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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

Prediction proportion judgment cyclic power models as used in Hollands and Dyre [31]and Barth and Paladino [26]. a) 1-cycle model, with no central reference point; b) 2-cycle model, with one central reference point. In both a) and b) β is the exponent in the power function describing the relationship of psychological to physical magnitude. Legend: Green β = 0.1, Aqua β = 0.3, Blue β = 0.5, Red β = 0.7, Black β = 1.0. NB. When β = 1, the function is linear.
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Figure 1: Prediction proportion judgment cyclic power models as used in Hollands and Dyre [31]and Barth and Paladino [26]. a) 1-cycle model, with no central reference point; b) 2-cycle model, with one central reference point. In both a) and b) β is the exponent in the power function describing the relationship of psychological to physical magnitude. Legend: Green β = 0.1, Aqua β = 0.3, Blue β = 0.5, Red β = 0.7, Black β = 1.0. NB. When β = 1, the function is linear.

Mentions: In addition to this analysis, we explored the proportion judgment power model adopted by Barth and Paladino [26]. On an individual basis, for both 1-cycle and 2-cycle models, values of R2 were determined, along with the parameter β (the exponent determining the shape of the power function relating psychological to physical magnitude). We selected the β with the highest R2 and subsequently compared the best R2 for the 1-cycle and 2 cycle models (Figure 1)[31]. These findings were interpreted in relation to the logarithmic-linear shift, with β = 1 corresponding to a linear model and then the further the value from 1, the closer to a logarithmic model. This additional model was then entered into a separate 3 × 3 ANOVA. Factors were: Year (Year 1, 2 or 3) × Model (Linear, Logarithmic or Power).


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)

Prediction proportion judgment cyclic power models as used in Hollands and Dyre [31]and Barth and Paladino [26]. a) 1-cycle model, with no central reference point; b) 2-cycle model, with one central reference point. In both a) and b) β is the exponent in the power function describing the relationship of psychological to physical magnitude. Legend: Green β = 0.1, Aqua β = 0.3, Blue β = 0.5, Red β = 0.7, Black β = 1.0. NB. When β = 1, the function is linear.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Prediction proportion judgment cyclic power models as used in Hollands and Dyre [31]and Barth and Paladino [26]. a) 1-cycle model, with no central reference point; b) 2-cycle model, with one central reference point. In both a) and b) β is the exponent in the power function describing the relationship of psychological to physical magnitude. Legend: Green β = 0.1, Aqua β = 0.3, Blue β = 0.5, Red β = 0.7, Black β = 1.0. NB. When β = 1, the function is linear.
Mentions: In addition to this analysis, we explored the proportion judgment power model adopted by Barth and Paladino [26]. On an individual basis, for both 1-cycle and 2-cycle models, values of R2 were determined, along with the parameter β (the exponent determining the shape of the power function relating psychological to physical magnitude). We selected the β with the highest R2 and subsequently compared the best R2 for the 1-cycle and 2 cycle models (Figure 1)[31]. These findings were interpreted in relation to the logarithmic-linear shift, with β = 1 corresponding to a linear model and then the further the value from 1, the closer to a logarithmic model. This additional model was then entered into a separate 3 × 3 ANOVA. Factors were: Year (Year 1, 2 or 3) × Model (Linear, Logarithmic or Power).

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