Computational Estimation Performance on Whole‐Number Multiplication by Third‐ and Fifth‐Grade Chinese Students

Liu, Fuchang

doi:10.1111/j.1949-8594.2009.tb18102.x

Cited by 12 publications

(20 citation statements)

References 31 publications

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“…These findings suggested that the computationally more-skilled Chinese participants emphasized proximity when deciding how to select a procedure for solving the problem, whereas Canadian participants favored simplicity. This pattern is consistent with the results reported by Liu (2009) for older versus younger Chinese children, by LeFevre et al (1993) for adults versus children, by Lemaire and Lecacheur (2011) for older versus younger French children, and by for more-versus less-skilled American children. In all cases, lessskilled solvers emphasized simplicity in their procedure selection, presumably in accord with their computational abilities, whereas more-skilled solvers used procedures that emphasized proximity.…”

Section: Present Researchsupporting

confidence: 93%

“…Imbo and LeFevre explained the differences in strategic processing between Chinese-and Belgian-educated individuals by referring to group differences in educational ap proaches, with Asian schooling focusing more on exact calculation and less on approximate calculation compared to Belgian school ing. The results of Experiment 1 (and the pilot study) supported the view that Chinese-educated individuals have a strong tendency to emphasize proximity in computational estimation (see also Liu, 2009). Chinese-educated participants were more likely than Canadian-educated participants to choose procedures that poten tially resulted in solutions closer to the exact solution when pro cedure choices were unconstrained.…”

Section: Implications For Previous Researchsupporting

confidence: 84%

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Strategic flexibility in computational estimation for Chinese- and Canadian-educated adults.

Xu¹,

Wells²,

LeFevre³

et al. 2014

Journal of Experimental Psychology: Learning, Memory, and Cogni

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The purpose of the present study was to examine factors that influence strategic flexibility in computational estimation for Chinese- and Canadian-educated adults. Strategic flexibility was operationalized as the percentage of trials on which participants chose the problem-based procedure that best balanced proximity to the correct answer with simplification of the required calculation. For example, on 42 × 57, the optimal problem-based solution is 40 × 60 because 2,400 is closer to the exact answer 2,394 than is 40 × 50 or 50 × 60. In Experiment 1 (n = 50), where participants had free choice of estimation procedures, Chinese-educated participants were more likely to choose the optimal problem-based procedure (80% of trials) than Canadian-educated participants (50%). In Experiment 2 (n = 48), participants had to choose 1 of 3 solution procedures. They showed moderate strategic flexibility that was equal across groups (60%). In Experiment 3 (n = 50), participants were given the same 3 procedure choices as in Experiment 2 but different instructions and explicit feedback. When instructed to respond quickly, both groups showed moderate strategic flexibility as in Experiment 2 (60%). When instructed to respond as accurately as possible or to balance speed and accuracy, they showed very high strategic flexibility (greater than 90%). These findings suggest that solvers will show very different levels of strategic flexibility in response to instructions, feedback, and problem characteristics and that these factors interact with individual differences (e.g., arithmetic skills, nationality) to produce variable response patterns.

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Section: Present Researchsupporting

confidence: 93%

Section: Implications For Previous Researchsupporting

confidence: 84%

Strategic flexibility in computational estimation for Chinese- and Canadian-educated adults.

Xu¹,

Wells²,

LeFevre³

et al. 2014

Journal of Experimental Psychology: Learning, Memory, and Cogni

View full text Add to dashboard Cite

show abstract

“…Currently, elementary school children, especially upper-grade ones, have a strong tendency to apply written algorithms mentally to obtain an exact answer when asked to estimate (Liu, 2009). If computational estimation and exact calculation are similar processes except for their exactness, there is reason to assume that discussion of estimation skills and the teaching and learning of such skills cannot be reasonably accomplished without attending to exact calculation skills.…”

Section: Research Problemmentioning

confidence: 99%

“…Computational estimation is defined as producing a rough but reasonable answer to an arithmetic problem in a relatively quick manner without resorting to any external devices such as paper and pencil (Liu, 2009). Computational estimation is defined as producing a rough but reasonable answer to an arithmetic problem in a relatively quick manner without resorting to any external devices such as paper and pencil (Liu, 2009).…”

Section: Exact Calculation and Computational Estimation As Different mentioning

confidence: 99%

“…On the other hand, if the two processes are found to operate on different, although certainly interrelated, mechanisms, the teaching and learning of estimation skills has to take a different route. Currently, elementary school children, especially upper-grade ones, have a strong tendency to apply written algorithms mentally to obtain an exact answer when asked to estimate (Liu, 2009). Moreover, it has been only a matter of three decades since the importance of computational estimation started to be recognized, and its many aspects are still being discussed.…”

Section: Research Problemmentioning

confidence: 99%

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Are Exact Calculation and Computational Estimation Categorically Different?

Liu

2013

Applied Cognitive Psychology

Self Cite

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This study examined, through the problem-size effect, whether exact calculation and computational estimation are categorically different. In Experiment 1, 26 teacher candidates, most of whom were female, Caucasian, and in their early 20s, estimated 27 randomly generated double-digit multiplication problems. In Experiment 2, 44 similar participants estimated and calculated a common set of double-digit multiplication problems. Analysis of reaction times and error rates indicates that the problem-size effect holds true for exact calculation but not for estimation. In estimation, as problem size increases, reaction times do not increase, nor does the rate of unreasonable estimates. Instead, the difference between a factor's unit digit and the nearest ten to be rounded to was a primary contributor to the variance of reaction times. It is concluded that exact calculation and computational estimation are computationally, cognitively, and structurally different processes. Furthermore, it is suggested that estimation skills be given separate, dedicated attention in schools.

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Estimation in the primary mathematics curricula of the United Kingdom: Ambivalent expectations of an essential competence

Andrews

Xenofontos

Sayers

2021

International Journal of Mathematical Education in Science and

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In this paper, we examine the national curricula for primary mathematics for each of the four constituent nations of the United Kingdom (England, Northern Ireland, Scotland and Wales) for the estimation-related opportunities they offer children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), the analyses indicate that computational estimation and measurement estimation were addressed in all four curricula, albeit from a skillsacquisition perspective, with only the Scottish offering any meaningful justification for their inclusion. The process of rounding, absent in the Northern Ireland curriculum, was presented as an explicit learning objective in the English, Scottish and Welsh curricula, although it was only the Scottish that made explicit the connections between rounding and computational estimation. In all curricula, both quantity estimation and number line estimation were effectively absent, as was any explicit acknowledgement that learning to estimate, irrespective of its form, has a developmental role in the learning of other mathematical topics.

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Computational Estimation Performance on Whole‐Number Multiplication by Third‐ and Fifth‐Grade Chinese Students

Cited by 12 publications

References 31 publications

Strategic flexibility in computational estimation for Chinese- and Canadian-educated adults.

Strategic flexibility in computational estimation for Chinese- and Canadian-educated adults.

Are Exact Calculation and Computational Estimation Categorically Different?

Estimation in the primary mathematics curricula of the United Kingdom: Ambivalent expectations of an essential competence

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