Children's strategy use in computational estimation.

Lemaire, Patrick; Lecacheur, Mireille; Farioli, Fernand

doi:10.1037/h0087336

Cited by 62 publications

(59 citation statements)

References 31 publications

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“…As noted above, one interesting aspect of computational estimation as a problem solving domain is that it requires consideration and balancing of two, sometimes competing, goals -simplicity and proximity (Lemaire, Lecacheur, & Farioli, 2000). Compare group students' adoption of the trunc strategy, which is very easy to implement but does not guarantee an accurate estimate, suggests that students in the present study tended to prioritize simplicity over proximity when computing estimates.…”

Section: Implications For Research On Computational Estimationmentioning

confidence: 68%

“…In this It Pays to Compare p. 7 example, round one leads to an estimate that is closer to the exact value than round both. Note these two goals often compete with each other, in that an easy-to-compute estimate is often not very proximal to the exact value, or conversely, the strategy leading to most proximal answer is not the easiest to compute (Lemaire, Lecacheur, & Farioli, 2000).…”

Section: Computational Estimationmentioning

confidence: 99%

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It pays to compare: An experimental study on computational estimation

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Rittle‐Johnson

2009

Journal of Experimental Child Psychology

127

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Comparing and contrasting examples is a core cognitive process that supports learning in children and adults across a variety of topics. In this experimental study, we evaluated the benefits of supporting comparison in a classroom context for children learning about computational estimation. Fifth-and sixth-grade students (n = 157) learned about estimation either by comparing alternative solution strategies or by reflecting on the strategies one at a time.At posttest and retention test, students who compared were more flexible problem solvers on a variety of measures. Comparison also supported greater conceptual knowledge, but only for students who already knew some estimation strategies. These findings indicate that comparison is an effective learning and instructional practice in a domain with multiple acceptable answers.

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Section: Implications For Research On Computational Estimationmentioning

confidence: 68%

Section: Computational Estimationmentioning

confidence: 99%

It pays to compare: An experimental study on computational estimation

Star

Rittle‐Johnson

2009

Journal of Experimental Child Psychology

127

View full text Add to dashboard Cite

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“…Given the challenges of mentally computing estimates, it is especially important to have a broad repertoire of estimation strategies and to select the most appropriate (often, computationally easiest) strategy for a given problem and goal (Dowker, Flood, Griffiths, Harriss, & Hook, 1996;LeFevre, Greenham, & Waheed, 1993;Lemaire, Lecacheur, & Farioli, 2000). Thus, students who lack strategic flexibility with computational estimation may experience difficulties in this domain.…”

Section: Flexibility: the Case Of Computational Estimationmentioning

confidence: 99%

“…Unfortunately, current instructional methods have not been particularly effective at supporting estimation knowledge. It is well documented that a large majority of students have difficulty estimating the answers to problems in their heads (Case & Sowder, 1990;Hope & Sherrill, 1987;Reys, Bestgen, Rybolt, & Wyatt, 1980;Sowder, 1992).Given the challenges of mentally computing estimates, it is especially important to have a broad repertoire of estimation strategies and to select the most appropriate (often, computationally easiest) strategy for a given problem and goal (Dowker, Flood, Griffiths, Harriss, & Hook, 1996;LeFevre, Greenham, & Waheed, 1993;Lemaire, Lecacheur, & Farioli, 2000). Thus, students who lack strategic flexibility with computational estimation may experience difficulties in this domain.…”

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confidence: 99%

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

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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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“…Past researches have focused mainly on (1) the age-related strategies that the participants used, including inversion problems solving skills [11,5,12], computational estimation skills [13][14][15] and other mastery skills [1,[16][17][18]], (2) performance level or learning abilities [19][20][21][22][23], (3) behaviors with learning disabilities [24][25][26][27] and (4) neuronal functionalities [28][29][30][31][32]. These researches have made great contributions to the understanding of primary arithmetic fact solving and mastery in the literature.…”

Section: Introductionmentioning

confidence: 99%