The purpose of this study is to examine the effects of a mathematics teaching methods course on pre-service elementary mathematics teachers&rsquo / content knowledge for teaching mathematics (CKTM). In order to accomplish this purpose, pre-service mathematics teachers&rsquo / understanding of basic concepts and procedures in school mathematics, use of mathematical definitions, presentation of mathematical content to students, identification of common errors, misconceptions and solution strategies and evaluation of unusual solution methods were examined with the help of a multiple choice test. The data were collected from 43 senior pre-service mathematics teachers from a teacher education program at a large public university in Ankara. The participants were given an 83-item test to measure their content knowledge for mathematics teaching at the beginning and after the methods course. The purpose of the pre- and post-test assessment was to measure the amount of change in the participants&#039 / knowledge for mathematics teaching. The test was developed and piloted at the University of Michigan in the USA for Learning Mathematics for Teaching (LMT) Project. Quantitative data analysis techniques were used to answer the research questions. The results indicated that there was a significant effect of the mathematics teaching methods course on pre-service teachers&rsquo / content knowledge for teaching mathematics. Moreover, the findings showed that there is no significant mean difference between male and female pre-service teachers, and between the pre-service teachers who have taken at least one mathematics teaching elective course and the ones who have not taken any elective course related to mathematics teaching in terms of their CKTM. Also, the study showed that there is a significant positive relationship between pre-service teachers&rsquo / CKTM and their academic achievement on undergraduate mathematics content courses. The study is expected to make important contributions to the literature by providing information about whether the methods courses significantly contribute to pre-service teachers&rsquo / understanding of knowledge for mathematics teaching. Moreover, the findings of the study is hoped to inform teacher educators and policy makers about the needs and improvements in teacher preparation programs.

The main purpose of the study was to investigate pre-service elementary mathematics teachers&rsquo / personal efficacy beliefs and outcome expectancies about using concrete models in teaching mathematics. Data were collected from the pre-service teachers in the middle of the spring semester of 2008-2009. Pre-service teachers were junior students enrolled in elementary mathematics teaching program at a public university. Six instructional sessions based on using concrete models in teaching mathematics were carried out during a three week period. In this study, the researcher was also the teacher of the instruction at the same time. A survey on pre-service mathematics teachers&rsquo / efficacy beliefs about using concrete models was administered to the students before and after the instruction to evaluate the contribution of the instruction on pre-service teachers&rsquo / efficacies. After the instruction, semi-structured interviews were conducted. The present study demonstrated that the instruction based on using concrete models had positive contributions on the pre-service elementary mathematics teachers&rsquo / self-efficacy beliefs and outcome expectancies about using concrete models in teaching mathematics. In addition, results revealed that pre-service elementary mathematics teachers had confidence in themselves about using concrete models both as learners and as teachers. Moreover, they believed that using concrete models in teaching mathematics would have positive consequences in teaching process and students&rsquo / learning. However, the interview data indicated that, pre-service teachers had relatively low personal efficacies and outcome expectancies about classroom management, when the concrete models were involved in the instruction.

The purpose of this study was to investigate the prospective teachers&rsquo / knowledge of mistakes held by elementary students in fractions and their proposed strategies to overcome those mistakes. The data were collected from 149 prospective elementary mathematics teachers enrolled in the elementary mathematics education programs from a public university in Central Anatolian Region. Fraction Knowledge Questionnaire was used to accomplish the purpose of the study. The data collection tool included nine open ended questions, and each question had two sub-tasks. In this study, the items in the &ldquo / Fraction Knowledge Questionnaire&rdquo / were analyzed in-depth in order to reach a detailed description of prospective teachers&rsquo / knowledge about students&rsquo / mistakes on fractions. The results of this study revealed that prospective elementary mathematics teachers mostly could identify the students&rsquo / mistakes. However, although prospective teachers could notice the students&rsquo / mistakes, they could give superficial reasons for these mistakes. Furthermore, verbal explanations, using area representation, using real life model, reviewing prior knowledge, teaching standard algorithm, asking guided questions, using simple examples, using counter examples, using drill and practice, making students aware of their mistakes, and increasing students&rsquo / motivation were the suggested strategies by prospective teachers in order to overcome students&rsquo / mistakes in fractions.

The purpose of this study was to investigate the views of upper elementary mathematics teachers and students about the use of manipulatives in teaching and learning mathematics. This study is a qualitative case study. The participants of this study were four elementary mathematics teachers in a private school and their 6th, 7th, and 8th grade students. The data were collected through one-to-one interviews, observations and analyzing documents consisting of annual plan, daily plan, notebooks of students, and the field note that the researcher kept throughout the study. This study revealed that although all the teachers advocate the use of manipulatives in teaching mathematics, they use traditional teaching techniques in their classes. They mentioned different factors affecting their use of manipulatives in teaching mathematics such as not knowing how to use them, grade level, availability of materials, time constraints, students&rsquo / reactions (seeing them as a toy or not being accustomed to them), school administration, classroom management, not finding materials appropriate for the subject being taught and classroom size. In fact, these are the factors that are seen on the surface level. This study indicated that even when teachers are provided with training about the use of manipulatives, supported by the school administration, and provided with manipulatives, the use of manipulatives is largely determined by their views / beliefs about the nature of mathematics, how students can learn mathematics, the effect of manipulatives and their knowledge in using them. Students seemed to like learning by using manipulatives. When conditions were arranged for learning, they were willing to learn through manipulatives.

published_or_final_version / Education / Doctoral / Doctor of Philosophy

Not available / text

published_or_final_version / abstract / toc / Education / Master / Master of Education

published_or_final_version / abstract / toc / Education / Master / Master of Education

The major focus of this study is to explore, using the 1990 British Columbia Mathematics Assessment data at the Grade 7 level, gender differences in mathematics teachers' beliefs. As well, this study compared these differences to gender differences of students' beliefs found in the same data. The theoretical rationale for this study is based on a model devised by this researcher, namely the Modified Cognitively Guided Instruction (CGI) Research Model, which is the combination of the Cognitively Guided Instruction Research Model (Fennema, Carpenter, and Peterson, 1989) and the Autonomous Learning Behavior (ALB) Model (Fennema & Peterson, 1985). Two way ANOVA as well as planned comparisons (t-test) were used to investigate gender differences within and across a random sample of two status groups (teachers and students). The analysis of the data suggested several conclusions. First, male and female teachers are more similar than different with respect to their beliefs regarding the importance and difficulty of selected mathematics topics. And, Numbers and Operations was the only topic under study in which male and female teachers differed significantly. Male teachers rated Numbers and Operations more important than female teachers. Second, gender differences existed only in students' beliefs about the difficulty of Geometry, and Numbers and Operations. Female students, compared to male students, believe Geometry and Numbers and Operations more difficult. Third, the findings of this study show that the gender differences within each status group are similar. In addition, significant gender difference was found only in overall male's and female's (regardless of their status) beliefs about the importance of Numbers and Operations. Males rated Numbers and Operations significantly more important than females. Further research which directly investigates gender differences in teachers' beliefs and students' beliefs is suggested, as well as further research into relationships between gender differences in teachers' and students' beliefs.

Made available in DSpace on 2016-06-02T19:35:32Z (GMT). No. of bitstreams: 1 2149.pdf: 1258390 bytes, checksum: 1dfb71051b4b6f8fa171900a4573af6b (MD5) Previous issue date: 2007-05-11 / This work is a result of the research about the characteristics of the knowledge related to specific content of mathematics matter that a teacher is developing/reworking throughout his professional career. This is a case study, which the participant has the characteristics to be egress of the university course of the education of mathematics teachers; to have sought specific training in mathematics after three years of the professional practice and have a positive relationship with math and with their work. The design of teacher s knowledge that served as the basis emphasizes the social and discursive dimension of knowledge, proposing consider it as an expression of the practical reason, which belongs more to the fields of argument and the trial, than the fields of cognition and of information. We associate to the concept of knowledge the notion of relationship with knowledge, which guides us to consider the contexts and practices, in which the teacher is mobilizing to learn, or mobilize their knowledge in their interaction with students, the school team, with teaching materials and with the circumstances and demands of the profession. Through interviews, investigate how these contexts and practices influenced the construction of logical structure (requirements of rationality) of the teacher's way of thinking, over his career, especially considering the content of mathematics with which he works. Among the results of the research, we noticed that extent, the consistency, organization, the mechanisms for selection and improvement of knowledge of the teacher, concerning to the content of mathematics, are very influenced by the nature and function of their activity and, thus, for his practice in different situations and contexts linked to school. Throughout his career, he presents an authentic (and enviable) mobilization to learn that feeds the process of acquisition and updating of their knowledge, from their professional needs. However, in their experiences into the course of the education of mathematics teachers he found little support to reflect and improve their knowledge and their practices. Considering that the requirements of rationality are the conditions of intelligibility that a person need for the speech and its action their and the other make sense and are acceptable as evidence of a coherent dialogue, we noticed that the experiences of this subject in the universitary course little nurture the dialogue between the higher-level math and its knowledge, leaving, one hand, of to contribute in a meaningful way with their problem and thinking about the content, on the other, working to consolidate perspective in which their knowledge had been constructed to from their practice. / O presente trabalho é resultado da investigação sobre as características dos saberes relacionados aos conteúdos específicos da matéria de ensino que um professor de matemática vem elaborando/reelaborando ao longo de sua trajetória profissional. Trata-se de um estudo de caso, cujo participante tem como características ser egresso do curso de licenciatura em matemática; ter buscado uma formação específica em matemática após três anos de exercício da profissão; e ter uma relação positiva com a matemática e com seu trabalho. A concepção de saberes docentes que nos serviu de base ressalta a dimensão discursiva e social do saber, propondo considerá-lo como a expressão de uma razão prática, a qual pertence muito mais ao campo da argumentação e do julgamento do que ao campo da cognição e da informação. A ela associamos a noção de relação com o saber, que nos orienta a considerar os contextos e as práticas, nas quais o professor se mobiliza para aprender, ou mobiliza seus saberes na interação com seus alunos, com a equipe escolar, com materiais didáticos e com as circunstâncias e exigências da profissão. Através de entrevistas investigamos como estes contextos e práticas influenciaram a construção das lógicas estruturadoras (exigências de racionalidade) da maneira de pensar do professor, ao longo de sua carreira, principalmente considerando os conteúdos de matemática com os quais ele trabalha. Entre os resultados da pesquisa, constatamos que a amplitude, a consistência, a organização, os mecanismos de seleção e aperfeiçoamento dos saberes do professor, referentes aos conteúdos de matemática, são bastante influenciados pela natureza e pela função de sua atividade e, portanto, por sua prática em diversas situações e contextos ligados a escola. Ao longo de sua carreira, ele apresenta uma autêntica (e até invejável) mobilização para aprender que alimenta os processos de aquisição e atualização de seus saberes, a partir de suas necessidades profissionais. Contudo, em suas experiências no curso de licenciatura em matemática ele encontrou pouco suporte para refletir e aperfeiçoar seus saberes e suas práticas. Tendo em vista que as exigências de racionalidade constituem as condições de inteligibilidade que o próprio indivíduo impõe para que o discurso e a ação seu e do outro façam sentido e sejam aceitáveis como elementos de um diálogo coerente, notamos que as experiências deste sujeito no meio universitário pouco oportunizaram o diálogo entre a matemática de nível superior e seus saberes, deixando, por um lado, de contribuir de maneira significativa com sua problematização e reflexão acerca dos conteúdos, por outro, colaborando para consolidar a perspectiva na qual seus saberes docentes vinham sendo construídos a partir de sua prática.