There are many researchers that emphasize the importance of how teachers’ knowledge will affect students’ learning. However, not much research is focused on an international comparison between preservice mathematics teachers’ procedural knowledge and conceptual knowledge. There were 91 preservice mathematics teachers involved in this study. A test on the operations on fractions, decimals, percentages, and integers knowledge showed a) the significant differences between the United States and Chinese preservice teachers’ (PTS) procedural knowledge, b) the significant differences between the United States and Chinese PTS’ conceptual knowledge, and c) the relationships between the United States and Chinese PTS’ procedural knowledge and conceptual knowledge. By comparing the results, the researcher determined the strengths and weaknesses of preservice mathematics teachers in the two countries. The researcher will provide PTS some information based on the results of the knowledge test.

The aim of this study was to investigate to what extent the preservice teachers perceived that they were ready for the teaching profession and the differences in preservice teachers&rsquo / readiness based on the year in the teacher education program, gender, high school type (teacher education high school or other), and existence of a teacher in the immediate family. The study was conducted at the Elementary Mathematics Education programs of universities in Ankara, Burdur, Bolu, Gaziantep, Izmir, Samsun and Sakarya in the spring semester of 2009-2010 academic year. The data were collected from 728 third and 4th year preservice mathematics teachers. Readiness of preservice mathematics teachers was assessed with a readiness scale which was developed by the researcher in the fall semester of 2009-2010 academic year. Data were analyzed with descriptive and inferential statistics. The results indicated that preservice mathematics teachers did not perceive their readiness at a high level. There was a significant difference in readiness scores for 3rd year preservice mathematics teachers and 4th year preservice mathematics teachers. It was found that the readiness of 4th year preservice mathematics teachers were significantly higher than the readiness of 3rd year preservice mathematics teachers. On the other hand, the results showed that there was no significant difference in readiness scores for female preservice mathematics teachers and male preservice mathematics teachers. Similarly, there was no significant difference in readiness scores for preservice mathematics teachers graduated from teacher education high school and preservice mathematics teachers graduated from other high school types, and between existence of a teacher in the immediate family of preservice mathematics teachers and nonexistence of a teacher in the immediate family of preservice mathematics teachers. Findings of the study indicated the need for improving the practice courses in order to increase preservice teachers&rsquo / readiness for the profession.

The purpose of this study was to examine the factors affecting preservice mathematics teachers&rsquo / decisions on probability teaching. The sample of the study was 248 preservice mathematics teachers from Gazi University, Hacettepe University, and Middle East Technical University. According to the gender the number of females and males were 170 and 78 respectively. To obtain necessary data for the study, the following measuring instruments were used: (1) Probability Achievement Test (PAT) / (2) Probability Misconception Test (PMT) / (3) Attitude toward Probability Teaching Scale (APTS) / (4) Attitude toward Probability Scale (APS). Only the third measuring instrument was developed and its reliability and validity was tested by the researcher. An interview was done with 12 preservice mathematics teachers from Gazi University, Hacettepe University, and Middle East Technical University. The data of the study were analyzed by using SPSS and with qualitative techniques. The results of the study demonstrated that there are some factors affecting preservice mathematics teachers&rsquo / decisions on probability teaching. These factors were their attitude toward probability, probability achievement and misconceptions. Subjects thought that gender would have no affect on their decision on probability teaching.

The tasks with which students engage in their mathematics courses determine, for a large part, what students learn. Therefore, it is essential that teachers are able to design tasks that are worthwhile for developing mathematical understanding. Since practicing teachers seldom incorporate worthwhile mathematical tasks in their lessons, we would expect that they did not become proficient at designing worthwhile tasks while in their teacher education programs. This thesis describes a study that investigated what preservice secondary teachers attend to as they attempt to design worthwhile mathematical tasks. Three participants were selected from a course at a large private university where preservice teachers are taught and practice the skill of task design. This "Task Design" course was observed, and the three participants were interviewed to determine what they attend to while designing tasks. There were seven main characteristics that the main participants in the study attended to the most often and thought were the most important: sound and significant mathematics, reasoning, appropriateness, clarity, communication, engagement, and openness. How the participants attended to these characteristics is described. Some implications for teacher education, such as requiring preservice teachers to explain how their tasks embody certain characteristics, are given based on the results.

The aim of this study is to investigate perceptions of preservice mathematics teachers&rsquo / technological pedagogical content knowledge (TPACK) regarding geometry. In addition, the purpose is to examine the relationships among the components of TPACK. Moreover, possible gender and year of enrollment differences related to preservice mathematics teachers&rsquo / technological pedagogical content knowledge dimensions are examined. This research study has been conducted with 780 preservice mathematics teachers who are enrolled in elementary mathematics education department of Education Faculties of seven public universities located in Central Anatolia. Perceived TPACK regarding geometry instrument has been developed to collect data. In order to determine the levels of preservice mathematics teachers&rsquo / perceptions related to TPACK in geometry, descriptive information have been used. The results indicate that preservice mathematics teachers&rsquo / perceptions of TPACK related to geometry is higher than moderate. Furthermore, correlational analysis was conducted to identify the relationship among dimensions of TPACK. Positive significant correlations among the components of the TPACK framework were found in correlational analysis. Besides, two-way MANOVA has been conducted to investigate a possible relationship between demographic information of preservice elementary mathematics teachers and their perceptions of TPACK. According to the MANOVA results, there are statistically significant differences between male and female preservice mathematics teachers in favor of male participants in three components of TPACK, namely technological knowledge, technological pedagogical knowledge and technological pedagogical content knowledge in favour of males.

The purpose of this study is to construct a valid and reliable mathematics related beliefs scale for determining preservice elementary mathematics teachers&rsquo / mathematics related beliefs in Turkey and investigating the impact of the gender and year level on the preservice mathematics teachers&rsquo / mathematics related beliefs. For the first purpose, the &ldquo / Mathematics Related Belief Scale (MRBS)&rdquo / was developed based on the combination of the belief frameworks in the literature. Data were collected from ten different universities from Ankara, Balikesir, Burdur, Bolu, Gaziantep, Izmir, Van, and Samsun in the spring semester of 2009-2010 academic year. A total of 584 third and fourth year preservice mathematics teachers participated in this study. Data were analyzed by descriptive and inferential statistics. The results showed that MRBS was a valid and reliable scale which measured Turkish preservice teachers&rsquo / mathematics related beliefs. MRBS had two components &ldquo / constructivist beliefs&rdquo / and &ldquo / traditional beliefs&rdquo / of mathematics and teaching mathematics. There was a significant effect of gender on preservice teachers&rsquo / mathematics related beliefs. No significant difference in preservice teachers&rsquo / mathematics related beliefs was detected in terms of year level in the teacher education program. The MRBS could be used for investigating preservice teachers&rsquo / mathematics related beliefs in order to determine effective teacher education program experiences.

Researchers have found that teachers' decisions affect students' opportunity to learn. Prior researchers have investigated teachers' decisions while planning, implementing, or reflecting on lessons, but few researchers have studied teachers' decisions and their reasoning throughout the teaching process. It is important to study teachers' reasoning for why they make the decisions they do throughout the teaching process. Furthermore, because inservice and preservice teachers differ in experience and available resources that they draw on while making decisions, it is helpful to consider the resources PSTs' draw on while reasoning. Curricular reasoning is a framework that describes teachers' thinking processes when making decisions during the teaching process. This study investigated secondary preservice teachers' decisions and curricular reasoning throughout the teaching process. Data were collected from two groups of secondary preservice teachers in a mathematics methods course focused on student thinking and mathematics. Results revealed that the preservice teachers used all seven curricular reasoning strands, especially drawing on mathematical meanings, mapping learning trajectories, and considering learners' perspectives. Specifically, this study demonstrates ways in which preservice teachers reason about their decisions and the intertwined nature of their curricular reasoning. The results from this study also imply that it may be helpful to consider the resources PSTs have access to, including their instructor, and that the order of their lesson planning may allow support for the mathematical learning trajectories within individual lessons. This study also provides validation for the curricular reasoning framework described by Dingman, Teuscher, Olson, and Kasmer (in press), provides subcategories of curricular reasoning strands, and has implications for teacher education.

<p>  </p> <p>Radian angle measure is central to learning trigonometry, with researchers providing evidence that a coherent understanding of radian contributes to a coherent understanding of trigonometric and inverse trigonometric functions. However, there are few opportunities for students to engage with curricular situations that involve radian angle measure. The purpose of this dissertation is to explore and provide insights into preservice mathematics teachers’ (PMTs’) conceptions of radian angle measure using three curricular situations. The first chapter reviews the relevant literature, which reported that PMTs’ conceptions of radian angle measure involve angles measured in terms of π, in relation to degrees, and in relation to the unit circle. In chapter two, I explored PMTs’ conceptions of radian angle measure using textbook representations. Seven PMTs participated in a think-aloud semi-structured interviews, where they defined radian angle measure from six textbook diagrams of radian, including a diagram of the unit circle. In chapter three, building on literature that reported that PMTs’ conceptions of radian angle measure involve relating radian to degrees, I explored how PMTs conceptualize this relationship. Five PMTs participated in semi-structured interviews, where they described radian angle measure given the angle measure in degrees. In chapter four, I explored the PMTs’ conceptions of radian angle measure given a novel context. Four PMTs participated in semi-structured virtual interviews, where they engaged with a digital activity that involves radian angle measure in the context of light reflection. Some of the dissertation’s findings align with previous research, where PMTs’ conceptualized radian angle measure in relation to the unit circle. However, this dissertation provides empirical evidence of why the PMTs refer to the unit circle. The PMTs acknowledged knowing the unit circle from memorization, but also explained that the purpose for using the unit circle is efficiency. At the same time, the PMTs acknowledged limitations in the unit circle and in their conceptions of it. Overall findings from the dissertation demonstrate the complexity of PMTs’ conceptions of radian angle measure. The PMTs’ conceptions were reported as concept definitions, ways of thinking, and spatial ways of thinking. The PMTs demonstrated flexibility with reasoning about radian angle measure using foundational conceptions in learning higher mathematics topics (e.g., proportional reasoning concepts, spatial ways of thinking). By positioning the PMTs as knowers and thinkers with valuable insights to provide, I was able to uncover and report a collection of conceptions that were demonstrated by PMTs when a curricular situation involved radian angle measure. The findings from this dissertation extend existing research that explored conceptions of angle measure and radian angle measure by reporting PMTs’ conceptions of radian angle measure given three different curricular situations. While there is still much that needs to be investigated about complexities in PMTs’ conceptions of radian angle measure, this dissertation represents one step toward providing insights about those complexities. </p>