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• Author or Editor: Barbara J. Reys
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## Estimation and Mental Computation

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## Estimation and mental Computation

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## Estimation and Mental Computation

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## Estimation and Mental Computation

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## Estimation and Mental Computation

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## Estimation and mental Computation

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## Implementing the Standards: Estimation—Direction from the Standards

Do you estimate? Of course you do. Everyone estimates. Research shows that estimation is used in real-world problem solving far more than exact computation. Furthermore, estimation relates to every important mathematics concept and skill developed in elementary school. It is a process that allows the user to form an estimate or to judge the reasonableness of a result.

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## Mental Computation Performance and Strategy Use of Japanese Students in Grades 2, 4, 6, and 8

This study assessed attitude, computational preferences, and mental computational performance of 176, 187, 186, and 206 Japanese students in grades 2, 4, 6, and 8, respectively. A sample of students in grades 4 and 8 scoring in the upper and middle quintiles on the mental computation test was interviewed to identify strategies used to mentally compute. All data were collected during the last month of the school year. A wide range of performance on mental computation was found with respect to all types of numbers (whole numbers, decimals, and fractions) and operations at every grade level; the mode of presentation (visual or oral) significantly affected performance levels, with visual items generally producing higher performance; and the range of strategies (initial and alternative) used to do mental computation was narrow, with the most popular approach reflecting a mental version of a learned “paper/pencil” algorithm.

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## Effectiveness of Systematic Instruction on Attitudes and Computational Estimation Skills of Preservice Elementary Teachers

This 12-week study examined attitudes and performance of 187 preservice elementary teachers on computational estimation and evaluated practice with and without instruction on specific mental estimation strategies. Three groups--a control group, a group receiving weekly practice on computational estimation, and a group receiving weekly practice and instruction in estimation techniques--were formed. Analysis showed significant differences (p<.01) on performance in estimation in favor of the groups receiving regular practice. No significant difference was found between groups receiving only practice and those receiving practice and instruction. The later group, however, did display a greater understanding of the processes involved in doing estimation.

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## Processes Used by Good Computational Estimators

Computational estimation is recognized as a basic mathematics skill. It is used more frequently in daily activities than exact computation, yet virtually nothing is known about the skills and thinking strategies used in computational estimation. Individuals demonstrating good computational estimation skills were selected from more than 1200 people tested. Structured individual interviews with 59 students (Grades 7-12) and adults were conducted. These data suggest the existence and use of several key processes (compensation, reformulation, and translation) interwoven with a variety of distinct estimation strategies (front-end and averaging). Several other specific characteristics of good estimators are also presented in a tentative framework.