The purpose of this study was to examine pre-service mathematics teachers&amp / #8217 / subject matter knowledge, pedagogical content knowledge, and the relationships between the two on multiplication and division of fractions. For this purpose, pre-service teachers&amp / #8217 / understanding of key facts, concepts, principles, and proofs, their knowledge on common (mis)conceptions and difficulties held by the elementary students, their strategies of teaching these concepts, and representations they use to reason their understanding on multiplication and division of fractions were examined. Qualitative case study was performed where / data was collected from the pre-service teachers at the end of the spring semester of 2004-2005. Pre-service teachers were senior students enrolled in a teacher education program at a public university. Results revealed that pre-service teachers could easily symbolize and solve the basic questions on multiplication and division of fractions. However, in terms of pre-service teachers&amp / #8217 / interpretation and reasoning of key facts and principles on multiplication and division of fractions, their subject matter knowledge could not be regarded as conceptually deep. Furthermore, although pre-service teachers have strong belief that they should teach multiplication and division of fractions conceptually, where the logical background of the operations is explained, they do not have sufficient knowledge to represent and explain these topics and relationships conceptually.

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.