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Representational change and strategy use in children's number line estimation during the first years of primary school.

White SL, Szűcs D - Behav Brain Funct (2012)

Bottom Line: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line).Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy.Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

View Article: PubMed Central - HTML - PubMed

Affiliation: University of Cambridge, Department of Experimental Psychology, Centre for Neuroscience in Education, UK. sl.white@qut.edu.au

ABSTRACT

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children.

Methods: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy.

Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development.

Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

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Related in: MedlinePlus

The absolute percent error for each target number, by year group. The error bars represent ± 95% confidence interval from the mean.
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Figure 3: The absolute percent error for each target number, by year group. The error bars represent ± 95% confidence interval from the mean.

Mentions: Figure 3 shows the marginally significant Target Number × Year interaction (F (14, 357) = 1.56, p = 0.087, η2 = 0.051). To increase the confidence of this marginal finding and protect against a potential type 2 error, univariate analyses were completed and indicated that there were significant differences between the year groups for target digits 11 and 13 (F (2, 53) = 3.38, p = 0.042, η2 = 0.117 and F (2, 53) = 6.10, p = 0.004, η2 = 0.193, respectively). Closer scrutiny demonstrated that for target digit 11 the Year 1 mean error was higher and marginally significant in comparison to Year 2 (p = 0.09) and significantly higher when compared to Year 3 (p = 0.01). A similar pattern was evident with target digit 13; Year 1 children had a mean error which was significantly higher than both Years 2 and 3 (p < 0.01). Years 2 and 3 produced no significant differences for target digits 11 and 13.


Representational change and strategy use in children's number line estimation during the first years of primary school.

White SL, Szűcs D - Behav Brain Funct (2012)

The absolute percent error for each target number, by year group. The error bars represent ± 95% confidence interval from the mean.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3344704&req=5

Figure 3: The absolute percent error for each target number, by year group. The error bars represent ± 95% confidence interval from the mean.
Mentions: Figure 3 shows the marginally significant Target Number × Year interaction (F (14, 357) = 1.56, p = 0.087, η2 = 0.051). To increase the confidence of this marginal finding and protect against a potential type 2 error, univariate analyses were completed and indicated that there were significant differences between the year groups for target digits 11 and 13 (F (2, 53) = 3.38, p = 0.042, η2 = 0.117 and F (2, 53) = 6.10, p = 0.004, η2 = 0.193, respectively). Closer scrutiny demonstrated that for target digit 11 the Year 1 mean error was higher and marginally significant in comparison to Year 2 (p = 0.09) and significantly higher when compared to Year 3 (p = 0.01). A similar pattern was evident with target digit 13; Year 1 children had a mean error which was significantly higher than both Years 2 and 3 (p < 0.01). Years 2 and 3 produced no significant differences for target digits 11 and 13.

Bottom Line: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line).Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy.Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

View Article: PubMed Central - HTML - PubMed

Affiliation: University of Cambridge, Department of Experimental Psychology, Centre for Neuroscience in Education, UK. sl.white@qut.edu.au

ABSTRACT

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children.

Methods: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy.

Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development.

Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Show MeSH
Related in: MedlinePlus