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This qualitative study documents the establishment of new social and sociomathematical norms in a second grade classroom. The teacher allowed students to speak directly to one another without having to raise their hands first during whole group mathematics instruction. Reform efforts in mathematics and the standards for mathematical practice contained in the Common Core State Standards call for students to discuss their reasoning with each other. Data were collected through interviews with the teacher and students, field notes, and video-recorded lessons over the course of 23 days. An online survey tool was utilized to share selected video of the teacher's instruction. Initial professional development topics were chosen from research in mathematics education related to the social construction of understanding. Ongoing professional development was responsive to what occurred during instruction. The literature suggests that teachers often utilize traditional teaching methods and struggle to deviate from established patterns regardless of their desire to implement change. The teacher in this study learned that allowing students to talk openly provided him with insight into their mathematical conceptions and misconceptions. The students initially viewed mathematics as a set of rules to follow and exhibited the role of passive recipients of information. This changed as students were provided opportunities to participate in discussions and in doing so developed a new understanding of their role during mathematics lessons. Mathematical errors became a catalyst for communication and were viewed by students as opportunities for assisting their peers.

In an attempt to examine classroom dialogue within a second grade classroom, I encouraged students to participate in mathematics discussions without needing to raise their hands before speaking. I challenged this traditional social norm and established sociomathematical norms as the study progressed. My study showed the effects of this change on the dialogue of students in my classroom. Focus was placed on the participation in classroom discussions when traditional social and sociomathematical norms were in place as well as when new norms were established. The study helped determine the effects of student-centered dialogue on conceptual understanding as demonstrated in the students' discussions, participation, and written expression.

The purpose of this study was to investigate the effect of teachers attending Cognitively Guided Instruction (CGI) professional development on students' problem solving strategies and the effect of students' use of strategies on their mathematics achievement as measured by a standardized test. First, the study analyzed the differences in students' use of strategies between treatment and control groups. The treatment was CGI professional development, and the teachers in the treatment group attended CGI workshops whereas the teachers in the control group did not. Next, the study analyzed the differences in the mathematics achievement of students between different strategy groups. A student posttest, which was ITBS (Math Problems and Math Computation), was used to compare students' mathematics achievement. A student pretest was used as a covariate. The results of this study showed that there were statistically significant differences in the students' use of strategies between the treatment and control groups at the second grade level. A greater percentage of treatment students used derived facts / recall strategies (the most advanced strategy for single-digit addition and subtraction) than control students did. The results related to the effect of students' use of strategies on their mathematics achievement showed that the students who used derived facst/recall strategies for single-digit problems had significantly higher mathematics achievement than students who used counting or concrete modeling strategies. Furthermore, the students who used invented algorithms for multi-digit problems had significantly higher mathematics achievement than the students who used standard algorithms.

The Florida Department of Education's Next Generation Sunshine State Standards were adopted in 2008 as a means of increasing the rigor of mathematics learning and teaching mathematics to depth. In this study teachers' beliefs about developmentally appropriate tasks were examined through a web-based survey. Participants' responses to the survey were compared to the Florida Department of Education's Next Generation Sunshine State Standards. These standards were created in accordance to the 2006 National Council of Teachers of Mathematics Curriculum Focal Points in Mathematics Prekindergarten through Grade 8. This study included 25 teachers from a large metropolitan school district in Florida. Results demonstrate that a difference does exist between teachers' beliefs regarding when certain tasks should appear in the curriculum and what is advocated by the Next Generation Sunshine State Standards. Teachers' demographic information such as years of experience, employment by Title 1 school, and number of different grades taught, were not found to be significant predictors of their responses to prompts regarding developmentally appropriate tasks.

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Many teachers report that they rarely engage in reflection. Asynchronous forums have been used to foster reflection among prospective teachers, but there is limited research about the allocation of time for reflection in an asynchronous forum for practicing teachers. The purpose of this qualitative case study was to (a) determine teachers' perceptions about the benefits and drawbacks of the use of an online forum to allocate time for reflection and (b) to classify the levels of the teachers' reflections in the forum. A conceptual framework based on select writings by Dewey, Hatton and Smith, and van Manen was used to guide this study. The research questions addressed teachers' perceptions of the benefits, drawbacks, and use of a forum to allocate time to reflect as well as the levels of reflection achieved by the teachers in the forum. Ten online discussions and 2 sets of questionnaires were analyzed and coded using constant comparative data analysis. Seven elementary mathematics teachers completed the study and 52% and 56% of the discussion postings were coded as critical reflections using Hatton and Smith's framework and a summary of van Manen's framework, respectively. The themes pertaining to the benefits of reflecting online were convenience, sharing, and learning. Peer-to-peer interactions, however, were infrequent, and the teachers indicated that time was a factor that limited participation. This study may effect positive social change by advancing knowledge about using online forums to provide teachers with time earmarked for reflection focused on improving mathematics teaching and learning. Furthermore, educators can use information from this study to design online professional development experiences that include opportunities for reflection and reflective practice.

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 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 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.