Numerical estimation in preschoolers.

Abstract

Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear representation and decrease their use of an intuitive, logarithmic one. We investigated the development of numerical estimation in a younger population (3.5- to 6.5-year-olds) using 0-100 and 2 novel sets of 1-10 and 1-20 number lines. Children's estimates shifted from logarithmic to linear in the small number range, whereas they became more accurate but increasingly logarithmic on the larger interval. Estimation accuracy was correlated with knowledge of Arabic numerals and numerical order. These results suggest that the development of numerical estimation is built on a logarithmic coding of numbers--the hallmark of the approximate number system--and is subsequently shaped by the acquisition of cultural practices with numbers.

Explaining the relationship between number line estimation and mathematical achievement: The role of visuomotor integration and visuospatial skills

“…Therefore, in addition, the widely reported relationship between number line estimation and other specific mathematical skills (e.g. simple addition, Booth & Siegler, 2008; knowledge of numerical order, Berteletti et al, 2010;identifying ordinal relations, Muldoon, Simms, Towse, Menzies & Yue, 2011) may at least be partially explained by their shared reliance on visuo-spatial and/or visuo-motor integration skills.…”

“…Specifically, it has been suggested that performance on the number line task is highly reliant on proportional reasoning skills, or the ability to accurately divide up space and/or number (Ashcraft & Moore, 2012;Barth & Paladino, 2011;Berteletti et al, 2010;Rouder & Geary, 2014). This explanation suggests that children primarily require sufficient number familiarity in order to make a proportional judgement based on the scale of the line (e.g.…”

Representational Structures of Arithmetical Thinking: Part I

“…In the minds of 5-year-old children, the linearly scaled number axis is activated when they must position numbers on the axis (0, 10). But if a task concerns positioning numbers on the axis (0, 20), they activate a logarithmically scaled mental number axis (Berteletti et al 2010). In accordance with the hypothesis of many-axes number representations, the child's mind activates the axis which is the most effective for the solution of a given arithmetic task.…”

“…The experimental results show that minds undergo a process of exchanging a logarithmic scaling of the mental number axis into a linear scaling. In other words, the development of mental competence causes a transition from logarithmic scaling of number representations to their linear scaling on the mental number axis (Siegler and Opfer 2003;Siegler and Booth 2004;Booth and Siegler 2006;Berteletti et al 2010). Some researchers (e.g., Siegler and Opfer 2003) postulate that this transition is gradual; that is, a child in some developmental period may use logarithmically scaled number representations as well as linearly scaled number representations, depending on the context of the task and the child's arithmetic competence.…”

Algebraic Models of Mental Number Axes: Part II

“…In this way, an algebraic, point-place scaffolding of mental number axes diminishes the high processing load which accompanies summation number axes. On the basis of empirical data (Siegler and Opfer 2003;Siegler and Booth 2004;Booth and Siegler 2006;Berteletti et al 2010;Barth and Paladino 2011;Cohen and Blanc-Goldhammer 2011), it is assumed in the model that CAPPAN-axes are logarithmically scaled.…”