Current educational leaders call for students to build his or her own mathematical understanding from experiences, coupled with feedback from peers, teachers, and themselves and gain a conceptual understanding of mathematics. Researchers agree that inquiry in the elementary mathematics classroom can help increase conceptual understanding. This case study focused on how elementary teachers define inquiry-based mathematics and implement it in their classrooms. Interviews, observations and lesson analysis were used to investigate what identities, relationships and activities look like in an elementary classroom that uses inquiry. All of the participants felt "problem solving" and "working collaboratively" were essential for inquiry but each teacher defined them differently. Questioning was also an important feature of inquiry according to the teachers. Professional development seemed to have a strong impact on why these teachers use inquiry in their classrooms. As far as the relationships necessary to teach using inquiry, teachers did not indicate that administrators’ nor peers’ support were necessary to continue using this type of pedagogy in their classrooms. The participants believed that including inquiry in mathematics was a best practice and continued to incorporate inquiry because they felt it allowed their students to gain a deeper understanding of mathematics. The local field of each teacher influenced the planning they did before the lesson and the activities they included in their inquiry instruction. The written plans of each participant differed greatly. The requirements of the district had an effect on how much detail the participants included in their planning documents. Also, whether they were planning for their entire grade level or just themselves influenced how much detail was included. Another aspect of the mathematics classroom that was influenced by the local field was including a software program, which is expected to be a part of students’ daily mathematics instruction. The various ways inquiry is carried out and how the local field influences this is important for educators at all levels to understand. This study has implications for teachers, administrators and teacher educators. Inquiry means a variety of things to elementary teachers within this study. If mathematics educator leaders, teachers and administrators want to infuse more inquiry into the classroom, the many ways it is carried out needs to be understood.

This thesis describes a one-year study of 120 fifth grade students whose teachers participated in a program entitled Project SMILE (Science and Mathematics Integrated with Literary Experiences). The purpose of the study was to investigate the extent to which the classroom implementation of Project SMILE positively influenced the classroom environment and student attitudes toward reading, writing and mathematics. This was accomplished by, first, facilitating a series of five professional development workshops with the teachers and, subsequently, asking these teachers to use the strategies with their students. Because Project CRISS (CReating Independence through Student-owned Strategies), the foundation of SMILE, had already proven to be successful nationwide for secondary students, this study focused on elementary (K-5) school students and their teachers. My evaluation of this unique program, that integrates children's literature and mathematics, focused on student attitudes and the nature of the classroom learning environment. My research represents one of the relatively few studies that have employed learning environment dimensions with students in the elementary school mathematics classroom as criteria of effectiveness in the evaluation of educational innovations. The My Class Inventory (MCI) and an adaptation of the 1988 NAEP (National Assessment of Educational Progress) Attitude Survey were administered to a sample of 120 Grade 5 students as measures of students' perceptions of the classroom learning environment and their attitudes. Qualitative data were composed of student and teacher interviews, classroom observations and work samples. Methodologically, my study supports previous research that successfully combined qualitative and quantitative methods of data collection. / The learning environment and attitude scales exhibited satisfactory internal consistency reliability and discriminant validity; additionally, the actual form of most learning environment scales was capable of differentiating between the perceptions of students in different classrooms. The implementation of SMILE was found to have a positive impact on the students and classes of the teachers who participated in the inservice program. In particular, students' attitudes to mathematics and reading improved, and there was congruence between students' actual and preferred classroom environment on the scales of satisfaction and difficulty. Therefore, others can implement SMILE with confidence. As well, prior research was replicated in that students' satisfaction was greater in classrooms with a more positive learning environment, especially in terms of student cohesiveness.

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 purpose of this study was to investigate the implementation process of the present and newly introduced instructional techniques in new elementary school mathematics curriculum in sixth grade through the reports of teachers, which has been piloted in some specific schools. Moreover, it was aimed to find out the effects of several parameters on implementation, like city where school teachers are working is located, teachers&amp / #8217 / gender, teaching experience and number of students in the classroom. In addition, difficulties faced by teachers during the implementation process and teachers&amp / #8217 / general opinions about the new curriculum are examined. The sample consisted of 80 teachers working at elementary schools located in Ankara, Istanbul, Bolu and Kocaeli (Izmit). The Teacher Questionnaire was administered to participants in the 2005-2006 academic year. In order to investigate the differences in Teacher Questionnaire&amp / #8217 / s sub-scales&amp / #8217 / scores (Learning-Teaching Process, Material Usage, Evaluation Techniques) of the participants with respect to city, gender, teaching experience, academic level and number of students in classes, separate Multivariate Analysis of Variance were run. The results of this study indicated that teachers&amp / #8217 / implementation of the new methods and techniques highlighted in the curriculum can be interpreted as at high level. MANOVA tests indicated that teachers&amp / #8217 / implementation of the new methods and techniques were not affected by number of students in the classrooms, gender and teaching experience. According to the results of the study, teachers&amp / #8217 / usage of recommended educational equipments was found as at average level and MANOVA tests indicated that teachers&amp / #8217 / usage of recommended educational equipments was affected by teaching experience but not by gender and number of students in the classroom. The results of this study also showed that teachers&amp / #8217 / implementation of new evaluation techniques was at average level and MANOVA tests indicated that teachers&amp / #8217 / implementation of new evaluation techniques were not affected by gender, teaching experience and number of students in the classrooms.

The purpose of this study was to analyze and interpret specific aspects and characteristics of classroom discourse of an elementary mathematics classroom. To examine the classroom discourse, a fifth grade mathematics classroom was observed during sixteen weeks, and twenty lessons in total. The analysis was based on two main categories: (1) Student Learning and (2) Teacher Moves. Student Learning further divided into two sub-categories as content and learning. Additionally, Teacher Moves also divided into content knowledge and pedagogy and creating learning environment sub-categories. Results of this study showed that despite the many efforts in mathematics education in Turkey and the accepted importance of student-centered classrooms / still in some elementary classrooms teacher-centered instruction continue to be dominating. Moreover, the teacher questions generally seemed to have short answer and low-level characteristics that require students to recall mathematical rules and procedures rather than high-level questions that require students to recall mathematics rules and procedures rather than high-level questions that require students think deeper and draw inferences on mathematical content. Although, the results did not meet the assumptions of discursive classroom at all / based on the results, it could be said that in classroom practices, mathematics teachers try to make connections between mathematical content and other disciplines where they tried to give examples from real-world situations and also encourage students in that way / as pointed out in new mathematics curriculum.

Mathematics education could and should benefit from technology in order to improve teaching and learning, particularly in topics where visualizations and connections to other concepts are needed. Handheld technologies such as graphing calculators can provide students with visualization, confirmation and exploration of problems and concepts they are learning. Handheld graphing technologies have been taken place widely in elementary and secondary level mathematics courses and considered to be beneficial in various means in mathematics education. Mathematics teachers have a crucial role in the use of GCs in mathematics classrooms. Therefore, pre-service teachers&rsquo / use of GCs and their views on the use of the tool in mathematics learning are considered to be valuable. The purpose of this study was to investigate the difficulties pre-service elementary mathematics teachers face, and the benefits and constraints they emphasize while learning elementary school algebra through using the Casio Classpad after receiving an instruction with graphing calculators. The graphing calculator used in the present study is the Casio Classpad 330, which is an evolved handheld device combining features of graphing calculators, dynamic geometry environment, computer algebra systems and more. The following two research problems guided the study: What are the difficulties do pre-service elementary mathematics teachers face while using Classpad in learning elementary school algebra after receiving an instruction with graphing calculators? What benefits and constraints do pre-service elementary mathematics teachers emphasize while learning elementary school algebra through using Classpad after receiving an instruction with graphing calculators? With the aim of investigating the views of a group of pre-service elementary mathematics teachers, qualitative research strategies were used. The data was collected and analyzed by means of a case study design. Classroom observations, a questionnaire, and focus group interviews were the main data sources of the existing study. The study was carried out with 21 pre-service elementary mathematics teachers. In the classroom studies elementary level algebra was taught to the participants with the use of Classpad as a main tool by giving one tool to each of the participants. Classroom observations ended in five weeks &ndash / 20 courses &ndash / including one week of a training period. After the classroom observations, participants filled out a questionnaire including five open-ended questions about the classroom studies. Finally, data collection procedure was ended with three focus group interviews. The data was analyzed with qualitative means by transcribing and analyzing the observation records, answers of the questionnaire, and records of the three interviews. Results revealed that pre-service teachers&rsquo / view Classpad in three categories / as a personal tool, as an educational tool, and the relationship between CP and motivation. They viewed CP as a personal tool that they were eager to use the tool in every level of mathematics from elementary to mastering degrees. As an educational tool, they preferred to use the tool as a teacher by giving some cautions that teachers and students should be careful with. Lastly, they considered that the tool has a positive effect on motivation when used appropriately. Pre-service elementary mathematics teachers faced some difficulties in the beginning courses of the classroom studies which was their learning period of how to use CP and they overcome most of the difficulties at the end of the classroom studies. As the new elementary school level mathematics curriculum encourages the use of various technologies in teaching and learning of mathematics, the results of this study will have useful implications for mathematics teachers and curriculum developers.

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 process of generalization in mathematics was identified by mathematics education and educational psychology research, out of many mental actions or operations, as a cognitive function fundamentally required in the thinking process. Moreover, the current changes in education in the United States bring forward the dual goal of mathematics teaching and learning: students should have strong and rigorous mathematical content knowledge and students should be involved in practices that define the status of doing mathematical work. This dual role is totally dependent on the process of generalization. This study uses theories and research findings from the field of algebraic thinking, teaching, and learning to understand how the third grade teacher’s edition textbooks of three mathematics curricula portray the process of generalization. I started my study with the development of a theoretical coding system obtained by combining Kaput’s theory about algebra (Kaput, 2008), Krutetskii’s two way of generalization (Krutetskii, 1976), and the five mathematical representations identified by Lesh, Post, and Behr (1987). Then, I used the coding system to identify tasks that have the potential to involve students in the process of generalization. The findings from my study provide evidence that following a well-structured theory, such as Kaput’s theory about algebra, allows us to identify tasks that support algebraic thinking and to create new ones with higher potential to involve children in the process of generalization. Such tasks may support the development of algebraic thinking as a continuous process that should start from early grades of elementary school.