This study looked at what components are in student solutions to computational estimation problems involving fractions. Past computational estimation research has focused on strategies used for estimating with whole numbers and decimals while neglecting those used for fractions. An extensive literature review revealed one study specifically directed toward estimating with fractions (Hanson & Hogan, 2000) that researched adult estimation strategies and not children's strategies. Given the lack of research on estimation strategies that children use to estimate with fractions, this study used qualitative research methods to find which estimation components were in 10 eighth-grade students' solutions to estimation problems involving fractions. Analysis of this data differs from previous estimation studies in that it considers actions as the unit of analysis, providing a smaller grain size that reveals the components used in each estimation solution. The analysis revealed new estimation components as well as a new structure for categorizing the components. The new categories are whole number and decimal estimation components, fraction estimation components, and components used with either fractions or whole numbers and decimals. The results from this study contribute to the field of mathematics education by identifying new components to consider when conducting future studies in computational estimation. The findings also suggest that future research on estimation should use a smaller unit of analysis than a solution response to a task, the typical unit of analysis in previous research. Additionally, these results contribute to mathematics teaching by suggesting that all components of an estimation solution be considered when teaching computational estimation, not just the overarching strategy.

The problem of this study was to investigate the strategies used by high school students of limited estimation ability for the estimation of the answers to computational problems. The Assessing Computational Estimation Test was administered to 460 students, and 40 of them were selected for interviews. Each student interviewed was asked to estimate the answers to fourteen computation and application problems.

The purpose of this study was to identify seventh grade students&rsquo / computational estimation strategies and factors associated with these strategies. A case study was conducted with five students. They were selected among 116 seventh grade students from a public elementary school in Aegean region. Two sessions of clinical interviews were carried out with each participant. In the first interview session, the Computational Estimation Test, which was consisted of 15 estimation questions, was administered to students with requesting explanations of solving procedure. In the second interview session, students answered to semi-structured questionnaire prepared by the researcher to understand their feelings and thoughts on estimation. The results of the study indicated that students used three kinds of computational estimation strategies, which were reformulation, translation, and compensation. Reformulation was the most used types of estimation and by all interviewees. It was divided into four sub-strategies, which were observed during the interviews, among them rule based rounding was the most preferred one. The most sophisticated strategy was compensation, which was used least frequently by the participants. The other kind of computational estimation strategy was translation, which means changing the operation for handling the questions more easily. Translation strategy was used students who performed well in number sense. Based on interviews and observations, there were some cognitive and affective factors, which were associated with the specified strategies. Number sense and mental computation were two sub categories of the cognitive factors. Besides these cognitive factors, confidence in ability to do mathematics, perception of mathematics, confidence in ability to do estimation, perception of estimation and tolerance for error, which were identified as affective factors, played important role for strategy selection and computational estimation. Good number sense may lead to use of multiple representations of numbers and use of translation strategies. Moreover, mental computation ability may enable students both to conduct reformulation and use compensation strategy easily. Interviewees who had both high confidence in ability to do mathematics and low confidence in ability to do estimation, preferred exact computation and more rule dependent estimation strategies, like rule based rounding. Low tolerance for error may influence students&rsquo / answers, in order to produce them in a narrow interval. Additionally, perception of estimation may lead students recognize estimation as useful and use of variety of computational estimation strategies. According to data analysis, feelings and thoughts about computational estimation may influence interviewees&rsquo / strategy usage, such as students, who had negative feelings on estimation and thoughts about mathematics wanted exactness, generally preferred exact computation process and did not use diverse computational estimation strategies. Students who had poor in number sense and mental computation could not conduct computational estimation strategies. Therefore, the research study may lead to better understanding of students&rsquo / perspectives on computational estimation. With understanding used strategies, and related factors are affecting computational estimation strategies, it might be produce effective instructional designs for teaching computational estimation.

The purpose of this study was to investigate the high school students&#039 / ability on estimation and computational estimation. The study was conducted in Denizli with 153 ninth grade students who enrolled to general, Anatolian and foreign language high schools. The Estimation Ability Test was utilized. The three formats which are number format, answer format and problem format of the test were analyzedby with respect to school types and gender. The design of the present research was one group pretest-posttest design. The hypotheses of the study were tesetd by using analysis of covariance at the significance level 0.05. The results of the study indicated that: 1. There were statistically significant differences among the mean scores of students enrolled to different kinds of high school with respect to estimation ability and computational estimation in favor of Anatolian High School students. 2. There were statistically significant mean differences of students enrolled to diffrent kinds of high school with respect to sub-categories of the estimation ability test in favor of Anatolian High School students. 3. There was no statistically significant mean difference between boys and girls on estimation ability. 4. There was statistically significant mean difference in some sub-categories of the estimation test in favor of boys.

This study was conducted to analyse aspects of mental computation within primary school mathematics curricula and to formulate recommendations to inform future revisions to the Number strand of mathematics syllabuses for primary schools. The analyses were undertaken from past, contemporary, and futures perspectives. Although this study had syllabus development in Queensland as a prime focus, its findings and recommendations have an international applicability. Little has been documented in relation to the nature and role of mental computation in mathematics curricula in Australia (McIntosh, Bana, & Farrell, 1995,p. 2), despite an international resurgence of interest by mathematics educators. This resurgence has arisen from a recognition that computing mentally remains a viable computational alternative in a technological age, and that the development of mental procedures contributes to the formation of powerful mathematical thinking strategies (R. E. Reys, 1992, p. 63). The emphasis needs to be placed upon the mental processes involved, and it is this which distinguishes mental computation from mental arithmetic, as defined in this study. Traditionally, the latter has been concerned with speed and accuracy rather than with the mental strategies used to arrive at the correct answers. In Australia, the place of mental computation in mathematics curricula is only beginning to be seriously considered. Little attention has been given to teaching, as opposed to testing, mental computation. Additionally, such attention has predominantly been confined to those calculations needed to be performed mentally to enable the efficient use of the conventional written algorithms. Teachers are inclined to associate mental computation with isolated facts, most commonly the basic ones, rather than with the interrelationships between numbers and the methods used to calculate. To enhance the use of mental computation and to achieve an improvement in performance levels, children need to be encouraged to value all methods of computation, and to place a priority on mental procedures. This requires that teachers be encouraged to change the way in which they view mental computation. An outcome of this study is to provide the background and recommendations for this to occur. The mathematics education literature of relevance to mental computation was analysed, and its nature and function, together with the approaches to teaching, under each of the Queensland mathematics syllabuses from 1860 to 1997 were documented. Three distinct time-periods were analysed: 1860-1965, 1966-1987, and post-1987. The first of these was characterised by syllabuses which included specific references to calculating mentally. To provide insights into the current status of mental computation in Queensland primary schools, a survey of a representative sample of teachers and administrators was undertaken. The statements in the postal, self-completion opinionnaire were based on data from the literature review. This study, therefore, has significance for Queensland educational history, curriculum development, and pedagogy. The review of mental computation research indicated that the development of flexible mental strategies is influenced by the order in which mental and written techniques are introduced. Therefore, the traditional written-mental sequence needs to be reevaluated. As a contribution to this reevaluation, this study presents a mental-written sequence for introducing each of the four operations. However, findings from the survey of Queensland school personnel revealed that a majority disagreed with the proposition that an emphasis on written algorithms should be delayed to allow increased attention on mental computation. Hence, for this sequence to be successfully introduced, much professional debate and experimentation needs to occur to demonstrate its efficacy to teachers. Of significance to the development of efficient mental techniques is the way in which mental computation is taught. R. E. Reys, B. J. Reys, Nohda, and Emori (1995, p. 305) have suggested that there are two broad approaches to teaching mental computation,,Ya behaviourist approach and a constructivist approach. The former views mental computation as a basic skill and is considered an essential prerequisite to written computation, with proficiency gained through direct teaching. In contrast, the constructivist approach contends that mental computation is a process of higher-order thinking in which the act of generating and applying mental strategies is significant for an individual's mathematical development. Nonetheless, this study has concluded that there may be a place for the direct teaching of selected mental strategies. To support syllabus development, a sequence of mental strategies appropriate for focussed teaching for each of the four operations has been delineated. The implications for teachers with respect to these recommendations are discussed. Their implementation has the potential to severely threaten many teachersf sense of efficacy. To support the changed approach to developing competence with mental computation, aspects requiring further theoretical and empirical investigation are also outlined.