The main purpose of the study was to understand preservice secondary mathematics teachers&rsquo / pedagogical content knowledge of composite and inverse functions. The study was conducted with three preservice secondary mathematics teachers in Graduate School of Education at Bilkent University. The instruments of the study were qualitative in nature and in four different types of data forms: observations, interviews, documents, and audiovisual materials. Observation data came from fieldnotes by conducting an observation of lessons participants taught at Private Bilkent High School. Interview data came from the transcriptions of semi-structured interviews. Document data came from survey of function knowledge, journal writings, vignettes, and lesson plans. Audiovisual data came from the examination of the videotape of the lessons participants taught. The findings reveal that preservice secondary mathematics teachers&rsquo / knowledge levels in components of pedagogical content knowledge were not at the desired levels and also they experienced difficulty while integrating that knowledge. The results of the study indicate that teacher education should provide courses that cover the content relevant to students in order to assure both depth and breadth in subject matter knowledge of the preservice teachers. Moreover, the activities which mimics the classroom cases and assures the integration of knowledge components like vignettes would be used in teacher education programs. Results can inform educational practices, and reforms in Turkey, and provide a basis for further research, with increased pedagogical content knowledge as the ultimate goal.

The purpose of this study was to investigate the preservice science teachers&rsquo / perceived technological pedagogical content knowledge (TPACK) on genetics. More specifically, the purpose was to examine the relationships among the components of TPACK and genetics knowledge of the preservice science teachers. Moreover, findings the effect of the demographic information on perceived TPACK was also aimed. This study was conducted with preservice science teachers who were enrolled in elementary science education department of Education Faculties of eight public universities located in Central Anatolia. 1530 preservice science teachers participated to the study. There were two instruments used in this research which were perceived TPACK questionnaire, which was later adopted by the researcher as perceived TPACK on genetics, and genetic concepts test. v Data were analyzed by using descriptive and inferential statistics. In order to answer the first research question, descriptive information about the components of TPACK was given. Correlational analyses were used to identify the relationship between each component of the perceived TPACK on genetics and their genetic knowledge. Another correlational analysis was conducted for the third research question which seeks the relationships among the components of the TPACK. Moreover, MANOVA was conducted to investigate the impact of gender and year of enrollment on perceived TPACK on genetics of preservice science teachers. The results revealed that genetic knowledge was correlated with each component except the perceived project specific technology knowledge. Moreover, there were positive significant correlations among the components of the TPACK. According to the MANOVA results, the mean scores of male and female preservice science teachers differ in five components of TPACK, namely project specific technology knowledge, pedagogical knowledge, pedagogical content knowledge, technological content knowledge and technological pedagogical content knowledge. The results of MANOVA for year of enrollment revealed that the mean ETK, GTK, PSTK, and CK scores of participants with different year of enrollment differ significantly.

The main purpose of this study is to assess pedagogical content knowledge (PCK) of in-service physics teachers about electricity topic in high school level by developing a paper-and-pencil instrument consisting of open-ended items. The instrument was developed with four different implementations by administration to the 278 in-service physics teachers. An exploratory and confirmatory factor analysis including only PCK items was conducted in validation processes. The relations among teachers&rsquo / job satisfaction levels, perceived self-efficacy levels, years of teaching experience and specific experiences, attendance to in-service training seminars related to physics teaching programs and teachers&rsquo / PCK were also analyzed by a confirmatory structural equation modeling study in validation of test scores. SPSS and AMOS programs were used in the analyses. Results of the study showed that teachers&rsquo / perceived self-efficacy level, attendance to in-service training seminars and specific experiences were significant predictors of their PCK. Teachers&rsquo / years of teaching experience and job satisfaction level were not significant predictors of their PCK. Inter-rater reliability scores were calculated as 0.86 and 78% for scoring and coding of the participant teachers&rsquo / responses respectively. Results also showed that there are many Turkish physics teachers whose PCK scores regarding students&rsquo / learning difficulties and misconceptions are below the average and participants mostly prefer to implement direct instruction in their classrooms as the instructional strategy.

Although the Technological Pedagogical Content Knowledge (TPACK) framework has shown a lot of promise as a theoretical perspective, researchers find it difficult to use it in particular environments because the requirements of the framework change in specific contexts. The purpose of this study was to explore and produce more flexible ways of using the TPACK for inservice mathematics secondary teachers. Three such teachers at an urban public school were observed in their classrooms and interviewed about their experiences of teaching mathematics and integrating computer technology in their day-to-day activities. Each participant had over 10 years experience in teaching mathematics in secondary schools in Ontario, and expertise in using computers in mathematics curriculum. The research questions were: 1) How do secondary school mathematics teachers describe their ways of integrating technology? 2) What difficulties do teachers have when they try to integrate technology into mathematics classrooms? The findings from the first research question show that teachers displayed a high degree of integration of technology. Their activities were very clearly designed, conferring clear roles to the use of integrating computer technology in mathematics classes. Teachers had specific approaches to integrate computer technology: a) to allow students opportunities to learn and experiment with their mathematical knowledge; b) to help them pass the content to the students in the process of teaching mathematics; and c) to assess and evaluate students’ work, and give them feedback. The findings from the second research question reveal that teachers had difficulties in purchasing and maintaining the computer equipment. They had some difficulties in trying to integrate new technologies as these required time, preparation, and dedication. In addition, teachers had some difficulties in making students use computers in a significant way. The implication for teacher education is that inservice teachers should have opportunities to update their computer and pedagogical skills, a long term perspective in integrating technology in mathematics education, and professional and technical support from teaching colleagues and administrators. Finally, the integration of computer technology in mathematics requires more intensive teamwork and collaboration between teachers, technical support staff, and administrators.

The Education Faculties within the universities are looking to meet the needs of their learners more completely. Teaching and learning strategies are being adopted to make educational provision more flexible by using computer supported collaborative learning environments. However, research has shown that in preservice teacher programs, many teachers do not have a complete knowledge of subject-matter or pedagogical content knowledge. This study investigated how a lesson-planning task within the context of a computer supported collaborative learning environment can facilitate the growth of teacher knowledge, specifically subject-matter knowledge and pedagogical content knowledge about the teaching of ratio and fraction. The findings from this research showed that using a lesson-planning task facilitated the development of teacher knowledge, specifically subject-matter knowledge and pedagogical content knowledge. Within the computer supported collaborative learning community, the preservice teachers were able to articulate their current understandings and re-define their knowledge of fraction and ratio. The thesis concludes with a conceptual framework and some specific guidelines for the design of a scaffolded computer-mediated community and discusses implications for the design of future collaborative learning environments.

No description available.

abstract: ABSTRACT The integration of technology into content area teaching while taking into account state standards is a continuing challenge for secondary teachers. To address this challenge, six high school teachers participated in one-on-one tutoring sessions conducted by the researcher. The Technological Pedagogical Content Knowledge (TPACK), which posits that teachers add technology into their practice by blending it with content and pedagogy, served as the theoretical framework and guided implementation of the project. During the one-on-one tutoring sessions, which occurred weekly in hour-long sessions for a five- to eight-week period, teachers selected the focus of the training sessions. To assess teacher perceptions of efficacy quantitative data were gathered prior to and following the intervention using an on-line survey tool. Although pre- to post-intervention scores on the survey increased, the difference was not significant. With respect to the qualitative data four themes emerged. First, there were specific processes and patterns that emerged within the sessions related to the TPACK framework. Teachers selected either technology or content to initiate sessions. Teachers did not begin sessions with high yield pedagogical strategies as a focus. Second, one-on-one tutoring fostered an initial sense of community, and as the project progressed, a community of practice emerged. Third, challenges emerged related to technology and high yield pedagogical strategies. At times technology did not work or teachers expressed there was too much to grasp and apply to their practice. Additionally, the appropriate applications of high yield instructional strategies also presented challenges to participants. Fourth, based on their participation in the project, teachers expressed an increased sense of efficacy with respect to conducting their work. The discussion was focused on how teachers created a community of practice to support their professional growth, which influenced efficacy for teaching as they became increasingly effective in blending technology, pedagogy and content. / Dissertation/Thesis / Ed.D. Educational Leadership and Policy Studies 2011

abstract: This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT. / Dissertation/Thesis / Ph.D. Mathematics 2011

abstract: Few would argue that teacher effectiveness is a key lever in education reform and improving the overall quality of public education, especially in poor and working class communities. To that end, the importance of supporting and developing beginning teachers is of utmost importance in education, thus requiring deep understandings of the process of learning to teach. Yet, most conceptions of teacher learning struggle to capture the social, cultural, and historical context of teacher learning, particularly in understanding how learning and the production of knowledge is situated, active, and complex. One example of this limitation comes from the field of research on pedagogical content knowledge (PCK) and its importance in developing effective beginning teachers. This study characterizes beginning teachers' production of PCK within a cultural historical activity theory (CHAT) framework. This study finds that the teachers produce PCK mostly based on their own individual experiences and reflections, receiving little assistance from the structures intended to provide them with support. The self-produced PCK is uneven, underdeveloped, and relies on teachers to use their sense of agency and identity to navigate dissonant and unbalanced activity systems. Over time, PCK production remains uneven and underdeveloped, while the individual teachers find it more and more difficult to bring balance to their activity systems, ultimately resulting in their exit from the activity system of teaching in their district and school. / Dissertation/Thesis / Ph.D. Educational Leadership and Policy Studies 2012

A autorregulação é um dos vários elementos considerados essenciais no processo de aprendizagem, pode-se afirmar que um aluno autorregulado em sua aprendizagem é aquele que aprendeu a planejar, controlar e avaliar seus processos cognitivos, motivacionais, afetivos, comportamentais e contextuais; possui autoconhecimento sobre o próprio modo de aprender, suas potencialidades e limitações. Com esse conhecimento o estudante controla e regula o próprio processo de aprendizagem em direção a seus objetivos e metas. Por sua vez o professor autorregulado é capaz de auxiliar no desenvolvimento dos processos autorregulatórios de seus estudantes e oferecer oportunidades para que também autorregulem sua própria atuação. É nesta perspectiva que este estudo pré-experimental se fundamenta, na instrução direta dos processos de autorregulação da aprendizagem. Com esse intuito foi proposta uma Oficina Online de Estratégias de Estudo, com um grupo de 76 estudantes universitários do Curso de Licenciatura em Matemática a Distância, da Universidade Federal de Pelotas, universidade participante do Consórcio Universidade Aberta do Brasil. Os participantes mostraram semelhanças ao perfil do aluno virtual brasileiro, sendo a maioria do sexo feminino, com idade média de 33 anos e que exercem atividade remunerada com dedicação média de 39 horas semanais. Buscou-se avaliar o impacto no processo autorregulatório da aprendizagem e no conhecimento pedagógico do conteúdo do futuro professor de matemática. Para avaliar o impacto da experiência de ensino com adaptação do Programa de Gervásio ao contexto online, foram analisadas quantitativamente as variáveis autorregulação da aprendizagem (IPAA), o conhecimento de estratégias de aprendizagem (CEA) e o conhecimento pedagógico do conteúdo equação do segundo grau (CPC), antes e após a experiência de ensino. Também foi realizada a análise dessas variáveis em função das variáveis categóricas pessoais e acadêmicas dos participantes. Para aferir a relação entre a autorregulação da aprendizagem e o conhecimento do conteúdo pedagógico foi realizada a análise de correlação entre o IPAA (pós), CEA (pós), CPC (pós) e as variáveis categóricas - idade e rendimento acadêmico médio. Além deste conjunto de análises, foi avaliada a variável entrega da atividade. Para uma interlocução com a análise quantitativa, foi realizada a análise dos dados qualitativos obtidos através do Chat e dos Fóruns de Discussão e, por fim, foram determinadas as frequências relativas das respostas à Ficha de Avaliação da Oficina, bem como realizada a análise qualitativa das questões abertas desta avaliação. Através desta investigação foi possível verificar que o ensino dos processos autorregulatórios, na educação a distância é um constructo fundamental e viável para formação de um educador matemático, pois permitiu uma mudança significativa no conhecimento declarativo das estratégias de aprendizagem e do conhecimento pedagógico do conteúdo matemático do futuro professor. Além das mudanças cognitivas decorrentes da experiência de ensino foi possível observar outros fatores que possibilitam a gerência dos comportamentos, pensamentos e sentimentos, voltados e adaptados para obtenção de metas pessoais e guiados por padrões gerais de conduta, tais como: a identificação de fatores que influenciam a aprendizagem, a antecipação dos resultados das ações, experimentação de satisfação com o próprio esforço, crenças de autoeficácia positivas, autorreflexão, gerenciamento do tempo disponível, o monitoramento do próprio desempenho, percepção do valor do aprendizado. Pelos resultados obtidos, parece pertinente, que a competência de autorregulação da aprendizagem componha a arquitetura pedagógica de cursos de formação inicial de professores de matemática, na modalidade a distância. / The self-regulation is one of several elements considered essential in the learning process, it can be said that a self-regulated learner in their learning is one who has learned to plan, monitor and evaluate their cognitive, motivational, affective, behavioral and contextual processes; it has self knowledge about the proper way to learn, its potential and limitations. With this knowledge the student controls and regulates the learning process itself toward its goals and objectives. On the other hand self-regulated teacher is able to assist in the development of self-regulatory processes of their students and provide opportunities for them to also self regulate their own performance. It is in this perspective that this pre-experimental study is based on the direct instruction of self-regulation processes of learning. In this sense, we propose an Online Workshop Study Strategy for a group of 76 college students of the Degree in Mathematics distance, from Federal University of Pelotas, which is participant of the university consortium “Universidade Aberta do Brasil”. The participants of Workshop showed similarities to the profile of Brazilian virtual student. The most of them are female with mean age of 33 years and performing paid work with dedication average of 39 hours per week. We sought to assess the impact on auto-regulatory process of learning and pedagogical content knowledge of future teachers of mathematics. To assess the impact of teaching experience with adaptation of Gervasio´s program to the online environment, were quantitatively analyzed the learning of self-regulation variables (IPAA), knowledge of learning strategies (CEA) and the pedagogical content knowledge of the quadratic equation (CPC) before and after the teaching experience. Also carried out analysis of these variables on the basis of personal and academic categorical variables of the participants. To assess the relationship between self-regulation of learning and knowledge in the educational content was performed the correlation analysis between the IPAA (post), CEA (post), CPC (post) and categorical variables - age, average academic performance. In addition to this set of analyzes, the variable delivery activity was evaluated. For a dialogue with the quantitative analysis, the analysis of qualitative data obtained through the Chat and Forums was held and, finally, were determined relative frequencies of responses to the Workshop Evaluation Form and carried out a qualitative analysis of open questions of this evaluation. Through this research we found that the teaching of self-regulatory processes in distance education is a fundamental construct and feasible to form a mathematics educator, it allowed a significant change in declarative knowledge of learning strategies and pedagogical knowledge of the mathematical content of future teacher. In addition to the cognitive changes resulting from the teaching experience we observed other factors that enable the management of behaviors, thoughts and feelings, directed and adapted for achieving personal goals and guided by general standards of conduct, such as the identification of factors that influence learning, the anticipation of the results of actions, trial of satisfaction with their own efforts, positive self-efficacy beliefs, self-reflection, available time management, monitoring one's own performance, perception of the value of learning. The results obtained, it seems pertinent that the competence of learning self-regulation compose the pedagogical architecture of initial training courses for mathematics teachers, in the distance.