Lic. avh. Luleå: Luleå tekniska univ., 2006.

Campus administrators from rural public school districts are continuously looking for creative innovative ways to respond to the educational challenges placed upon them by federal and state-legislated accountability requirements. Advances in interactive videoconferencing (ITVC) technologies provide a way to address these challenges. However, these advancements sometimes lack needed resources to make a network of this magnitude work. The Mid-Rio Collaborative was established to share educational resources and knowledge between Texas A&M International University in Laredo, Texas, and surrounding rural public school districts in South Texas. The established collaborative provided the backdrop for the study while meeting the educational needs of this region. The purpose of this study was to examine the use of interactive videoconferencing as a viable alternative for the delivery of high school Algebra. A mixed methods case study of four campuses explored the perceptions of administrators teachers, and students in the use of interactive videoconferencing. The sampled population included 4 administrators, 4 teachers, 35 students (12 experimental and 23 control) from selected rural districts. Qualitative and quantitative research methodologies were utilized in identifying perceptions of participating principals, teachers, and students. Major findings of this study included (a) campus administrators’ values and beliefs influence teacher use of interactive videoconferencing; (b) a difference exists in experienced and novice teacher perceptions regarding the impact of ITVC, (c) perceptions are dependent upon the Teacher Partner role in the teaching and learning process; (d) increased interaction between students, teacher, content, other learners, and technology exists with instruction delivered through ITVC; (e) perceptions of cognitive and classroom conditions differed between students receiving instruction via face-to-face and interactive videoconferencing; finally, (f) students receiving instruction through ITVC did not demonstrate academic gains in state-mandated tests (TAKS). Study results support the current body of research that contends there is no significant difference between instruction delivered face-to-face and instruction being delivered via interactive videoconferencing.

Submitted by DANIELA MIRANDA FERNANDES SANTOS null (danymifesa@gmail.com) on 2016-05-20T01:00:42Z No. of bitstreams: 1 tese_doutorado_daniela_miranda_fernandes_santos.pdf: 2659899 bytes, checksum: a862ae59b25bd39008f6030cb06e5bc4 (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-05-23T20:12:23Z (GMT) No. of bitstreams: 1 santos_dmf_dr_prud.pdf: 2659899 bytes, checksum: a862ae59b25bd39008f6030cb06e5bc4 (MD5) / Made available in DSpace on 2016-05-23T20:12:23Z (GMT). No. of bitstreams: 1 santos_dmf_dr_prud.pdf: 2659899 bytes, checksum: a862ae59b25bd39008f6030cb06e5bc4 (MD5) Previous issue date: 2016-03-31 / Secretaria da Educação do Estado de São Paulo / A presente pesquisa, vinculada à linha “Processos Formativos, Ensino e Aprendizagem”, foi implusionada pela questão: Qual a relação entre a álgebra acadêmica e a álgebra escolar expressa nas concepções dos licenciandos e professores do curso de licenciatura em matemática? E, teve como objetivo geral investigar a relação entre a álgebra acadêmica e a álgebra escolar expressa nas concepções de álgebra e do seu ensino entre professores e licenciandos matriculados no curso de licenciatura em matemática da FCT – Unesp de Presidente Prudente, tendo em vista subsidiar reflexões sobre a formação inicial de professores de matemática. O referencial teórico constitui-se das teorias da educação matemática acerca da álgebra, da relação entre álgebra acadêmica e álgebra escolar, das concepções de álgebra e do seu ensino e da formação inicial de professores de matemática. Com abordagem qualitativa e delineamento descritivo analítico, a pesquisa teve como procedimentos metodológicos: análise documental, questionário e entrevista, realizados ao longo do curso. O material de análise incluiu o Projeto Pedagógico do referido curso, os questionários aplicados aos licenciandos no 1º e 3º ano, as entrevistas realizadas com os licenciandos no 2º e 4º ano do curso bem como as entrevistas realizadas com professores que ministraram disciplinas diretamente relacionadas à álgebra. A análise documental associada às entrevistas realizadas com professores e licenciandos indicou que o curso atende às orientações legais vigentes. No entanto, não há justificativa para a escolha de disciplinas da grade curricular, tendo em vista a sua relevância para a formação do futuro professor. Nas proposituras do plano de ensino das disciplinas Álgebra Elementar e Álgebra I observou-se nuances da relação entre a álgebra acadêmica e a álgebra escolar, mas o seu desenvolvimento mostrou-se incoerente com tais proposituras. Na prática, priorizava-se o ensino do conhecimento matemático, caracterizando-se no modelo da racionalidade técnica, reforçando procedimentos vivenciados e internalizados durante o processo de escolarização anterior à licenciatura. No curso analisado, a ênfase curricular, quando se trata de álgebra, recaiu sobre a álgebra das estruturas. Relacionando os modelos relativos ao ensino de álgebra destacados pelos licenciandos em diversos momentos ao longo do curso, foi possível perceber que se trata de modelos pautados na definição, seguida de exemplos, resolução de exercícios, que no geral, se aproximam expressivamente da álgebra acadêmica. Quando os licenciandos definem álgebra, salienta-se à concepção estrutural. Por outro lado, ao se referirem à aplicabilidade da álgebra, destaca-se a concepção ferramenta. Considerando que a concepção ferramenta se sobressaiu entre as demais, conclui-se que as concepções dos licenciandos encontram-se em consonância com a álgebra escolar, com algumas marcas da álgebra acadêmica, representada pela concepção estrutural. As concepções de álgebra dos professores se aproximaram à concepção estrutural. Explicitam que, para ser um bom professor de matemática basta ter domínio sólido de conteúdo e saber ensinar; desse modo apontaram a supervalorização das disciplinas específicas em detrimento das disciplinas pedagógicas, enfatizando a álgebra acadêmica. O presente estudo concluiu que a relação entre a álgebra acadêmica e álgebra escolar na formação inicial do licenciando não é significativa a ponto de ressignificar os conhecimentos sobre ensino de álgebra do futuro professor. / This research, linked to the line "Formative Processes, Teaching and Learning," was driven by the question: What is the relationship between academic algebra and school algebra expressed in the conceptions of undergraduate and professors of mathematics degree course? And has had as general goal to investigate the relationship between academic algebra and school algebra expressed in algebra concepts and their teaching between professors and undergraduates enrolled in the Mathematics degree of FCT - UNESP of Presidente Prudente, in order to subsidize reflections on initial training of mathematics teachers. The theoretical framework was constituted of mathematics educational theories about algebra, the relationship between academic algebra and school algebra, the algebra concepts and their education and initial training of mathematics teachers. Using qualitative approach and descriptive analytic design, the research has had as methodological procedures: document analysis, questionnaire and interview, conducted throughout the course. The analysis material included the pedagogical project of that course, the questionnaires given to undergraduates in the 1st and 3rd year, interviews with undergraduates on the 2nd and 4th year of the course as well as interviews with teachers who taught subjects directly related to algebra. The documentary analysis associated with interviews carried out with professors and undergraduates indicated that the course meets the statutory guidelines. However, there is no justification for the choice of the curriculum subjects, in view of its relevance to the formation of the future teacher. In the propositions of the teaching plan of the subjects elementary algebra and Algebra I, it was observed nuances of the relationship between academic algebra and school algebra, but its development was found to be inconsistent with such propositions. In practice, the mathematical knowledge education was prioritized, and characterizing itself in the model of technical rationality, reinforcing procedures experienced and internalized during the process prior to the school degree. Over this course, the curricular emphasis when it comes to algebra, has fell on the structures algebra. Relating the models to the teaching of algebra highlighted by undergraduates at several points along the course, it was revealed that it is guided by models in the definition, followed by examples, exercises solving, which overall approach expressively of academic algebra. When the undergraduates define algebra, structural design is stressed. On the other hand, when referring to the algebra applicability, the design tool is highlighted. Considering that the tool design stood out among the others, it is concluded that the conceptions of undergraduates are in line with the school algebra, with some marks of academic algebra, represented by the structural design. The algebra concepts of the teachers have approached to the structural design. They explain that to be a good mathematics teacher it‟s just necessary to have solid domain content and know how to teach; thereby they pointed to the overvaluation of specific subjects at the expense of educational disciplines, emphasizing academic algebra. This study has concluded that the relationship between academic algebra and school algebra in the initial formation of the undergraduate is not significant enough to reframe the future teacher‟s knowledge related to the algebra teaching.

In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.

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