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Open Access Research

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

Sonia LJ White12 and Dénes Szűcs1

Author Affiliations

1 University of Cambridge, Department of Experimental Psychology, Centre for Neuroscience in Education, Downing Site, CB2 3EB, UK

2 Queensland University of Technology, School of Early Childhood, Faculty of Education, Victoria Park Road, Kelvin Grove, 4059, Australia

Behavioral and Brain Functions 2012, 8:1  doi:10.1186/1744-9081-8-1

Published: 4 January 2012



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.


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.


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.


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.