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The purpose of this study was to introduce problem posing activity to third grade students who have never met before. This study was also explored students' metaphorical images on problem posing process. Participants were from Public school in Marmara Region in Turkey. Data was analyzed both qualitatively (content analysis for difficulty and limitedness of pose problems and metaphorical imagination) and quantitatively (non-parametric Wilcoxon Sign Test). Since experimental and control group were not used in the study, this study was nonexperimental study. The participants were mingled with problems for warming up to generate a problem by themselves. After that they were offered three semi-structured problematics situations. Students were asked create a systematic structure to given problematic situations. Comparisons were made by means of pre-test and post-test. The results of this study revealed that the students were successful in structured type considerably. Further, students' insight on problem posing was identified by metaphors.

International comparative studies revealed that US students' mathematics performance is not at the level of expectation of mathematics education community. The latest of such study is, Third international Mathematics Science Study-Repeat (TIMSS-R, 1999) continued show poor performance of US students in international arena. Total of 38 countries had participated in TIMSS-R and focus was the mathematics achievement of 8th graders. In TIMSS video study only 6 counties participated along with the US. Five participated in TIMSS 1999 video study outperformed the US in mathematics achievement. Since the teachers and their decisions on teaching plays significant role in students learning, future US mathematics teachers can learn from accomplished practices in international arena. The purpose of this study is to investigate preservice teachers' analyses of such practices. The study is qualitative in nature. Data collection included students' written analyses on videotaped lessons and follow up interviews.

The aim of this study is to investigate the metaphors images of gifted students about mathematics. The sample of the study consists of 82 gifted students, which are 2, 3, 4, 5, 6, 7 graders, from Istanbul. Data were collected by asking students to complete the sentence: "Mathematics is as …, because…". In the study content analysis was used. The metaphors which were generated by students were categorized in terms of perceptions of mathematics. Metaphors were classified by three categories as content of mathematics, function of mathematics and exhibit attitude to mathematics. Chi-square test was used for examining relationship between two qualitative variables which are grades and metaphors. One of the findings is that gifted students generated metaphors according to their attitudes to mathematics.

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers reported here as a result of focusing visual (geometric) and analytical instruction in number theory, initial cognitive dissonance, rich discussions in their learning groups, and ramifications for changes in their future teaching practices. (Contains 5 figures.)

The objective of this study was to investigate and characterize the geometric thinking and understanding of four pre-service middle and secondary mathematics teachers while considering their spatial ability levels. To investigate the differences, if any, that existed among these pre-service middle and secondary teachers with different spatial ability levels and understanding geometry, pre- and post-test designs were employed using Mayberry's (J. Mayberry. "An investigation of the Van Hiele levels of geometric thought in undergraduate pre-service teachers," Unpublished Doctoral dissertation, University of Georgia, Athens, GA, 1981) protocol. Four contrasting cases in terms of spatial ability scores are examined using the van Hiele model to provide a description of geometric understanding. The study participants were chosen using "the Purdue visualization of rotations test" (ROT; G.M. Bodner and R.B. Guay, "The Purdue visualization of rotations test," "Chem. Educ." 2 (1997), pp. 1-18) from among a pool of pre-service middle and secondary mathematics teachers at a major research university in the southeast United States. The results were supportive of previous research in this area. Learners with low spatial abilities are more challenged geometry learners. While learners identified with mid-range spatial abilities showed the most change in van Hiele levels after instruction, the low spatial ability student showed the least amount of change. The student with high spatial ability showed some change after instruction. It was identified that instructional activities that afford opportunities for fostering spatial abilities must be included in pre-service programmes so that future teachers have a mathematical foundation from which to teach geometry. (Contains 8 figures.)

The importance of visualisation and multiple representations in mathematics has been stressed, especially in a context of problem solving. Hanna and Sidoli comment that "Diagrams and other visual representations have long been welcomed as heuristic accompaniments to proof, where they not only facilitate the understanding of theorems and their proofs, but can often inspire the proof of the theorem, and point out approaches to the construction of the proof itself". Apostol, a teacher of calculus for more than 50 years and author of a couple of textbooks on the subject, in his seminal article titled "A visual approach to calculus problems", points out that he "was stunned to learn that many standard problems in calculus can be easily solved by an innovative visual approach that makes no use of formulas". In this article, the author describes some different ways of visualising the sum of a series. (Contains 1 table.)

One way to teach Pythagoras' Theorem is through use of puzzles. Marshall (2004:1) points out that, "in creating their individual solutions to puzzles, students may reveal mathematical thinking on which approaches to the standard curriculum could be based." This article describes a puzzle-like spatial structuring activity related to Pythagoras' Theorem. The activity described is based on partitioning a square into four figures and constructing two new squares from them. (Contains 17 figures, 2 tables and 1 note.)

The Committee of Union and Progress (CUP), the Young Turk organization with the strongest influence on Turkish politics before and after World War I, mistrusted all Great Powers and the assumptions many researchers have made about the Young Turks' Anglophilia are over-simplified. The CUP's willingness to affiliate with either the Central or the Entente Powers indicates that it did not prefer either group. In fact, the CUP may have taken power in 1908 with greater anti-British and anti-French leanings than any other Ottoman government of the 19th and early 20th centuries., Although scholarly interest has focused on the Young Turks' organizational structure end their internal politics, no attempt has been made to analyse the main components, basic motives and aims that [...]

Lord Owen is one of those many unfortunates who, in the period of terminal decline of the British Empire, was sent off to sup with devils, equipped only with an [...]

Forest villages, which are home to 41% of the rural population in Turkey, differ from other villages in terms of their settlement characteristics and demographic structures. Many forest villagers (7.1 million) live in poverty in terms of their socioeconomic assets and per capita income. Many have joined a stream of continuous migration to cities in Turkey [1].The aim of this study was to analyze the relationships between numbers of migrants and their average age, the size of the households they leave, the infrastructure facilities in the villages from which they migrate, and the total amount of land available to their families by using the multiple linear regression model. The data were collected from 200 participants in five randomly selected forest villages in &#Kütaha Province in Turkey: Doğa, Eynegazi, Körpe, Suluköy, and Sünnetyenice. The analysis showed that the decision to migrate was affected mainly by the migrant’s household size prior to leaving. Our multiple linear regression model explained about 30% of the variability. Seventy-three percent of the migrants were 15 to 24 years of age, and therefore marriage and educational opportunities, which would affect their income levels, were at the forefront of their goals. Marriage was the main reason for leaving for 40% of the migrants, unemployment for 24%, and lack of educational opportunities for 20%. The researchers hope that the information will help governmental agencies to provide more subsidies for forest villagers so they will have regular and sustained incomes. [ABSTRACT FROM AUTHOR]

As well as being important for school mathematics, spatial thinking is a big component of advanced mathematical studies too. As Jones (2001:55) points out, "Much of the thinking that is required in higher mathematics is spatial in nature. Einstein's comments on thinking in images are well known. Numerous mathematicians report using spatial skills when they visualize mathematical relations." According to Wheatley (1990:11) "Spatial and analytic reasoning play complementary roles in mathematical thought, and neither should be emphasized at the expense of the other." This article presents some types of activities with dice that are intended to improve spatial ability. These tasks have been used with 8th grade to college students and also with pre-service middle and secondary mathematics teachers in the US and Turkey, and with inservice teachers in the US. (Contains 6 figures and 1 table.)

The counter-revolution, or the Incident of the 31 March 1909 against the Committee of Union and Progress (hereafter the CUP) (the Young Turks as they are known in Western historiography) [...]

Turkey needs to send a message to the UK that British inactivity in the former Yugoslavia may harm the country's relations with Moslem states. After the Gulf War, Turkey tried to establish close contacts wit the disintegrating Yugoslavia but also concerned itself with Western relations.Due to deterioration in situation in Bosnia, Turkish policy underwent a change as the Moslem question was involved. It formulated a two-fold policy for West and Moslem countries and through NATO and OIC it tried to enlist member countries' support to respond positively towards Bosnian crisis. But its policy underwent change from early 1993 due to failure of peace plans.

Images of cubic figures representing the sum of products of 2 consecutive integers are presented.