This paper combines data from two different international research studies that used problem posing in analyzing elementary teacher candidates’ understanding of rational numbers. In 2007, a mathematics educator from the United States and a mathematician from Northern Ireland collaborated to investigate their respective elementary teacher candidates’ understanding of addition and division of fractions. A year later, the same US mathematics educator collaborated with a mathematics educator from South Africa on a similar research project that focused solely on the addition of fractions. The results of both studies show that elementary teacher candidates from the three different continents share similar misconceptions regarding the addition of fractions. The misconceptions that emerged were analyzed and used in designing teaching strategies intended to improve elementary teacher candidates’ understanding of rational numbers. The research also suggests that problem posing may improve their understanding of addition of fractions.

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).

Made available in DSpace on 2014-07-29T15:00:24Z (GMT). No. of bitstreams: 1 Dissertacao Leonardo S L Marengao.pdf: 887501 bytes, checksum: 6b25c419c0a97b5c52f3e266699ffd4a (MD5) Previous issue date: 2012-01-30 / In this study we investigated the possibility of students identify problems in physics in their daily lives after they have classes of Mechanics under the dialogical process of questioning, through the Three Pedagogical Moments. The survey was conducted with students of the night course of Technician Cargo Transportation, in the form PROEJA from Federal Institute of Goias - Annapolis Campus. Data collection occurred in two stages: first were applied to all students‟ questionnaires consisting of open questions and then were held semi-structured interviews with some of these students. Throughout the development stages of the Three Moments students draw up proposed Pedagogical problems in physics. The interpretation of the questionnaire responses and interview transcripts through the content analysis suggests that the development of the Three Pedagogical Moments with the development of problems by the students, allows for a relative ownership of such problems by themselves, which helps them develop an awareness of the presence of physics in situations of everyday life, yet they demonstrate conceptual difficulties. The dialogical approach the teacher and the students' active participation throughout the process were also key features to which students were able to build physics problems outside the school environment. / Nesta pesquisa investigamos a possibilidade de os estudantes identificarem problemas de Física em seu cotidiano após terem aulas de Mecânica segundo o processo de problematização dialógica, por meio dos Três Momentos Pedagógicos. A pesquisa foi realizada com estudantes do período noturno do curso Técnico em Transporte de Cargas, na modalidade PROEJA do Instituto Federal de Goiás Campus Anápolis. A coleta de dados ocorreu em duas etapas: primeiramente foram aplicados a todos os estudantes questionários constituídos de perguntas abertas e, posteriormente foram realizadas entrevistas semi-estruturadas com alguns desses estudantes. Ao longo do desenvolvimento das etapas dos Três Momentos Pedagógicos propusemos os estudantes elaborassem problemas de Física. A interpretação das respostas aos questionários e das transcrições das entrevistas através da Análise de Conteúdo sugere que o desenvolvimento dos Três Momentos Pedagógicos, com a elaboração de problemas pelos próprios estudantes, permite que haja uma relativa apropriação de tais problemas pelos mesmos, o que os auxilia a desenvolver uma percepção da presença da Física em situações do seu cotidiano, ainda que eles demonstrem dificuldades conceituais. A postura dialógica do professor bem como a participação ativa dos estudantes ao longo do processo também foram características fundamentais para que os estudantes conseguissem construir problemas de Física fora do ambiente escolar.

Title: Problem Posing Process: Comparison of Posers on Various Levels of Experience Author: PhDr. Eva Patáková Department: Department of Math. And Math. Education, Pedagogical Faculty, Charles University in Prague Supervisor: doc. RNDr. Jaroslav Zhouf, Ph.D. Abstract: The aim of the thesis is to compare the problem posing process of problem posers on various experience levels: Novices have no experience, specialists pose problems but not more than their teachers profession requires, experts pose problems profesionally, e.g. for Mathematical competitions. There were two phases of the research - both of them consisting of the pilot phase and the main study. The participants posed difficult and original Mathematical problems for approximately 15-year-old students. In the first phase methods derived from the grounded theory were used to analyze self-reflections, questionnaires and other written materials of problem posers. The second phase was based on qualitative analysis of videotyped problem posing process of respondents. The problem posing process of the three groups of respondents was different. With increasing level of experience the ratio of intentional ideas increased as well as the ratio of posers finding inspiration in the existing problem. Opinion to how a good problem should look like is also different for...

This paper combines data from two different international research studies that used problem posing in analyzing elementary teacher candidates’ understanding of rational numbers. In 2007, a mathematics educator from the United States and a mathematician from Northern Ireland collaborated to investigate their respective elementary teacher candidates’ understanding of addition and division of fractions. A year later, the same US mathematics educator collaborated with a mathematics educator from South Africa on a similar research project that focused solely on the addition of fractions. The results of both studies show that elementary teacher candidates from the three different continents share similar misconceptions regarding the addition of fractions. The misconceptions that emerged were analyzed and used in designing teaching strategies intended to improve elementary teacher candidates’ understanding of rational numbers. The research also suggests that problem posing may improve their understanding of addition of fractions.

The purpose of this youth participatory action research (YPAR) project was to challenge the pedagogy of traditional literacy instruction for low-income Latino/a students, particularly the overuse of scripted curricula and standardized tests mandated through the No Child Left Behind (NCLB) Act. Twelve student participants served as co-teachers and co-researchers as they created, implemented, and evaluated a critical literacy class based on the theoretical frameworks of critical pedagogy and critical literacy and the methodology of youth participatory action research (YPAR). The YPAR Critical Literacy Group and research took place at one of a network of small, independent-study alternative schools called Future Horizons Charter High School (FHCHS, a pseudonym), located in southern California. Critical pedagogy and critical literacy formed a theoretical foundation upon which the students and teacher built a class based on the tenets of dialogue, problem-posing, and generative themes based on the interests of the student co-researchers. This alternative practice of co-creating knowledge with students was paramount in facilitating young peoples’ learning to think critically about their positionality within their political and social spheres. Critical literacy does not focus simply on the development of decoding and comprehension skills for reading, but students of critical literacy must “read the word and the world” (Freire & Macedo, 1997), grounding their acquisition of literacy skills through their own experiences and social contexts. This research examined the capacity of critical literacy and YPAR methodology to transform both learner and teacher. The YPAR Critical Literacy Group at FHCHS positively impacted the student coresearchers. Elements of qualitative research, including interviews and transcription positively impacted the students co-researchers’ traditional literacy skills. Student coresearchers evaluated the course as a positive experience throughout, and engaged in and comprehended texts far above their traditionally-defined decoding and reading comprehension reading levels. Attendance and engagement in the class for the 4-month period was consistently higher in the critical literacy class than in other reading classes offered at the school. The students experienced preliminary transformation and early stages of critical consciousness from the beginning to the end of the course, evidenced by the evolution of their reflective writings and progressively sophisticated analyses of social injustice at the school and within the broader community.

Made available in DSpace on 2016-12-23T14:01:45Z (GMT). No. of bitstreams: 1 Catia Aparecida Palmeira.pdf: 2026141 bytes, checksum: 76c3aa34b76e5a684c0eb3138ecd5344 (MD5) Previous issue date: 2012-11-27 / This master work with focus in mathematics education is linked with the Graduate Education Program at Center of Education at Federal University of Espírito Santo. Our study took place in 2011 in a state public school from the city of Vitoria, ES. Our research of qualitative nature investigates the possibilities of mathematics learning in a regular 3rd year secondary class having also students with visual deficiency. We have tried to answer the question: What possibilities of mathematics learning do happen in a 3rd year class of secondary school that has 4 students with visual deficiency when it incorporates a practice of solving and posing problems and incentives interaction among students? We have used Vygotsky/ s ideas to analyze interactions in the learning process. The perspectives from Polya, Santos and Santos-Wagner have guided us to interpret students/ mathematics learning in tasks of problem solving and problem posing. We have developed mathematics activities from equations from 1st and 2nd grade, linear systems, trigonometry and probabilities based on the questions proposed by Pitombeira (2008). We have collected data through questionnaires, mathematics tasks and workshops. In the analysis from these students/ tasks we have found evidences of changes in their studies habits outside school. We have noticed the development of student autonomy by searching new mathematics learning and strategies to solve and pose problems. We have also identified major interaction between teacher/students and among students with visual deficiency and the others. Our work has showed that it is possible to include all the youth students of secondary school in the process of mathematics learning. We do hope that this work offers inspiration to other teachers to develop pedagogical practices that try to assure participation and learning of all students in their classes. We also dream that teachers will be inspired by this research to consider peculiarities, particularities and skills of all the involved in the process of mathematics teaching and learning / Trabalho de mestrado, com foco em educação matemática, vincula-se ao Programa de Pós-Graduação em Educação do Centro de Educação da Universidade Federal do Espírito Santo. Nosso estudo ocorreu em 2011, em uma escola estadual do município de Vitória, ES. Nossa pesquisa de cunho qualitativo investiga as possibilidades de aprendizagens em matemática, em uma turma de 3º ano de ensino médio regular que também tem alunos com deficiência visual. Procuramos responder à pergunta: Que possibilidades de aprendizagem matemática ocorrem em uma turma de 3º ano de ensino médio, com quatro alunos com deficiência visual quando se incorpora uma prática de resolução e elaboração de problemas e incentiva-se interação entre os alunos? Nós usamos ideias de Vygotsky para analisar interações no processo de aprendizagem. As perspectivas de Polya, Santos e Santos-Wagner nos orientaram para interpretarmos a aprendizagem matemática dos alunos em situações de resolução e formulação de problemas. Desenvolvemos atividades matemáticas de equações do 1º e 2º graus, sistemas lineares, trigonometria e probabilidade, a partir de questões de Pitombeira (2008). Coletamos dados por meio de questionários, tarefas matemáticas e oficinas. Na análise dessas tarefas dos estudantes, encontramos indícios de mudanças nos hábitos de estudos deles fora da escola. Percebemos o desenvolvimento de autonomia estudantil ao buscarem novas aprendizagens matemáticas e estratégias para resolver e elaborar problemas. Identificamos maior interação entre professora/aluno e entre os alunos com deficiência visual com os demais. Nosso trabalho mostrou que é possível incluir todos os jovens estudantes de ensino médio no processo de aprendizagem matemática. Esperamos que este trabalho inspire outros professores em desenvolver práticas pedagógicas que procurem garantir participação e aprendizagem de todos os alunos de suas turmas. Sonhamos também que professores sejam inspirados por esta pesquisa a considerar peculiaridades, particularidades e habilidades de todos os envolvidos no processo de ensino e aprendizagem matemática

本研究嘗試從現代民主政治與教育兩百多年的發展歷程中，考察三種不同類型的教育命題或觀點，分別是：涂爾幹的「教育是一種社會化的過程」、弗雷勒的「教育即是自由的實踐」，以及傅柯的「關懷自身的倫理作為自由的實踐」。三種政治─教育立場分別著重於不同的人類圖像：教師、學生、知識分子。為考察上述三種不同類型的命題，從「社會環境與人類圖像」這樣的視角，我們將命題置於具代表性的政治社會化時代脈絡中，亦即：「民主社會─道德人」、「解放社會─人性化」與「規訓社會─生存美學」，在各自不同且具代表性的現代教育類型（道德教育、提問式教育、關懷自身的倫理作為自由的實踐）中進行研究。 基本上，本文所探討的三種教育類型是在與盧梭《愛彌兒》所揭示的教育問題對話過程中依序進行的。首先，愛彌兒這個理想的教育人類圖像對現代教育而言具有某種類似原型的影響力。原因在於，盧梭所虛構創造的愛彌兒是擺脫一切人類不平等，對自由有著深刻體認的道德人。由於日後在民主化的浪潮下，人們所欲培育的道德公民標示出封建君主教育與現代民主教育的根本差異，且是現代民主社會教育的主要特點之一，因此愛彌兒有其奠基性的重要作用。不同於盧梭以愛彌兒作為建構道德社會的起點，弗雷勒依循馬克思主義的思路，強調社會階級的差異，並以資本主義所具有的壓迫剝削性質的理解，提出受壓迫者教育學，凸顯出人類圖像與世界觀的相關性，在教學形式上主張人性化的提問式教育，由此一來也顯現出民主與教育的融合和開展。有別於傳統道德教育思想以及追求人性解放的革命理想，傅柯指出，由於現代國家知識─權力的流動與滲透形成了規訓社會，在這樣的情況下也就益發地凸顯出關懷自身（生存美學）的重要，亦即關注自身的學習成長挑戰了長期以來以國家為教育目的的正規性框架，由此一來便為現代教育研究帶來了深刻的思想衝擊。 在研究發現中，研究者回顧現代人類圖像變遷及其可能的相關發展，嘗試指出人類圖像的議題置入教育學三種不同政治─教育取向典範時，彼此之間在知識上形成一種既同又異的張力關係，從而呈現出對理解現代教育樣貌的不同詮釋角度，希望能作為教育學知識探討的背景，使我們對教育有更深度的思考，開拓出更多理論思考的面向。在後續研究建議裡，在以康德的教育疑問為背景下，研究者認為我們應對當下人類遭遇的諸多危機有所認識，以從教育的立場上做出適時的貢獻，故研究者整理當代法國哲學家莫翰於西元1999年為聯合國教育、科學及文化組織撰寫的教育改革建議書中的討論，考察教育對人類的重要意義，作為本文的研究結語。 / This research attempts to investigate three different forms of educatinal propostions or pespectives from the process of developing modern democracy and education over the 200-year period. It contains by examining the Emile Durkheim’s notion of “education is a process of socialization”, the notion of “education as the practice of liberty” which had its roots in Paulo Freire, as well as notion of “the ethics of the concern for self as a practice of freedom” which drew directly from Michael Foucault. From the political-education standpoint of view, they concentrated on particular human picture, including teacher, students and intellectuals. To explore the content of three educatinal propostions, I will put these into the context of typical politicization of society: democracy- moral people which means moral education, empancipating society- humanity which stands for posing education, and disciplinary society- aesthetics of existence which is supported by the idea of the ethics of take care of self as the practice of freedom. In essense, three educational forms of this research are implemented in sequence which is linked to the dialogue process of revealing educational problems by Rousseau, notably in Emile. First of all, the ideal-educated human picture origining from Emile had potentially influenced on modern education because Emile, who was moral person created by Rousseau, got rid of human inequality and acknowledged significantly importance of freedom. In the enlightment of democracy, people wanted to nurture moral citizenship, which was the main charactersitic of modern-democratic education, that represented the essential differences between feudal-monarchy education and modern-democratic education. Therefore, Emile had laid the foundation for modern-democratic education. Unlike the notion of Emile as a beginning to construct moral society, Freire followed the route of Marxism, and stressed the differences of social classes. In addition, he advocated pedagogy of the oppressed to raise the relationships between human picture and worldview based on understanding of nature of oppression and exploitation in the Capitalist context. As a result, he proposed posing education as a form of enhancing humanity in teaching as well as illustrating the inclusion and development between democracy and education. The flow and infiltration of national knowledge had shaped disciplinary society, which was pointed out by Foucault, was distinct from traditional moral education and evoluational provision of pursuiting humanity-emacipating. In this context, Foucault had raised the importance of concerning for self: aesthetics of existence, in other words, by means of concerning learning growth for self, it could challenge the formal frames of educational aims building on the basis of nation so as to bring the conflict on way of thinking for modern educational researches. As the results shown, after reviewing the shift of modern human picture and the possibility of related development, researcher attempts to indicate the tension with the differences and the similarities among the knowledge relationship when human picture are put into three forms of political-educational paradigm of pedagogy. As a result, the findings, which represent different explanation to acknowledge the modern education, are recognized as background of discussing educational knowledge so that we can have profound thinking about education, as well as in the expansion of dimensions of educational theories. In the follow-up research, researcher suggest that we should acknowledge various risks from human encountering at the moment based on the queries from the Kent’s educational problem and make appropriately contribution to education as educational practitioners. In my conclusion, I quote the conclusion that discussed the significances of education on UNESCO’s educational reforms in 1999, which was written by contemporary French philosopher Edgar Morin.

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.

On-line writing workshops provide educational spaces within which aspiring writers can learn their craft. In order to understand the dialogic mechanisms behind that learning, this thesis examines ways in which one workshop, the Internet Writing Workshop (IWW), functions as a Freireian culture circle. The exegesis identifies several key characteristics that defined Paulo Freire's concept of the culture circle. It compares these characteristics with the structure and practice of interaction within the IWW. It unpacks some of Freire's ideas about dialogue as a means of achieving critical consciousness, and compares them to current learning theory and the ways in which dialogue takes place within the IWW community. The exegesis also examines some of the political axioms behind Freire's pedagogy, and examines ways in which the IWW community might be viewed as emancipatory or liberatory. I examine these areas in light of the development of a novel, Suicide Girls. The second draft of this novel was influenced and informed by my participant-observation of the IWW. This working draft of the novel is provided as a process document to demonstrate findings made in the exegesis and is annotated to reflect relevant process and development issues.