Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-12-09T12:17:44Z No. of bitstreams: 1 PDF - Adriano Alves de Silveira.pdf: 5754090 bytes, checksum: 3f1ff5d850c2e62808aa80d8184050a0 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-02-02T18:18:37Z (GMT) No. of bitstreams: 1 PDF - Adriano Alves de Silveira.pdf: 5754090 bytes, checksum: 3f1ff5d850c2e62808aa80d8184050a0 (MD5) / Made available in DSpace on 2017-02-02T18:18:37Z (GMT). No. of bitstreams: 1 PDF - Adriano Alves de Silveira.pdf: 5754090 bytes, checksum: 3f1ff5d850c2e62808aa80d8184050a0 (MD5) Previous issue date: 2016-10-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This research analyses how an approach in the classroom via Problem Solving, Exploration and Posing can potentialize the teaching and learning of Combinatorial Analysis. A literature review was performed aiming to understand the contributions of other researchers on the researched theme, so that it could be possible to realize what is possible to deepen and add for the scientific community, regarding the teaching and learning process of the Combinatorial Analysis. Besides this, an interview with mathematics teachers was performed, aiming to know their ideas on teaching and learning of Combinatory Analysis and, afterwards, scrutinize until where they could help to plan a sequence of activities. The research was conducted according to a qualitative approach, aiming to search meanings, interpreting and comprehend the information obtained. The modality of research can be characterized as teacher research; according to which the professor is the researcher of his or her own classroom (LANKSHEAR AND KNOBEL, 2008). The teaching and learning Methodology chosen to work in the classroom was the one of the problem solving, exploration and posing, developed with a sequence of activities in a group of the 2nd year of Secondary School of a public school in the city of Alagoinha-PB, Brazil. During the intervention, this researcher acted as a researcher teacher, working in the classroom as a regent teacher, giving a utonomy to the students on the construction of the essential ideas of the Combinatory Analysis, in such a way that the author acted as a mediator and instigator. Data were collected during the lessons through observation and records of the materials used by the students, as well as sound recording. Twenty-one meetings were performed, totaling 25 lessons, each lesson lasting, at most, 45 minutes. The classroom was organized in groups of three students and, in some cases, in pairs, in order to carry out a cooperative and collaborative work, where it was considered important, in this process, the mutual respect among them, respecting the ideas arisen on the search of the problem solution. The results of the research highlighted that through the Mathematics teaching and learning approach via Problem Solving, Exploration and Posing it was possible to monitor the growth of the students, who created their own ideas to solve the problems, and, consequently, found multiple strategies for solution of them; posteriorly, justify their solutions, participating effectively of the construction of their knowledge. Besides this, the students engaged in activities of mathematical exploration, which enabled the comprehension of the essential ideas of Combinatorial Analysis, as well as assuming the role of investigators in the classroom, generalizing, formulating new problems and, afterwards, solving them. From which it follows that such methodology allows learning with more comprehension, strengthening the student to solve problems of Combinatorial Analysis with focus not only on the search of the problem solution, but also on the process of the solution and being able to go far beyond, like the performance of a work of problem posing and exploration. / A presente pesquisa analisa como uma abordagem em sala de aula via Resolução, Exploração e Proposição de problemas pode contribuir/potencializar com o ensino-aprendizagem de Análise Combinatória. Foi realizada uma revisão de literatura com o intuito de compreender as contribuições de outros pesquisadores acerca do tema pesquisado, para que se pudesse perceber o que é possível aprofundar e acrescentar para a comunidade científica, no que diz respeito ao processo de ensino-aprendizagem da Análise Combinatória. Além disso, foi realizada uma entrevista com professores de Matemática, com o intuito de conhecer as suas ideias acerca do ensino-aprendizagem de Combinatória e, posteriormente, perscrutar até que ponto elas poderiam colaborar a planejar uma sequência de atividades. A pesquisa foi empreendida segundo uma abordagem qualitativa, visando buscar significados, interpretar e compreender as informações obtidas. A modalidade de pesquisa pode ser caracterizada como pedagógica, segundo a qual o professor é o pesquisador de sua própria sala de aula (LANKSHEAR E KNOBEL, 2008). A Metodologia de ensino-aprendizagem escolhida para trabalhar em sala de aula foi a de resolução, exploração e proposição de problemas, desenvolvida com uma sequência de atividades em uma turma do 2ª ano do Ensino Médio de uma escola pública na cidade de Alagoinha-PB. Durante a intervenção, o presente pesquisador agiu como professor-pesquisador, trabalhando em sala de aula como professor regente, dando autonomia aos alunos na construção das ideias essenciais de Combinatória, de modo que o autor agiu como mediador e incentivador. Os dados foram levantados durante as aulas através das observações e registros dos materiais utilizados pelos alunos, bem como de gravação sonora. Foram realizados 21 encontros, totalizando 25 aulas, cada aula com duração de, no máximo, 45 minutos. A sala foi organizada em grupos de três alunos e, em alguns casos, em duplas, com o intuito de se realizar um trabalho cooperativo e colaborativo, onde se considerou importante, nesse processo, o respeito mútuo entre eles, respeitando as ideias levantadas na busca da solução dos problemas. Os resultados da pesquisa evidenciaram que através da abordagem via Resolução, Exploração e Proposição de problemas foi possível acompanhar o crescimento dos alunos, que criaram suas próprias ideias para resolver os problemas, e, consequentemente, encontraram múltiplas estratégias de resolução deles; posteriormente, justificam suas soluções, participando efetivamente da construção do seu conhecimento. Além disso, os alunos engajaram-se em atividades de exploração matemática que lhes possibilitaram a apreensão de ideias essenciais de Análise Combinatória, como também assumiram o papel de investigadores em sala de aula, fazendo generalizações, formulando novos problemas e, em seguida, os resolvendo. De onde se conclui que tal metodologia permitiu um aprendizado com mais compreensão, potencializando o aluno para resolver problemas de Análise Combinatória com foco não apenas na busca da solução do problema, mas no processo da resolução e podendo ir muito além, como a realização de um trabalho de proposição e exploração de problemas.

This dissertation chronicles my search to engage high school English students in inquiry as part of a formal research process. The perspective of critical literacy theory is used to describe the four phases of the problem posing process in shaping student research and action. Grounded in Freire's approach and consistent with Dewey and others who advocate inquiry, action and relevance, Wink's process is built into the instructional plan described in this study. Because of the real-life context of the classroom and the complex social phenomena being considered, a case study methodology was utilized in which multiple sources of data converged to develop the themes. Data sources included the work and artifacts of ten students in a tenth grade English class during the spring semester of 2008. The analysis focuses on the supports, the constraints and the impact of problem posing on the high school research assignment. The analysis, findings, and conclusions contribute to the literature in three areas: audience, reflection and grading.

TITLE: Studentsʼ problem posing as an indicator of mathematical culture of lower secondary students AUTHOR: Mgr. Jiří Bureš DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis is focused on studentsʼ problem posing as an indicator of mathematical culture of lower secondary students. The theoretical background consists of research on problem posing, word problems in mathematics, mathematical culture and the Theory of didactical situations in mathematics. The goal of the thesis is to analyse links between problem posing and studentsʼ mathematical culture through the analysis and description of the posed problems. The thesis consists of two parts, theoretical and research part. In the theoretical part, there are the main findings about studentsʼ problem posing and some approaches to the concepts of word problems and mathematical culture, and the main concepts of the Theory of didactical situations used in the thesis. The research part starts with the analysis of the pre-experiment, which constitutes the basis for creation and characteristics of the conception of mathematical culture of problem posing. These parts are followed by the analysis of the main experiment, which provides the complete description of the posed problems...

Problem-posing is recognized as an important component in the nature of mathematical thinking (Kilpatrick, 1987). More recently, there is an increased emphasis on giving students opportunities with problem posing in mathematics classroom (English& Grove, 1998). These research has shown that instructional activities as having students generate problems as a means of improving ability of problem solving and their attitude toward mathematics (Winograd, 1991). In this study, teaching Taxicab Geometry which is a non-Euclidean geometry is aimed to mathematics teacher candidates by means of computer game-Simcity- using real life problems posing. This studies’ participants are forty mathematics teacher candidates taking geometry course. Because of using Simcity computer game, this game is based on Taxicab Geometry. Firstly, students had been given Taxicab geometry theory for two weeks and then seperated six each of groups. Each of groups is wanted to posing problem and solving from real life problems at Taxicab geometry. In addition to, students applied to problem solving at Simcity computer game. Studens were model into Simcity game. They founded ideal city, healty village, university campus, holiday village, etc. interesting of each others.

Central to this article is networking in math lessons, whereby concentration is placed on the construction of a student-focused teaching method for the networking of mathematical knowledge in the lower secondary. Firstly, normative standards and descriptive results will be compared. Secondly, several already existing teaching methods for networking in math lessons will be added to the method of „chapter-spanning task variation“. Using this method, attention is be placed on the integration of mathematical content and specific social netowrk-form (e.g. teacher led classes, group-work etc.). This paper will be concluded with the presentation of the testing of the method in the school context).

Title: Interpretation of calculations in word problems - looking for a question Author: Tereza Legová Department: Department of Mathematics and Mathematical Education Supervisor: prof. RNDr. Naďa Vondrová, Ph.D., Department of Mathematics and Mathematical Education Abstract: This thesis deals with an exploratory study of the introduction of modified word problems into the teaching of mathematics. The modification of the classical word problem consists in setting the context of the word problem and calculation. The task of pupils is to find out what we get by the given calculation, what question the calculation answers and substantiate their claims. The aim of the thesis was to describe how pupils think in solving this type of problem. Specifically, it investigated what strategies pupils elect and what difficulties arise in solving. The theoretical part of the thesis is a search of literature on the topic of solving word problems and their possible implementation in teaching. The practical part is divided into two phases. A test consisting of three problem contexts was given to pupils. The aim was to determine the meaning of the three given calculations for the each context. Before solving the test, a sample problem was discussed with the pupils. In the first phase, interviews were conducted with six pupils...

Die Brasiliaanse opvoedkundige Paulo Freire word as een van die belangrikste opvoeders van die twintigste eeu beskou. Sy benadering tot volwasse onderrig is op verskeie terreine toegepas maar nooit direk as teenvoeter vir geweld teen vroue en kinders aangewend nie. Die doel van hierdie studie was om vas te stel op welke wyse Paulo Freire se benadering tot leer en onderrig in volwasse basiese onderrig as teenvoeter kan dien vir die kultuur van geweld teen vroue en kinders in Suid-Afrika. Die studie bestaan uit ’n analitiese literatuurstudie en ’n kwalitatiewe studie met elf deelnemers. Ten einde die navorsingsvraag te beantwoord neem die studie ‘n aanvang met ’n literatuurstudie oor die redes vir geweld teen vroue en kinders. Daarna val die fokus op volwasse basiese onderrig [VBO], volwasse leer en die knelpunte in VBO in Suid-Afrika. In die volgende hoofstuk word die literatuur ten opsigte van Freire se werk en sy benadering tot volwasse onderrig bespreek. Kernelemente van sy benadering word getabuleer waarna kritiek op en die belang van sy benadering, sowel as die toepassing daarvan, in Afrika en Suid-Afrika bespreek word. In die kwalitatiewe empiriese studie word die resultate van die vrae in die onderhoudsgids met betrekking tot geweld en VBO bespreek waarna die resultatate in die laaste hoofstuk in die lig van die literatuurstudie geanaliseer word. Nadat die data beoordeel is, word aanbeveel dat, hoewel kennis geneem moet word van die uitdagings in VBO en Freire se benadering, die benadering steeds as ’n middel in basiese volwasse onderrig gebruik kan word om geweld die hoof te bied. ’n Praktiese voorstel vir teengeweldonderrig word gemaak met behulp van ’n teengeweldlesplan vir VBO. Die navorsing sluit af met beperkings van die studie en voorstelle vir optrede. / The Brazilian educator Paulo Freire is considered to be one of the most important educators of the twentieth century. His approach to adult education has been applied to various fields, but never directly to prevent violence against women and children. The purpose of this study was to ascertain how Freire’s approach to learning and teaching can be used as an antidote against violence against women and children in South Africa. The study consists of an analytical literature review and qualitative study with eleven participants. To answer the research question, the study commences with a literature study on the reasons for violence against women and children. Therafter the focus shifts to the adult basic education, adult learning and the restraints in adult basic education in South Africa. In the next chapter Freire’s work and his approach to adult education is dis-cussed. Key elements to his approach is tabled whereafter critique on and the im-portance of his approach, as well as its application in South Africa, is discussed. In the qualitative empirical study the results of the questions in the interview guide with regard to violence and adult basic education is discussed, whereafter the results are analised in the final chapter in view of the literature study. After the consideration of the data, it is recommended that cognisance must be taken of the challenges to adult basic education and Freire’s approachwhich can still be utilised as a medium in adult basic education to combat violence. A practical proposal for antiviolence education is made through a antiviolence lesson plan for ABE. The research concludes with limitations and recommendations. / ABET and Youth Development / M. Ed. (Adult Education)