Abstract
Three theoretical accounts have been put forward for the development of children’s response patterns on number line estimation tasks: the log-to-linear representational shift, the two-linear-to-linear transformation and the proportion judgment account. These three accounts have not been contrasted, however, within one study, using one single criterion to determine which model provides the best fit. The present study contrasted these three accounts by examining first, second and sixth graders with a symbolic and non-symbolic number line estimation task (Experiment 1). In addition, first and second graders were tested again one year later (Experiment 2). In case of symbolic estimations, the proportion judgment account described the data best. Most young children’s non-symbolic estimation patterns were best described by a logarithmic model (within the log-to-lin account), whereas those of most older children were best described by the simple power model (within the proportion judgment account).
Highlights
In the past decade, mental representations of numbers and their development have been investigated intensively (e.g. Defever, Sasanguie, Vandewaetere & Reynvoet, 2012; Kucian & Kaufman, 2009; Reynvoet, De Smedt & Van den Bussche, 2009; Siegler & Opfer, 2003)
In accordance with the twolinto-lin developmental account, the symbolic number line data demonstrated that, with increasing age, children evolve from a twolinear to a simple linear estimation pattern
When comparing several developmental accounts, in case of the symbolic number line estimation task, our findings revealed that the proportion judgment account best reflected the development of symbolic number line estimation patterns in all grades
Summary
Mental representations of numbers and their development have been investigated intensively (e.g. Defever, Sasanguie, Vandewaetere & Reynvoet, 2012; Kucian & Kaufman, 2009; Reynvoet, De Smedt & Van den Bussche, 2009; Siegler & Opfer, 2003). Sasanguie et al: The Development of Number Line Estimations numbers are mentally represented akin to a ‘mental number line’, on which each number is represented as a Gaussian distribution around the corresponding mental magnitude (Dehaene, 1997) These representations are assumed to obey Weber-Fechner’s law (Fechner, 1860), referring to larger overlapping Gaussian distributions with increasing magnitude. Berteletti, Lucangeli, Piazza, Dehaene & Zorzi, 2010; Dehaene, Izard, Spelke & Pica, 2008; Sasanguie, De Smedt, Defever & Reynvoet, 2012; Siegler & Opfer, 2003) In this task, participants are typically asked to place a given number on an empty number line which is bounded by a starting value, usually zero or one, at the beginning of the line, and another value, such as 100 or 1000, at the end of the line. These numbers can be either symbolic (e.g. Arabic digits) or non-symbolic (e.g. dot patterns)
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