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In this study, the levels of mathematical literacy and visual math literacy self-efficacy perceptions of middle school students and the relationship between them were investigated. For this aim, the study was desgined as a correlational research model. The study group was determined according to convenience sampling. 328 middle school students (5th, 6th, 7th, and 8th graders) participated in this study with this sampling. In order to collect data, first, “Mathematical Literacy Scale” was developed. It was seen that the scale has just one dimension according to the exploratory factor analysis. It was found that the ratio χ2/df of the scale was found as 2.16 according to confirmatory factor analysis. This value showed that the scale indicates perfect fit. Besides, “A Visual Math Literacy Self-Efficacy Perception Scale” was used in order to measure the visual math literacy self-efficacy perceptions of middle school students. As a result, it was determined that middle school students’ mathematical literacy levels and their visual math literacy self-efficacy perceptions’ level are high. It was found that there is a high positive significant relationship between middle school students’ mathematical literacy and their visual math literacy self-efficacy perceptions.

Development of mathematical understanding is an active process involving mathematical structures and actions. Why do students not understand mathematics? What are the reasons for that? Students have some difficulties to understand mathematics and one of them is anxiety. Mathematics anxiety is defined as an uncomfortable feeling experienced when performing a mathematical task, which is seen as an obstacle to learning mathematics. For this reason, the aim of this study was to investigate the relationship between middle school students’ mathematics anxiety and their mathematical understanding. In addition to this, possible relationship was analyzed according to gender and grade levels variables. The relational screening model was used. The study was carried out with 466 middle school students. “Determining the Mathematical Understanding Levels Scale” and “Mathematics Anxiety-Apprehension Survey” were used as data collection instruments. According to the results of the study, there was a significant strong positive correlation between middle school students’ mathematics anxiety and their mathematical understanding. On the other hand, the results showed no significant differences between students’ mathematics anxiety and their mathematical understanding with respect to gender. However, the findings revealed significant differences in both students’ mathematics anxiety and their mathematical understanding with respect to grade levels.

The purpose of this research is to analyze the understanding factorial concept processes of 7th grade students who have low academic achievements with Pirie-Kieren theory. The research participants are composed of two 7th grade students who are studying at a public primary school in the Inegol Province of the city of Bursa. This research has been designed according to case study design since it was carried out with two students who had low academic achievements in a constructive learning environment. The research participants were selected among voluntary students by considering their mathematics achievement test scores and their grades stated in the previous year' reports. Mathematics achievement test was composed of 15 questions that were covering pre-cognitive knowledge of the factorial concept. Educational games, group work, puzzles, worksheets and activities designed for the objectives in the factorial concept were used in the research. The data of the research was collected by through a semi-structured interview, participant observation and document analysis for each student in the study group. The obtained data was analyzed by using a descriptive analysis method. According to the findings, students who have low academic achievements were able to construct concepts difficulty by interpreting activities and they reached formalising level according to Pirie and Kieren theory. In the light of the findings of this study, the researchers have developed suggestions. (C) 2015 The Authors. Published by Elsevier Ltd.

The aim of this study is to analyze the role of meta-cognition while solving indefinite integral problems. In this study, there are particularly three objectives to be obtained. These are; i) observe meta-cognitive behaviors of prospective mathematics teachers while solving problems, ii) determine the importance of meta-cognition in problem solving and iii) determine challenges, typical errors and points to be considered for solving indefinite integral problems. The study is a qualitative research. Data collection tools are; i) Problems Form (PF) and ii) Meta-Cognitive Skills Questionnaire (MSQ). In this context, this study was completed by 60 prospective mathematics teachers. All prospective mathematics teachers are sophomore students at a university. Data collection tools were filled by the prospective mathematics teachers in 50 minutes. Collected data were analyzed descriptively. The analysis of the problem which were solved by the prospective mathematics teachers and the examination of completed questionnaires are to provide an understanding for the meta-cognitive aspects of solving indefinite integral problems. In conclusion, the challenges faced by prospective mathematics teachers that are subject to recall, choose incorrect solution and not knowing where to start in problem solving. The common mistakes are incorrect solutions and calculation errors. On the other hand, the point that should be considered in the problem solving is to choose a strategy. (C) 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Academic World Education and Research Center.

Problem posing means either posing new problem situations in terms of given conditions or re-formulating an already written problem. In this study, the aim is to evaluate problems written by prospective mathematics teachers about ratio and proportion subjects in terms of criteria specified according to problem posing methods. According to this purpose, 'Problem Posing Form about Ratio and Proportion Subject' including questions for determining the tasks of free problem posing, semi-structured problem posing, structured problem posing and for determining which one is the most challenging problem posing task, was developed by the researchers. The data form was applied to 45 sophomore students who are studying in Kocaeli University, Teaching Primary School Mathematics department. The data collected throughout this study was evaluated by considering; i) Problem text (language and expression), ii) The compatibility of the problem with the mathematical principles, iii) The type/structure of the problem and iv) The solvability of the problem. In conclusion, it was concluded that prospective mathematics teachers posed clear and understandable problems which are compatible with the mathematical principles in the form of activity and which can be solved by students. The challenging sides of problem posing appeared as the hesitation on posing problems which are suitable to students' levels, the difficulty in remembering the subject clearly and not having sufficient information about problem posing. (C) 2015 The Authors. Published by Elsevier Ltd.

The main purpose of this study is to reveal the thoughts that prospective teachers studying at the department of teaching mathematics at primary schools possess with respect to the concept of 'Mathematics' through metaphors. The study was carried out with 106 female and 44 male students, total of 150 prospective teachers, who study at Kocaeli University Educational Faculty, Department of Teaching Mathematics at Primary Schools, during the fall semester in the 2011-2012 academic year. The data for the study was obtained by having students complete the blanks in the sentence 'Mathematics is like .......; Because .......'. The study had a descriptive nature, since it is an attempt to reveal an existing situation as it is. The metaphors developed by the participant prospective teachers on the concept of 'mathematics' were analyzed and interpreted by using qualitative research methods under the positive, negative and conceptual categories. In this context, the perceptions of prospective teachers studying at the department of teaching mathematics at primary schools regarding the concept of mathematics provide different perspectives. (C) 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of Prof. Dr. Huseyin Uzunboylu

The purpose of this research is to investigate the number sense of 5th grade Turkish students on the topic of decimal numbers. The research participants are composed of 121 5th grade students from two different elementary schools.. All of the students have already completed the 5th grade mathematics curriculum. The data of the research was collected by number sense test about decimal numbers (NSTDN). It contained 16 questions and four components of number sense. The results of this quantitatively analysed research have shown that the 5th grade students' number sense on decimal numbers is low. There was no significant difference in number sense between the genders. These findings are consistent with the previous researches. (C) 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of Prof. Dr. Huseyin Uzunboylu

The purpose of this study is to analyze the 6th Grade primary students' solving word problem skills that require extraneous knowledge. With this purpose in mind, 109 6th grade primary students from a primary school in Istanbul attended this research. Two types of test were used in this research. In the first test, the students were asked five word problems but in the second test an unnecessary data which was not necessary to solve these problems were added. The scores which were taken from tests which were carried out a week apart were compared by using paired-sampling t-test. The results of the research reveal the fact which is supported by the literature that students cannot distinguish that the extraneous information is not necessary for solving the problem and as a result they became less successful in solving extraneous problems than normal problems. (C) 2011 Published by Elsevier Ltd.

The aim of this study is to evaluate free problem posing studies of prospective mathematics teachers about Ratio and Proportion Subject', to determine the difficulties faced by the prospective teachers during problem posing process and to elicit suggestions regarding the experienced difficulties. For this purpose a data form was created by the researchers. This data form has three parts which were; i) The task of posing free problems, ii) The difficulties faced during problem posing process and iii) Suggestions for solutions of the difficulties. The data form was applied to 114 prospective primary mathematics teachers. During the analysis of the data regarding the first part of the data form, the following criteria were considered; i) Problem text (language and expression), ii) The compatibility of the problem with the mathematical principles, iii) The type/structure of the problem and iv) The solvability of the problem. In the analysis of the data obtained from the second and third parts of the form, content analysis was conducted and the program which is called as NVivo 10 was used. In conclusion, it was concluded that prospective mathematics teachers posed clear and understandable problems which were compatible with the mathematical principles in the form of exercise type and which can be solved by students. The difficulties faced during problem posing process determined as; lack of experience, lack of the content knowledge, not recognizing the cognitive levels of the students, lack of curriculum knowledge and difficulties in writing problem texts. The solutions which were suggested in the scope of this study were as the following; emphasizing problem solving and posing studies, in depth analysis of the curriculum, teaching special teaching methods in details and resorting to resources during problem posing process. (C) 2015 The authors Published by Elsevier Ltd.

This research aims to assess the concept maps related to the function concept generated by undergraduate students. In our study, firstly students were asked to write down the concepts that they know about the functions then generate a concept map by using these concepts. After this application a five-item questionnaire was also applied in order to get students' opinions about concept maps. The maps generated by students were analyzed according to the systematic of Varghese (2009) and the answers to the questionnaire were separately examined. It was observed from the findings that the students had difficulties in generating concept maps and relating the function concept with the other concepts. (C) 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Academic World Education and Research Center.

The aim of this study is to examine whether there is a relationship between gender and proof schemes used by first and final year preservice teachers attending primary and secondary education mathematics teaching program of a state university in 2011-2012 and also to investigate their general views towards proof. The study was carried out on a total of 98 preservice mathematics teachers. In order to describe current situation screening model was used. Students were asked to solve 9 problems and which proof schemes were belonged to their answers were determined. So as to set down proof schemes classification which was constituted by Harel and Sowder (1998) was used. According to the gender regarding proof schemes used by preservice teachers in the justification process of problems t table was created. Preservice teachers were interviewed so as to determine their views on proving 4 open ended questions were asked. Conversational data was given in the form of examples and in general terms. According to the results of analysis as significant differences was detected by gender in the use of some of schemes, some was concluded that the difference was not significant. Suggestions have been made on the basis of the data obtained at the end of the research. (C) 2013 The Authors. Published by Elsevier Ltd.

The aim of this study is to determine the hopelessness level of 3rd grade elementary mathematics preservice teachers and their perspectives about future at agovernment university in 2011 - 2012 academic year. The sample of the study is 73 elementary preservise teacher. Because the existing situation aimed to be determine screening model used. The 20 item Beck Hopelessness scale scale that was generated by Beck et. al (1974), and raliability and validity test was made by Seber (1991) and Durak (1994) is used to determine the hopelessness level of 3rd grade elementary mathematics preservice teachers and their perspectives about future. The hopelessness interval is determined by calculating the avarage score. 4 open ended questions are also asked. Suggestions made in accordance with the results of teh study. (C) 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Academic World Education and Research Center.