Thesis (Ph. D.)--Michigan State University. Dept. of Teacher Education, 2008. / Title from PDF t.p. (viewed xxx). Includes bibliographical references (p. 268-273). Also issued in print.

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.

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 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.

The purpose of this study is developing valid and reliable scales in order to measure beliefs and perceived self-efficacy beliefs towards using origami in mathematics education and then, investigating beliefs and perceived self-efficacy beliefs of Turkish prospective elementary mathematics teachers in using origami in mathematics education. Furthermore, gender differences in prospective teachers&#039 / beliefs and perceived self-efficacy beliefs in using origami in mathematics education were investigated. Data for the current study was collected in the spring term of 2011-2012 academic year from 299 prospective elementary mathematics teachers. These teacher candidates are from three universities located in three different regions of Turkey and all the participants have elective origami course experience. Origami in Mathematics Education Belief Scale (OMEBS) and Origami in Mathematics Education Self-Efficacy Scale (OMESS) were used as data collection instruments. Exploratory and confirmatory factor analysis results showed that OMEBS and OMESS are valid and reliable instruments in order to measure beliefs and perceived self-efficacy beliefs in using origami in mathematics education. Descriptive analysis results indicated that, Turkish prospective elementary mathematics teachers strongly believe that origami is beneficial and suitable to be used in mathematics education. However, their perceived self-efficacy belief level is at little higher than moderate level. Lastly, independent sample t-test results revealed that female teacher candidates have significantly higher belief and perceived self-efficacy beliefs in using origami in mathematics education when compared with male teacher candidates.

The purpose of this study was to examine elementary teachers&rsquo / and elementary mathematics teachers&rsquo / perceptions of mathematically gifted students in terms of teachers&rsquo / gender, year of experience and area of teaching. The data were collected from 176 elementary teachers and 90 elementary mathematics teachers from 60 state elementary schools in the center of Trabzon, in the fall semester of 2011-2012 academic year. In order to determine teachers&rsquo / perceptions of mathematical giftedness, the instrument called as Teachers&rsquo / Judgments of Gifted Mathematics Student Characteristic (TJGMSC) was used. The results were evaluated in terms of three dimensions of TJGMSC: school smart mathematics student, mathematics perspective for the real world and creative problem solver. Besides, in order to analyze the data, one-way MANOVA was conducted. The results of the study illustrated that there were no significant differences among teachers&rsquo / TJGMSC scores, in terms of their gender and year of experience. However, a significant difference was found between elementary teachers and elementary mathematics teachers in terms of their TJGMSC scores for only the dimension of school smart mathematics student. To illustrate, elementary teachers&rsquo / scores regarding this dimension were higher than those of elementary mathematics teachers.

This study analyzes the kinds of beliefs pre-service elementary mathematics teachers hold about mathematical problem solving, and investigates whether, or not, gender and university attended have any significant effect on their problem solving beliefs. The sample of the present study consisted of 244 senior undergraduate students studying in Elementary Mathematics Teacher Education programs at 5 different universities located in Ankara, Bolu, and Samsun. Data were collected in spring semester of 2005-2006 academic years. Participants completed a survey composed of three parts as demographic information sheet, questionnaire items, and non-routine mathematics problems. The results of the study showed that in general the pre-service elementary mathematics teachers indicated positive beliefs about mathematical problem solving. However, they still had several traditional beliefs related to the importance of computational skills in mathematics education, and following predetermined sequence of steps while solving problems. Moreover, a number of pre-service teachers appeared to highly value problems that are directly related to the mathematics curriculum, and do not require spending too much time. Also, it was found that although the pre-service teachers theoretically appreciated the importance and role of the technology while solving problems, this belief was not apparent in their comments about non-routine problems. In addition to these, the present study indicated that female and male pre-service teachers did not differ in terms of their beliefs about mathematical problem solving. However, the pre-service teachers&rsquo / beliefs showed significant difference when the universities attended was concerned.

The current study seeks to investigate pre-service elementary mathematics teachers&rsquo / (PEMTs&rsquo / ) self-regulated learning (SRL) strategies within the context of their teaching practices in the field work. It was aimed to explore the SRL processes and strategies of four PEMTs while preparing mathematics lessons at their practice schools. In addition to PEMTs&rsquo / SRL strategies, the changes and adaptations through their teaching practices and reasons of those changes were also examined in the study. In total 22 pre-interviews and 22 post-interviews were made through the study. Observations were also performed for each teaching practice. Besides observations, PEMTs&rsquo / end of semester reflection papers in the context of Teaching Practice course were examined in the study. In addition to those multiple data sources, initial interviews representing detailed information about the participants were also analyzed. The overall data were analyzed by using the SRL framework combined and adapted from Zimmerman&rsquo / s and Pintrich&rsquo / s SRL models. The findings of the pre-interviews revealed that PEMTs began with a &lsquo / lesson planning process&rsquo / reflecting the forethought phase. This phase included searching resources, arranging and organizing the available sources, asking for help and feedback when needed, mental planning of the lesson, and setting goals for the teaching session. These strategies were considered as cognitive self-regulation strategies. In addition to cognitive SRL strategies, motivational factors such as self-efficacy, perception of task, and intrinsic interest were appeared in the study. Post-interviews reflecting the self-reflection phase revealed that PEMTs had a self-evaluation process covering various issues for their teaching sessions as a final step through the study. Finally, it was seen that contextual issues related to teaching practice played a substantial role in PEMTs&rsquo / SRL strategies.

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.