Abstract
Number line estimation (i.e., indicating the position of a given number on a physical line) is a standard assessment of children's spatial representation of number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of number magnitude. Yet, so far there are no children data available for the unbounded number line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded number line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded number line estimation task to be a valuable tool for assessing children's spatial representation of number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children—at least in number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.
Highlights
The metaphor of a mental number line (Moyer and Landauer, 1967; Restle, 1970) describing the representation of number magnitude is widely recognized and considered in the currently most influential model in numerical cognition research [i.e., the Triple Code Model (Dehaene, 1992; Dehaene and Cohen, 1997; Dehaene et al, 2003)]
It is interesting to take a closer look at the development of the mental number line representation in children
With increasing age and experience, the authors suppose children to develop a linear representation of number magnitude reflected by an estimation pattern fitted best by a linear function
Summary
The metaphor of a mental number line (Moyer and Landauer, 1967; Restle, 1970) describing the (spatial) representation of number magnitude is widely recognized (for overviews see Hubbard et al, 2005; De Hevia et al, 2006) and considered in the currently most influential model in numerical cognition research [i.e., the Triple Code Model (Dehaene, 1992; Dehaene and Cohen, 1997; Dehaene et al, 2003)]. Behavioral (e.g., Dehaene et al, 1993; Fischer, 2001, 2003) as well as neuropsychological (e.g., Zorzi et al, 2002) data provide evidence for an automatic activation of number magnitude on an analogous left-to-right oriented number line in Western cultures (see Shaki et al, 2009, for other cultures) Against this background, it is interesting to take a closer look at the development of the mental number line representation in children. The positions of relatively large numbers are compressed toward the end of the scale which results in relatively high estimation errors (Siegler and Opfer, 2003; Booth and Siegler, 2006; Laski and Siegler, 2007) To account for this estimation pattern, Siegler and colleagues proposed children’s estimations to represent a quite isomorphic reflection of a logarithmic underlying representation of number magnitude as the authors found a logarithmic function to fit the observed estimation pattern best. This representational change, referred to as log-to-linear shift, is interpreted to reflect the development toward a linear representation of number magnitude in older children and adults (Siegler and Opfer, 2003; Siegler and Booth, 2004; Booth and Siegler, 2006, 2008)
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