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An investigation of seventh grade students’ computational estimation strategies and factors associated with them

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2009
Boz, Burçak
The purpose of this study was to identify seventh grade students’ 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’ 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’ 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’ 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.