The purpose of this study is to interpret observations of three 6th grade elementary mathematics classrooms throughout a unit in detail. Specifically, this study examined the patterns and traditions related with teaching practices in the context of teaching a unit, teaching a topic, and single lessons, and described frequently observed teaching features in mathematics lessons. This study presented a detailed description and analysis of teaching practices of three experienced mathematics teacher from three public elementary schools. The participated teachers were directly observed through teaching a different mathematics unit. The teaching and learning practices in each classroom was described and analyzed both separately and together. The results of this study indicated that teaching a mathematics unit could be described as the combination of separately taught topics where the sequences of topics are strictly determined by elementary mathematics curriculum. There was no specific practice aiming to construct relation between unit&rsquo / s concepts and other school subjects, other mathematics concepts, and among these concepts. Teaching practices throughout a topic showed explicit similarities so that a pattern for teaching a topic can be described as demonstrating the new content, practicing the new content, and assigning and doing homework. It was not possible to draw a pattern for teaching practices in elementary mathematics lessons by using single lesson periods as a unit of analysis. &lsquo / Practicing&rsquo / was the most occurred activity in elementary mathematics lessons. Based on the findings some suggestions for future research studies were proposed, and some implications for teachers, teacher educators and policy makers were delivered.

ABSTRACT EFFECTS OF GRAPHING CALCULATORS ON EIGHTH GRADE STUDENTS&amp / #8217 / ACHIEVEMENT IN GRAPHS OF LINEAR EQUATIONS AND CONCEPT OF SLOPE &Ouml / n&uuml / r, Yurdag&uuml / l M.S., Department of Elementary Science and Mathematics Education Supervisor: Assist. Prof. Dr. Ayhan K&uuml / rSat ERBAS May 2008, 76 pages The purpose of this study was to investigate the effects of graphing calculators on eight grade students&amp / #8217 / achievement in graphing linear equations and concept of slope. Pretest-posttest experimental-control group design was utilized in the study. While the students in experimental group (EG) received instruction about graphs of linear equations and concept of slope with graphing calculators, the students in control group (CG) was taught the same topics without using graphing calculators. There were 27 students (13 girls and 14 boys) in each group. Students in both EG and CG was administered an achievement test (i.e., MAT) consisting of questions related to graphing linear equations and slope concept before and after the instruction. Additionally, the teacher and six students from the EG were interviewed. The data obtained from students&amp / #8217 / post test scores of MAT were analyzed by Analysis of Variance (ANOVA). A statistically significant difference was found between the achievements of students in experimental and control groups. However, gender had no statistically significant effect on students&amp / #8217 / post test scores of MAT. Additionally, students&amp / #8217 / pre-test scores of MAT and their mathematics grades of the second semester of the seventh grade (MGS) were analysed by independent samples t-test. The results showed no statistically significant difference. On the other hand, the analysis of interview data revealed that graphing calculators affected students&amp / #8217 / attitudes towards mathematics in a positive way. Students had no considerable difficulty while using graphing calculators and they found studying with graphing calculators enjoyable. In summary, the results of the study showed that when graphing calculators used at elementary school level, they had positive effects on students&amp / #8217 / achievement and in some respects to their attitude. Consequently, integration of graphing calculators to elementary mathematics curriculum may be beneficial for students and teachers.

The purpose of this study was to investigate primary school and mathematics teachers&rsquo / efficacy beliefs and perceptions in the context of the new primary mathematics curriculum and identify differences, if any, in teachers&rsquo / efficacy beliefs and perceptions based on their area of certification, gender, experience and number of students in classroom. The sample consisted of 805 teachers, 696 of whom were primary and 105 of whom were mathematics teachers working in elementary schools located in Mersin, Eskisehir, Bolu, Ankara and Istanbul. The questionnaire administered to participants was adapted by the researcher throughout the study. Results of exploratory factor analysis suggested six dimensions: Utility and Impact of the Curriculum, Impact of the Curriculum regarding Efficacy Beliefs, Efficacy Beliefs regarding the New Curriculum, Utilization of Curriculum, Utilization of Special Techniques, and Teachers&rsquo / Sense of Efficacy. The results of the MANOVA analysis indicated that teachers&rsquo / area of certification and experience had a significant role on the collective dependent variables, while number of students and gender did not. Analysis further revealed that primary teachers had significantly stronger efficacy beliefs about the new curriculum than mathematics teachers. Moreover, teachers with 11-15 and 21 and more years of experience were significantly found to perceive a higher utilization of special techniques than teachers with 10 years or less experience. In a similar sense, teachers with 16-20 years of experience were found to have a significant higher perceived utilization of special techniques than teachers with 5 years or less experience.

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 aim of this study was to investigate the changes on what the prospective elementary mathematics teachers noticed as they watched video cases and discussed online. More specially, I wanted to answer the question &ldquo / To what extent the elementary prospective mathematics teachers&rsquo / noticing with respect to reform-minded teaching changes during their video case-based teacher education, in terms of teacher and student roles?&rdquo / With this question in mind, I asked senior prospective mathematics teachers at METU to watch six video cases depicting real elementary mathematics classrooms, and then discuss these cases in an online forum. The research was conducted during the 2008-2009 fall semester. Participants were asked to write reflection papers after watching a video each week. The online discussions took place in Metu Online-Net ClassR online forum, and each discussion was about a long week. The research study was qualitative in nature. Specifically, it was a case study research. Prospective teachers&rsquo / reflection papers on the videos, the online discussions, and interviews with the selected 15 focus participants at the beginning, in the middle and at the end of the study were the data sources. The data were analyzed through the qualitative data analysis techniques. The findings suggested that prospective teachers&rsquo / noticing skills with respect to the teacher and student roles in reform-minded teaching and learning were developed throughout the online video-case based discussions.

The purpose of this study was to trace the reflections of critical issues, such as neo-liberalism, cultural differences based on social class, gender stereotyping, and nationalism in the elementary mathematics education in Turkey. Critical discourse analysis was conducted to examine these possible reflections. By researching mathematics education from a critical perspective, this study aimed to contribute constructing a starting point for socially responsible mathematics education. There were four main data sources in the study: elementary mathematics curriculum, 6th, 7th, and 8th grade elementary mathematics textbooks, workbooks and teacher&rsquo / s guide books, 7th grade mathematics classroom observations, and pre- and post-interviews with participant teacher. The discourse analysis of mathematics education contexts implied that elementary mathematics discourse: (i) oriented students to use their mathematical abilities and skills for the benefit of private corporations instead of public welfare / (ii) replaced the &lsquo / real life&rsquo / in mathematics problems with the life of middle and upper middle classes / (iii) included sexist expressions / and (iv) fostered nationalism via ignoring ethnic and non-Muslim groups living in Turkey. It appeared that teachers might not be aware of such discourse. Findings have addressed that policy makers and textbook writers should consider these critical issues in order to reach all students and teachers&rsquo / awareness should be increased. Future research should clarify these issues in a broad sense including pre-service teachers, teachers, students, and mathematics instruction in schools.

To date, research of computer science education in the elementary classroom has focused on technology-dependent tools like Alice, Scratch, LOGO and LEGO Mind-storms. While these tools seem to have the potential to support learning in accordance with constructionist theory, they have not lived up to expectations. Results of this research, in particular the impact of programming instruction on student achieve- ment, have been weak or mixed. Possible reasons for this are many, including the corresponding threshold and friction associated with technology-dependent learning. Inspired by a trend of non-technology-dependent instruction of computer science topics, as demonstrated by the success of Computer Science Unplugged by Tim Bell, Mike Fellows and Ian Witten, we have chosen instead to investigate the impact of unplugged computer science instruction on Grade Six students. The shift away from programming instruction may also serve to help dispel the myth that computer science is programming. Computer science is a broad and diverse field which impacts the lives of all people in a multitude of ways. It is not yet clear what the best approach is for integrating computer science education into the elementary classroom. One suggestion is to teach computer science topics such that they support other areas of elementary education. For example, students are encouraged to adopt many different problem solving strategies, as supported by the British Columbia Ministry of Education’s K-7 Mathematics Integrated Resource Package (IRP). These strategies include “draw a picture”. Graph theory has the potential to support problem solving as a means of representing complex connections and relationships in a clear and concise manner. Alternatively, a standalone computer science curriculum may be appropriate, in the spirit of the Computer Science Teacher’s Association (CSTA) “A Model Curriculum for K-12 Computer Science”. Whatever the approach, an important, and fundamental, step in making curricular change is to support the need for change with sound educational research. Only then can we hope to earn the support of the stakeholders, such as school districts and teacher education programs, who can make this change a reality. In this pilot study, we investigate the impact of graph theory lessons in two Grade Six math classes. Because of the small class sizes and somewhat reduced participation rates, the results of this study need to be verified with further, larger scale studies. However, early indications are that Grade Six students are capable of learning graph theory, and applying it when working on mathematical word problems. In some cases, there appears to be an association between students’ ability to apply graph theory as one of many problem solving strategies, and the correctness of their solutions to problems.

Too often teachers see mathematics as a culturally neutral subject. Teacher educators need to be aware of their own practice and how it impacts the facilitation of preservice teacher learning, in particular in relation to elementary mathematics and culturally responsive teaching. This qualitative self-study focused on understanding a teacher educator’s enactment of an espoused platform in an integrated instructional third space of an elementary field experience and an elementary mathematics methods course in relation to culturally responsive teaching and mathematics. The research questions guiding this self-study were: (1) In the context of the selfstudy, to what extent do I enact my espoused teacher education platform in the integrated instructional third space that exists at the intersection of an undergraduate elementary field experience and an undergraduate elementary mathematics methods course in relation to culturally responsive teaching and mathematics?; with one sub question (a) What facilitators and challenges do I face as I try to navigate living out my espoused platform within this third space?; (2) In the context of the self-study, how do I transform as a teacher educator while engaging in the process of framing and reframing my platform within this integrated instructional third space? The study took place in the unique context of an integrated instructional third space with the same person who served as the instructor of the mathematics methods course and field supervisor. Data collection included the researcher’s teacher education platform, field notes from observations, and field notes from pre and post conferences with preservice teachers, documents and artifacts from teaching, and a researcher’s journal. The findings pointed to a set of routines of practice for teacher educators to engage in while facilitating preservice teacher learning about culturally responsive teaching and mathematics knowledge for teaching. The routines of practice included: probing questions, utilizing personal connections, offering suggestions, modeling, and targeted activities. The findings also included facilitators and barriers to the process of working with preservice teachers in the integrated instructional third space in relation to their learning of culturally responsive teaching and mathematics; they include: relationships with preservice teachers, relationships with collaborating teachers, and critical conversations. This study has implications for teacher education program design, mathematics course development, field experience course development, and teacher educator professional development.

The purpose of this project is to provide an instructional computer program that will be an alternative way to teach and reinforce basic mathematics skills for any student that is having difficulty in any given area and for students that are falling behind in the regular math class.

The primary purpose of this study was to evaluate the effect of basic multiplication mastery (0-12) and self-efficacy outcomes for elementary age students attempting to master multiplication facts in a Computer-Assisted Instructional (CAI) environment. Timez Attack (TA), a modern Internet based 3-D multiplication video game, was the computer program used in this study. Four third- and four fourth-grade classes of students at a public charter school received either 12 20-minute Teacher-Led Instructional (TLI), or TA multiplication practice sessions. Pre- and post Math Attitude Survey (MAS), timed multiplication tests, observations, and informal interviews were used to assess and compare TA and TLI's learning environments, performance, and self-efficacy outcomes. Both third- and fourth-grade TA students' level of multiplication mastery improved significantly after intervention. Results from the post-MAS also revealed significantly higher self-efficacy beliefs, and reduced nervousness in learning multiplication facts amongst some TA students. Statistical data analysis revealed no significant performance outcome differences between TLI and TA third-grade classes; however, post-test comparisons between fourth-grade TLI and TA students showed TA students significantly outperforming their comparison group counterparts by answering approximately 50% more problems in a given time and feeling significantly less nervous toward learning new multiplication math facts. The TA program's motivational, self-paced, and self-evaluative features seemed to produce a positive learning environment, which encouraged student learning. Educators should consider using CAI with features similar to TA's to improve students' academic performance and self-efficacy.