as a part of teaching and learning process; and error regarded as an indicator to evaluate and reevaluate the pedagogical practice. Concerning the identified errors, it was possible to discuss about some errors with procedural feature, regarded as syntax errors, and others related to interpretation of meaning and concepts, regarded as errors with semantic feature. It was perceived that, at the end of meta-analysis, the researches that presented more procedural errors are aligned with structural fundamentalism, analogical fundamentalism and linguistic pragmatic conceptions of algebra teaching. However, the researches aligned with the exploratory conceptions, with algebraic thinking and language developing, that emphasized the production and negotiation of meaning and understanding of algebraic concepts, evidenced errors of semantic feature, even in the investigation of situations with syntax feature. In summary, the obtained results reinforced the initial hypothesis that errors made or showed in algebra are directly related to the conception that teachers and researchers have about algebra teaching. / Mestrado / Ensino de Ciencias e Matematica / Mestra em Multiunidades em Ensino de Ciências e Matemática

Orientadores: Dario Fiorentini, Dione Lucchesi de Carvalho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-21T03:13:05Z (GMT). No. of bitstreams: 1 Gomes_AdrianaAparecidaMolina_D.pdf: 6606302 bytes, checksum: 01453cd23e82ca18a566fbbbc148e023 (MD5) Previous issue date: 2012 / Resumo: Os objetivos desse trabalho são: (1) compreender as práticas pedagógicas que geram discursos produtores e mobilizadores de conhecimentos e saberes nas aulas de matemática da Educação de Jovens e Adultos (EJA); (2) identificar as contribuições trazidas para o processo de ensino da matemática. Os sujeitos da pesquisa são alunos e alunas 1º termo, 2º termo e 4º termo do Ensino Fundamental da Educação de Jovens e Adultos (EJA) e 1º termo A do Ensino Médio da EJA, da rede pública de Louveira/SP. Tem-se como questão central: "Em um contexto de diversas culturas e de múltiplos (con)textos, que práticas pedagógicas podem produzir discursos produtores de conhecimentos e saberes em aulas de matemática da EJA?". Trata-se de uma pesquisa qualitativa, cujos instrumentos adotados para construção da documentação são: videograções e audiogravações das discussões em grupos e no coletivo da sala de aula, produções escritas, relatórios, entrevistas semiestruturadas, diário e notas de campo. As produções escritas incluem questionários, cartas, registro de jogo, exercícios, tarefas exploratório-investigativas, memoriais e formulação de problemas. Para análise, cruzaram-se instrumentos e informações. Define-se, assim, como objeto de investigação, os contextos, as práticas discursivas, as interações, os modos de representações matemáticas propostos pelos sujeitos, as estratégias envolvidas no processo de resolução de uma tarefa exploratório-investigativa, a mediação, a intervenção, a comunicação, a apropriação e a (inter)ação. A análise, centrada na perspectiva histórico-cultural, possibilitou constatar que os jovens e os adultos se mobilizaram e se engajaram na resolução de tarefas escolarizadas de cunho matemático, o que possibilitou que estes e estas tivessem vozes, (trans)formassem suas vozes em escritas, expressassem suas ideias e seus pensamentos matematicamente, o que propiciou o desenvolvimento da autonomia intelectual e crítica e, consequentemente, sua inclusão social e educacional. Outra questão percebida, nas análises, é que no contexto de diversas culturas e de múltiplos (con)textos da EJA, as aprendizagens, as significações e as apropriações se entrelaçam e se entremeiam aos sentidos, ao sentir, ao saber ouvir, escutar e estar com o outro. / Abstract: The aims of this study are, firstly, to understand the pedagogical practices in mathematics lessons, within the Brazilian Youth and Adult Education System (EJA), that generate discourse to foster and stimulate knowledge and understanding; and, secondly, to identify contributions to the process of mathematics teaching. The subjects of the study are male and female students from EJA elementary education classes 1, 2, and 4 and EJA secondary education class 1A, in the city of Louveira, São Paulo state. The central question is: "In a context consisting of diverse cultures and multiple (con) texts, what are the pedagogical practices that are able to generate discourse to stimulate knowledge and understanding in EJA mathematics lessons?". The study is a qualitative one, using the following tools to gather information: video and audio recordings of group and classroom discussions, written texts, reports, semi-structured interviews, journal and field notes. The written texts consist of: questionnaires, letters, game results, exercises, exploratory-investigative tasks, worksheets, and problem formulation. For the purpose of analysis, the tools and information were interconnected. Thus, the object of the investigation is the contexts, discourse practices, interactions, kinds of mathematical representations proposed by the subjects, strategies involved in solving exploratory-investigative tasks, mediation, intervention, communication, appropriations, and (inter)action. The focus on a historical-cultural perspective, allows the analysis to show that the young people and adults were mobilized and engaged in the solving of mathematical tasks in the classroom context, enabling these students to have a voice, allowing them to (trans)form their voices into writing, to express their ideas and thoughts mathematically. This conciliated development of intellectual and critical autonomy, and consequently, social and educational inclusion. Another issue seen in the analysis is that in the context of the cultural diversity and multiple (con)texts of the EJA, learning, meanings, and appropriations intertwine and mesh with the senses, with sensibility, ability to hear, listen, and to be with others. / Doutorado / Ensino e Práticas Culturais / Doutor em Educação

Orientador: Marcia Regina Ferreira de Brito / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-04T03:33:49Z (GMT). No. of bitstreams: 1 Alves_EricaValeria_D.pdf: 1163734 bytes, checksum: 3e1d15f522b3121acf5d9aedf463b9cb (MD5) Previous issue date: 2005 / Resumo: O presente estudo teve o objetivo de compreender e analisar as relações entre a memória, os conhecimentos declarativo e de procedimento e o desempenho na solução de problemas matemáticos. Para tanto, 177 estudantes do primeiro e último ano do ciclo II do Ensino Fundamental e último ano do Ensino Médio provenientes de uma escola pública e uma escola privada foram solicitados a responder um questionário informativo, uma prova matemática para avaliar o domínio dos conhecimentos declarativo e de procedimento e o desempenho na solução de problemas matemáticos, e uma prova para avaliar a memória matemática. A partir do desempenho obtido nesses instrumentos trinta e dois sujeitos foram selecionados e submetidos ao teste de Cópia e Reprodução de Figuras Complexas de Rey. Os resultados indicaram que a memória matemática está intimamente relacionada com o desempenho na solução de problemas e que a capacidade de perceber os elementos de forma analítica e sintética favorecem a representação do problema influenciando o desempenho na solução. Também foi verificado que a percepção desempenha um papel fundamental nos processos cognitivos superiores, uma vez que constitui a mais imediata das reações humanas diante de uma situação inédita, pois, antes de representar, reter, ou recuperar uma informação na memória, o sujeito a percebe / Abstract: The objective of this investigation was to understand and to analyze the relationship between memory, performance and procedural and declarative knowledge memory in problem solving. Subjects were 177 elementary and high school students from two private and public schools. Instruments were a questionnaire, a mathematical test to evaluate procedural and declarative knowledge and a mathematical memory test. After this, 32 subjects was selected and submitted to Rey Complex Figures Test. The results indicated that were relationships between mathematical memory and problem solving performance, and synthetic and analytic problem perception improves representation and problem solving performance. It was found, also, that perception performs a primordial role in the higher cognitive processes therefore constitutes the most immediate of the human reactions in front of an uncommon situation, because before recall, retention or representation an information, the person perceives that / Doutorado / Educação Matematica / Doutor em Educação

Hur använder lärare matematikboken i dagens undervisning? Dominerar boken undervisningen eller fungerar den som ett redskap, en så kallad artefakt? Syftet med denna studie är att undersöka matematikbokens vikt i dagens undervisning i årskurs tre, genom en kvalitativ metod. Studiens två forskningsfrågorundersökgenom observationer och semistrukturerade intervjuer med tre olika respondenter och tre olika skolor. Datainsamlingen analyseras med fenomenografisk forskningsansats skolinspektionens analysschema. Samtliga lärare som medverkade i studien hävdar att matematikboken är grundläggande i undervisningen samt att matematikboken används till åttio procent i undervisningen. Lärarna belyser att tiden är knapp och matematikboken underlättar tidsmässigt. Resultaten som framkom i studien är att matematikboken dominerar undervisningen. Elever arbetar i stora drag enskilt i matematikboken eller med material som är framtaget från matematikboken under lektionerna. Slutsatsen i denna studie är att det inte råder någon större individualisering eller socialt samspel i klassrummen på grund av den stora del enskilda arbete, lärare använder till största del material från matematikboken eller matematikboken. Slutligen visar både observationer och intervjuer att matematikboken dominerar undervisningen tidsmässigt. Stora undersökningar som TIMSS och PISA visar att nordiska länder använder matematikboken mer än övriga länder, samt ett nedåtgående resultat i matematik för Sverige. I denna studie undersöks matematikbokens vikt i dagens undervisning. / How do teachers use the mathematic textbook in teaching today? Is the mathematic textbook dominant in teaching or is it used as a tool, a so-called artefact? The purpose is to examine the importance of mathematical textbook in today´s teaching in grade three, through a qualitative method. The study two research questions are examined by observations and semi-structured interviews with three different respondents and schools. The data collection is analyzed with phenomenografic research approach. All teachers that participated in the study claim that the mathematic textbook is fundamental in the teaching and that the textbook is used to eighty percent in teaching. The teachers assert that there is very little time and that the mathematic textbook facilitates time. The results that emerged from the study are that the mathematic book dominates the teaching. Pupils generally work individually in the mathematics book or with material that is proceed from the mathematic book during the lessons. The conclusion in this study is that there is no major individualization or social interaction in the classroom because of the large proportion of individual work, teachers mostly use materials from the mathematics book or the mathematic book. Finally, both observations and interviews show that the mathematical book dominates teaching in time. Large studies such as TIMSS and PISA shows that Nordic countries use the mathematics book more than other countries, and a falling result in mathematics in Sweden.  The importance of mathematical textbook in teaching is examined in this study.

Master’s thesis deals with comparsion and rating the compressed natural gas as an aircraft piston engine fuel. An information search of conventional fuels and differences of the fuel systems for AVGAS and CNG is included. Next part describes the aircraft and its engine on which is the mathematic model based. After that perfomance and consumption data are calculated for both fuels and the results are then compared. At the end of the thesis, a design of the CNG fuel system with components selection is described.

In the fall of 2018, programming was implemented in the swedish curriculum and then became a new element in mathematics education for grades 1-3. Teachers who took their degree before the implementation, lacks education in programming and there is interest in finding out how teaching about programming is conducted since it became part of the curriculum. The purpose of this study was to contribute with knowledge about how teachers have implemented programming in their teaching even though they lack education in it. Four semi-structured interviews have been conducted where the data from the interviews has been analyzed from Mathematical Knowledge for Teaching. The result shows that teachers without education in programming find it difficult to plan instruction in programming by themselves. In the teaching of programming the teachers focus on the central concepts in programming and that the programming should interest the students. It was difficult for teachers to assess the students in programming and the only assessment that teachers make is the formative assessment. / Hösten 2018 implementerades programmering i den svenska läroplanen och blev då ett nytt moment inom matematikundervisningen för årskurs 1-3. Lärare som innan detta tog sin lärarexamen saknar utbildning inom programmering och det finns intresse att ta reda på hur undervisningen kring programmering bedrivs sedan det blev en del av läroplanen. Syftet med denna studie var att bidra med kunskap om hur lärare har implementerat programmering i sin undervisning trots att de saknar utbildning inom det. Fyra stycken semistrukturerade intervjuer har gjorts där datan från intervjuerna har analyserats utifrån Mathematical Knowledge for Teaching. Resultatet visar på att lärare utan utbildning inom programmering har svårigheter att på egen hand planera undervisning i programmering. Under genomförandet av undervisningen fokuserar lärarna på att befästa centrala begrepp inom programmering och att väcka ett intresse hos eleverna. Det upplevdes svårt för lärarna att bedöma eleverna inom programmering och den enda bedömning som lärarna gör är den formativa bedömningen.

The aim of this diploma thesis is software designed to simulate landing of the paragliding wing. It means the development of the mathematic model describing the final stage of flight and landing. The model comprises the effects of controls (brakes, speed bar, weight-shifting). One part of the thesis is the description of the implementation in C# language with complete source codes.

The concept of fractions is necessary and vital knowledge in mathematics and has an essential role in perceptions of other mathematical areas. But many claims that this concept is both hard to teach and difficult to understand and thus avoids teaching and using fractions. To find out how the pupils perceive and reason about fractions, didactic theory, George Pólya's, and Frank Lester's problem-solving strategies and the subject theory has been used as a theoretical framework. In the study, which is a case study, participated 24 pupils the ages were between 9 and 10 and performed three diagnoses with a specific focus at part of a whole and part of a number. The diagnostic results were analyzed quantitatively, and then semi-structured interviews were conducted with six pupils according to the selection has obtained from the percentage of the solution frequencies. The results from the diagnoses show that the pupils' solution frequency on the diagnoses was between 14% and 90%. The analyzes from the semi-structured interviews show that the pupils with a lower solution frequency had inadequate knowledge of the concept of fractions and insufficient knowledge of the subject theory and used problem-solving strategies to a very meager extent. The pupils with a higher solution frequency had good perceptions of fractions and had good knowledge of the theory of the subject, and use problem-solving strategies to a much greater extent.

The main objectives of the thesis Correctif processies of structured wholes are to find out whether and under what conditions is the child able to identify an error in a structured whole in the last year of pre-school education and whether her is able to correct the identified errors. To meet the objectives, there was used the qualitative research to select 30 children from two pre-school classes. The research included five activities focused on different types of structured wholes, but also on different correction processes. The observed phenomenas were recorded in tables and graphs that are part of the work or listed in the appendix. From the series of created tasks, observation of children and subsequent data recording and analysis, the child in the last year of pre-school education does not have the experience of identifying and correcting errors and the approaches of childer to solve the tasks are in different ways.

Syftet med denna kvalitativa studie är att undersöka hur matematiklärare arbetar för att motverka matematikängslan hos elever i årskurs 4–6. Den valda datainsamlingsmetoden är semistrukturerad intervju. Resultatet visar att elever uttrycker sig negativt när de utför matematiska uppgifter eller är med på matematiklektioner. De intervjuade matematiklärarna beskriver olika orsaker bakom matematikängslan, en orsak är att elever har brister i grundläggande kunskaper i matematik. En slutsats som går att dra är att matematiklärare är medvetna om matematikängslan.