The study investigated the impact of Thai preservice middle school mathematics teachers' knowledge of subject matter and of students' conceptions of division of rational numbers with respect to their classroom practices in a teaching environment controlled by a required national curriculum. Four preservice teachers were selected with different knowledge of subject matter and of students' conceptions of division of rational numbers: high knowledge of subject matter and high knowledge of students' conceptions, high knowledge of subject matter and low knowledge of students' conceptions, low knowledge of subject matter and high knowledge of students' conceptions, and low knowledge of subject matter and low knowledge of students' conceptions. Each preservice teacher was observed three weeks, each class day during the teaching of units on division of decimals, representing fractions as decimals, and division of fractions. Formal interviews were conducted with each of the four preservice teachers prior to and after teaching each unit. Informal interviews were conducted prior to and after teaching each lesson. Materials used in the normal teaching of the class were collected. Interviews with the preservice teachers' mentors were conducted before and after each unit. The mentors were interviewed daily before or after the instruction. Interviews with supervisors were conducted each time they supervised the preservice teachers. Results showed that all preservice teachers planned and taught division of rational numbers procedurally following an algorithmically-based national curriculum. The preservice teachers with higher subject matter knowledge used multiple examples. They could make up examples when the students asked questions. In contrast, the lower subject matter knowledge preservice teachers rarely created new examples while they were teaching. The high knowledge of students' conceptions preservice teachers used their knowledge of students' conceptions throughout the lessons more often than the low knowledge of students' conceptions preservice teachers. After teaching the lessons, they all gained knowledge of subject matter and of students' conceptions of division of rational numbers. The depth of knowledge of subject matter and of students' conceptions of division of rational numbers is as essential for preservice middle school mathematics teachers' teaching in a nonvoluntary curriculum as it is in a voluntary curriculum. / Graduation date: 2003

This study described how and why a Korean elementary teacher taught mathematics as he did. Specifically, the study sought to describe his beliefs about the teaching and learning of mathematics and relate them to patterns of classroom interaction and norms. An ethnographic inquiry guided the study of one third grade 10-year veteran teacher over three months in Korea. Through participant observation, the researcher observed Teacher Lee's teaching paying special attention to the mathematics lessons for one class of 45 students daily Monday through Saturday. Formal and informal interviews were used to collect data on the teacher and 17 of his students as well as other teachers (such as four teachers in the third grade), two principals, two mothers, and three beginning teachers. In addition to participant observation and interviews, a variety of documents were also collected, including newspapers, articles from journals, test items used in the teacher's classroom, daily worksheets, curriculum guide book, mathematics textbook, the school's newspaper. All videotapes and audiotapes were transcribed for inductive analysis. The analysis generated six major themes of the teacher's beliefs about the teaching and learning of mathematics and how those beliefs impacted the interactions and norms: (a) behave orderly, think freely; (b) teaching mathematics with understanding; (c) manipulative activities and games; (d) discourse-oriented teaching practices; (e) mathematical tasks; and (f) professional development. The teacher's beliefs about the teaching and learning of mathematics were closely related to the interaction patterns and classroom norms. This close relationship implies that identifying interaction patterns and classroom norms may shed light on understanding teachers' beliefs and teaching practices. The teacher's study group activity was a major professional development factor in promoting the consistent relationship. Implications and recommendations included (a) the need for more study of classroom norms and interactions as practical knowledge of teaching mathematics, (b) the need for investigating the effect of a study group to support teacher change, (c) the importance of the relationship between pedagogical content knowledge and teachers' beliefs, and (d) the need for more study of classroom management for teaching mathematics using understanding and discourse as an instructional strategy. / Graduation date: 2000

The purpose of this study was to develop a valid and reliable, instrument for determining the mathematics subject matter knowledge of Thai preservice elementary teachers at eight (8) teachers' colleges in eight (8) provinces in northern Thailand. The focus of the content of interest was the operation of division of rational numbers in the context of an appropriate taxonomy of the cognitive domain categories suggested by Wilson (1971). The Delphi technique, item analysis, and "known group" techniques were utilized in the instrument development phases of the study. Hypotheses were tested to determine whether significant differences existed between colleges and between teachers with different backgrounds. The dependent variable was the mean test score for preservice teachers at eight Thai teachers' colleges. The study included the testing of significance for colleges, background, and whether there was significant interaction between colleges and teachers' backgrounds (liberal arts and science). The pilot instrument consisted of 52 items representing four cognitive levels (computation, comprehension, application, and analysis). Based on an analysis of pilot test data, 10 items were eliminated. The final draft instrument consisted of 42 items and was administered to 272 preservice elementary teachers. When field test data were analyzed and compared to "known group" data, 10 items were found to be outside of the acceptability range for difficulty. Item difficulty was used for selecting items for inclusion in the final instrument to measure the operation of division of rational numbers with Thai college preservice elementary teachers. This step in the research served to reduce the number of test items to 32, which constituted the content for the final instrument. The internal consistency reliability was .81 for the 42-item instrument. Content and construct validity were verified by various procedures. / Graduation date: 1994

The main purpose of this study was to investigate elementary teachers&rsquo / and elementary mathematics teachers&rsquo / attitudes toward and beliefs about mathematical problem solving in terms of gender and grade level being taught. Moreover, the relationship between elementary teachers&rsquo / and elementary mathematics teachers&rsquo / attitudes and beliefs was evaluated in this study. The data were collected from 141 in-service elementary teachers who are teaching 4th and 5th graders and elementary mathematics teachers who are teaching 6th, 7th and 8th graders in Nevsehir. The measuring instruments used to collect data were Whitaker Mathematical Problem Solving Attitude Scale (WMPSAS) and, Belief on Mathematical Problem Solving Scale (BMPSS). The results showed that, in general, in-service elementary teachers and elementary mathematics teachers indicated positive attitudes and rich beliefs toward mathematical problem solving. In addition, there was a significant difference between grade level being taught regarding attitudes and beliefs. The elementary mathematics teachers had significantly higher attitudes and beliefs scores than the elementary teachers. The results also revealed that there was not significant main effect for gender on both attitudes and beliefs. In other words, regardless of grade level being taught, female elementary teachers and female elementary mathematics teachers had higher attitude and belief scores than male elementary teachers and male elementary mathematics teachers. Finally, Pearson product-moment correlation analysis indicated a significantly positive correlation between attitude and belief scores.

The purpose of this study was to determine performance of prospective elementary mathematics teachers on answering the items handling the probabilistic misconceptions. The other aim was to investigate the underlying reasons behind these misconceptions of prospective elementary mathematics teachers. To address these aims, qualitative approach was performed. The sample of this study was obtained through convenience sampling. Data were gathered during 2011-2012 spring semester by administering Probability Misconception Questionnaire to 12 senior prospective elementary mathematics teachers studying at faculty of education in Sakarya and through semi-structured interviews conducted with those prospective teachers. None of the participants provided correct answers to items addressing misconceptions regarding time axis fallacy and compound event. Furthermore, less than half of the participants provide the correct answer to items handling misconceptions regarding conditional probability, effect of sample size, conjunction fallacy and representativeness. Also, in this study, reasons behind those misconceptions were determined. Particularly, focusing on the first event was found to be a reason underlying time axis fallacy misconception. Also, another reason behind this misconception was misinterpretation of the problem, which also resulted in misconception regarding conditional probability. Furthermore, focusing on the ratio was found to be a reason underlying misconception regarding effect of sample size. Several participants solely focused on the narrative, which lead to misconception regarding conjunction fallacy. Moreover, seeking representativeness in samples was found to be a reason underlying misconception regarding representativeness. Lastly, in this study, it was found that ignoring order of outcomes resulted in misconception regarding compound event.

The purpose of this study was to investigate the views of elementary school teachers about their implementation of assessment techniques recommended in the new mathematics curriculum. The study was conducted with 306 elementary school teachers from 29 public schools in Kirikkale, Malatya and Ankara in the 2006-2007 academic year. &lsquo / Opinions about Assessment Questionnaire&rsquo / was used as the instrument for assessing the opinions of the teachers about assessment techniques offered in new mathematics curriculum. The results showed that, teachers did not have negative views towards the implementation of the new assessment techniques in mathematics lessons. However, they needed support from curriculum experts about more suitable implementation of the assessment process. To assess the effects of teaching experience, class size and grade level they teach on the views of the teachers about their implementation of assessment techniques recommended in new mathematics curriculum, the Univariate Analysis of Variance was used. The results revealed that the opinions of the teachers about their implementation of assessment techniques offered in new mathematics curriculum did not show any significant difference according to the experience of the teachers, class size and grade level teachers teach.

This study analyzes the preservice elementary mathematics teachers&rsquo / self efficacy beliefs and outcome expectancies about using manipulatives and investigates whether, or not, university and gender differences have any significant effect on their self efficacy and outcome expectancies. In mathematics education, students&rsquo / conceptions about abstract mathematical ideas and being able to convert them into concrete ideas are very important. For this reason, it is very beneficial to use manipulative materials in the mathematics lessons. However, most of the preservice mathematics teachers in Turkey lack knowledge about using manipulatives. The sample of present study consisted of 77 senior undergraduate students studying in Elementary Mathematics Teacher Education programs at 2 different universities located in Ankara and Izmir. Data were collected in spring term of 2006-2007 academic years. The survey items were adopted from previously developed teacher efficacy instrument, which partly ensures the items to be parallel with the existing theory about the construct. The survey consisted of three parts / demographic information, knowledge about the manipulatives, and &lsquo / The Instrument of Preservice Mathematics Teachers&rsquo / Efficacy Beliefs about Using Manipulatives&rsquo / (EBMU). The present study demonstrated that the gender differences did not effect preservice elementary mathematics teachers&rsquo / personal manipulative use teaching efficacy whereas the university differences had a significant effect on their personal manipulative use teaching efficacy. In addition, the gender and university attended produced statistically significant main effect on preservice elementary mathematics teachers&rsquo / outcome expectancies.

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 aim of this study was to investigate the roles of year in teacher education program and gender on prospective elementary mathematics teachers&rsquo / knowledge of history of mathematics and their attitudes and beliefs towards the use of history of mathematics in the teaching and learning of mathematics. Moreover, the relationship between prospective teachers&rsquo / knowledge of history of mathematics and their attitudes and beliefs about the history of mathematics usage was examined. The data of the study were obtained from 1593 prospective teachers who were enrolled in first, second, third, and fourth years of Elementary Mathematics Education undergraduate program of nine universities located in seven geographical regions of Turkey through clustered random sampling. The scales used in the data collection were Knowledge of History of Mathematics (KHM) Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education (ABHME) Questionnaire. The two-way ANOVA results clarified that prospective teachers&rsquo / knowledge of history of mathematics improved as the years enrolled in the program increased. Results also revealed that males had significantly higher mean scores on KHM Test than females in the first two years of the program. In the third and fourth years, this situation reversed such that females had higher KHM mean scores, but this difference was not statistically significant. Results also showed that prospective teachers&rsquo / ABHME mean scores increased as years of enrollment in the program increased. More clearly, senior prospective teachers&rsquo / relevant mean scores were significantly higher than that of freshmen and sophomores, and juniors&rsquo / attitudes and beliefs were significantly higher than that of freshmen. In addition, females&rsquo / ABHME mean scores were significantly higher than that of males for all years. Lastly, a positive correlation between prospective elementary mathematics teachers&rsquo / KHM mean scores and ABHME mean scores was found through Pearson product-moment correlation analysis.

The purpose of this study was to investigate the prospective elementary mathematics teachers&rsquo / use of strategies and their achievement levels in solving mathematical problems with respect to year level. The data were collected from 250 prospective elementary mathematics teachers enrolled in an elementary mathematics education program from a state university in Central Anatolian Region. Problem Solving Test (PST) was used to accomplish the purpose of the study. The data collection tool adapted by the researcher included nine open ended problems. In this study, item based in-depth analysis was employed to determine a variety of problem solving strategies used by prospective teachers.The frequencies and percentages of categories were gathered for each item and for each year level. The results of this study revealed that prospective elementary mathematics teachers&rsquo / problem solving achievement was moderately high. Prospective elementary mathematics teachers in each year level were able to use various problem solving strategies to a certain extent. More specifically, the results indicated that &lsquo / making a drawing&rsquo / and &lsquo / intelligent guessing and testing&rsquo / strategies were among the most prominent strategies frequently used by prospective teachers. Setting up an equation and using a formula was other strategies used by prospective teachers. On the other hand, finding a pattern strategy was the least frequent strategy used by prospective teachers.