Computational Estimation Performance and Strategies Used by Fifth- and Eighth-Grade Japanese Students

Reys, Robert E.; Reys, Bárbara J.; Nohda, Nobuhiko; Ishida, Junichi; Shimizu, Katsuhiko

doi:10.2307/749553

Cited by 25 publications

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“…This lack of estimation strategy supports the findings of Reys et al (1991), which state that 'estimation skills do not necessarily evolve from the development of traditional written computation algorithms' (p. 55). This is also consistent with the belief that computational estimation skills are highly dependent on number sense, and that the absence of estimation skills is due to a lack of number sense (Reys et al, 1991;Sowder, 1992aSowder, , 1992bMarkovits & Sowder, 1994;Yang, 1995).…”

Section: Discussionsupporting

confidence: 86%

Number sense strategies used by 6th‐grade students in Taiwan

Yang

2005

Educational Studies

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In an interview setting, 21 6th-graders from four public schools in south Taiwan were asked a series of questions, related to whole and decimal numbers, designed to assess their number sense. Eight students were randomly selected from both low and middle performance levels, and five were selected from a high-performance level, according to their mathematical capabilities. Results indicated that, regardless of performance level, very few number sense strategies (e.g. using benchmarks, estimation or numbers of magnitude) were used. The evidence also revealed that Taiwanese students tended to apply rule-based methods and standard written algorithms to explain their reasoning. Their inclination to use paper-and-pencil procedures narrowed their thinking and reasoning powers: this heavy reliance on written algorithms seemed to be a major impediment to the development of number sense. RationaleThe recent Third International Mathematics and Science Study (Mullis et al., 2004) confirmed the evidence from previous research that Taiwanese students consistently achieve high marks in mathematics performance, involving written computation (Stevenson et al., 1986;Stigler et al., 1991;Stevenson et al., 1993;Beaton et al., 1997). However, McIntosh et al. (1992) claim that students who are highly skilled in paper-and-pencil computation (often the gauge by which success in mathematics is measured) may or may not have developed good number sense. The study of Reys & Yang (1998) confirmed that Taiwanese students' proficiency, in exact written computational performance, is not necessarily accompanied by good number sense. The Israeli teacher Muneer (1999) repeated this study with 9th-grade students and

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Section: Discussionsupporting

confidence: 86%

Number sense strategies used by 6th‐grade students in Taiwan

Yang

2005

Educational Studies

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“…For this example problem, truncation yields 2 x 4 or 8, and then adding two zeros yields an estimate of 800. Note that truncation is a less familiar strategy than the other two, but it is relatively easy and fast and has been advocated for by researchers on computational estimation for these reasons (e.g., Reys, Reys, Nohda, & Ishida, 1991;Reys, Rybolt, Bestgen, & Wyatt, 1982;Sowder & Wheeler, 1989).Flexibility in estimation includes choosing the most appropriate strategy for computing an estimate for a given problem. Choosing an appropriate strategy in estimation is complicated by the presence of multiple, at times competing goals.…”

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confidence: 99%

The role of prior knowledge in the development of strategy flexibility: the case of computational estimation

Star

Rittle‐Johnson

Lynch

et al. 2009

ZDM Mathematics Education

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The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Acknowledgements. Thanks to the University School of Nashville and Hale County Schools for participating in this research. Thanks also to Holly Harris for her help in collecting, coding and analyzing the data reported here. This research was supported with funding from U.S. Department of Education grant R305H050179.Prior knowledge and flexibility 2 AbstractThe ability to estimate is a fundamental real-world skill; it allows students to check the reasonableness of answers found through other means, and it can help students develop a better understanding of place value, mathematical operations, and general number sense. Flexibility in the use of strategies is particularly critical in computational estimation. The ability to perform complex calculations mentally is cognitively challenging for many students; thus it is important to have a broad repertoire of estimation strategies and to select the most appropriate strategy for a given problem. In this paper, we consider the role of students' prior knowledge of estimation strategies in the effectiveness of interventions designed to promote strategy flexibility across two recent studies. In the first, 65 fifth graders began the study as fluent users of one strategy for computing mental estimates to multi-digit multiplication problems such as 17 x 41. In the second, 157 fifth and sixth graders began the study with moderate to low prior knowledge of strategies for computing mental estimates. Results indicated that students' fluency with estimation strategies had an impact on which strategies they adopted. Students who exhibited high fluency at pretest were more likely to increase use of estimation strategies that led to more accurate estimates, while students with less fluency adopted strategies that were easiest to implement. Our results suggest that both the ease and accuracy of strategies as well as students' fluency with strategies are all important factors in the development of strategy flexibility.Prior knowledge and flexibility 4The Role of Prior Knowledge in the Development of Strategy Flexibility: The Case of Computational EstimationEstimation is a critically useful skill in everyday life and in mathematics. We often must make quick computations or judgments of numerical magnitude without the aid of calculator or paper and pencil. In addition to being a fundamental, real-world skill, the ability to quickly and accurately perform mental computations and estimations has two additional benefits: 1) It allows students to check the reasonableness of their answers found through other means, and 2) it may help students develop a better understanding of place value, mathematical operations, and general number sense (Beishuizen, van Putten, & van Mulken, 1997; National Research Council, 2001). These benefits are encapsulated in the "Adding It Up" report from the National ResearchCouncil: "The curriculum should provide opportunities for students...

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“…Though there are some different findings which are in favour of male students ( [11,30,34,41]), there are many findings in parallel to this finding ( [5,15,28,35,36]). …”

Section: Discussion and Suggestionsmentioning

confidence: 58%

The Relationship between Eighth Grade Elementary Students’ Operational and Measurable Prediction Skills and Mathematical Literacy

Çetin¹,

Köse²

2015

EDUCATION

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This study aimed to investigate relationship between eighth grade elementary students' operational and measurable prediction skills and their mathematical literacy. Mathematical literacy is a very broad term but in the present study it was narrowed with students' daily life issues and used for regarding students' mathematics usage in their daily life according to their levels. In the study, quantitative methodology to investigate the levels of the students' prediction skills and mathematical literacy and qualitative methodology to determine the students' strategies in the prediction question were chosen. The participants of the study were chosen with a stratified sampling random strategy from a medium-scaled city of East Anatolian Region of Turkey in the academic year 2011-2012. The participants were 221 eighth grade students from 20 national elementary schools. As data collection tools, a "Measurable and Operational Prediction Skill Test" including ten questions for the prediction skill and "Mathematical Literacy Test" including 20 questions were used. The findings showed that there was a significant relationship between measurable and operational prediction skills. Also it was observed that the students having high score of measurable and operational prediction skills became more successful in the mathematical literacy test. The gender did not have any significant impact on these variables.

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Computational Estimation Performance and Strategies Used by Fifth- and Eighth-Grade Japanese Students

Cited by 25 publications

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Number sense strategies used by 6th‐grade students in Taiwan

Number sense strategies used by 6th‐grade students in Taiwan

The role of prior knowledge in the development of strategy flexibility: the case of computational estimation

The Relationship between Eighth Grade Elementary Students’ Operational and Measurable Prediction Skills and Mathematical Literacy

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