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

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.Estimation is a required skill for everyday life. Numerical estimation skills are an example of what Piaget [1] described as logico-mathematical knowledge. While Piaget did not carry out numerical estimation tasks specifically he considered logic-mathematical knowledge to be the mental relationships between and among objects/representations. Understanding the development of numerical estimation is particularly important to psychologists and educators, as several studies indicate the benefits of advanced estimation skills. For example, many studies (e.g. [2-5]) have determined a strong, positive correlation between the accuracy of numerical estimation and standardized tests of mathematics achievement. Furthermore, LeFevre, Greenham and Waheed [6] propose the tendency of skilful estimators to have a better conceptual understanding of mathematics, as well as better counting and arithmetic skills. Here we provide an investigation of numerical estimatio