The number line task is often used to assess children and adults' underlying representation of integers. Traditional bounded number line tasks, however, have limitations that can lead to misinterpretation. Here we present a new task, an unbounded number line task that overcomes these limitations. In Experiment 1, we show that adults use a biased proportion estimation strategy to complete the traditional bounded number line task. In Experiment 2, we show that adults use dead reckoning integer estimation strategy in our unbounded number line task. Participants revealed a positively accelerating numerical bias in both tasks, but showed scalar variance only in the unbounded number line task. We conclude that the unbounded number line task is a more pure measure of integer representation and using these results, we present a preliminary description of adults' underlying representation of integers.The number line task is often used to assess children and adults' underlying representation of integers (e.g., Berteletti, Lucaneli, Piazza, Dehaene & Zorzi, 2010;Geary, Hoard, Nugent & Byrd-Craven, 2008;Opfer & DeVries, 2007;Siegler & Booth, 2004;Siegler & Opfer, 2003). The traditional task consists of a bounded number line with labeled endpoints (e.g. 0-100) and a target number. On each trial, the participant is asked to indicate the position on the number line that the target number would occupy. Bounded number line tasks, however, have limitations (e.g., Barth & Paladino, In Press). Here, we (a) demonstrate the bounded number line task is an invalid measure of integer representation, (b) present a new task, an unbounded number line task, that overcomes the limitations of the bounded number line task and produces data consistent with integer representation, and (c) present a preliminary description of adults' underlying representation of integers, using the unbounded number line data.One's intuitive understanding of an integer (also referred to as an analogue quantity representation or analogue magnitude) can be described as a distribution of quantities. For example, each time we see 15, we understand its quantity to be slightly different (sometimes greater than 15, sometimes less). The distribution of quantities one associates with an integer describes one's psychological understanding of that integer. There is much debate in the literature concerning the placement and variance of these psychological distributions in relation to each other. The debate concerns whether integers are best described by a psychological representation in which (a) the mean distances between successive integers are logarithmically spaced and the perceptual errors associated with successive integers has a fixed variance (logarithmic models; e.g

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Children’s understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this has often been interpreted as evidence of a change in the child’s psychological representation of integer quantities. The present article presents theoretical and empirical evidence that the change in number-line performance actually reflects the development of measurement skills used in the task. We compare 2 versions of the number-line task: the bounded version used in the literature and a new, unbounded version. Results indicate that it is only children’s performance on the bounded task (which requires subtraction or division) that changes markedly with age. In contrast, children’s performance on the unbounded task (which requires only addition) remains fairly constant as they get older. Thus, developmental changes in performance on the traditional bounded number-line task likely reflect the growth of task-specific measurement skills rather than changes in the child’s understanding of numerical quantities.

The study presented a theoretical and empirical approach to the adult drawing process. Four possible sources of drawing inaccuracies were described: misperception of the object, inability to make good representational decisions, deficient motor skills, and misperception of the drawing. In four studies the degree to which the latter three sources contributed to drawing inaccuracies was assessed. The results suggest that (a) motor coordination is a very minimal source of drawing inaccuracies, (b) the artist's decision-making process is a relatively minor source of drawing inaccuracies, and (c) the artist's misperception of his or her work is not a source of drawing inaccuracies. These results suggest that the artist's misperception of the object is the major source of drawing errors.

There is increasing evidence that the major source of drawing errors lies in the initial perception of the to-be-drawn object. In four experiments, the authors explore the relation between an artist's susceptibility to perceptual transformations, as measured by a simple shape constancy task, and drawing accuracy. The data reveal a robust negative relation between errors on the shape constancy task and drawing accuracy in general, and specifically the accuracy of the rendering of spatial relations. The data further suggest that the perceptual processes that lead to errors on the shape constancy task occur during the initial encoding of the stimuli. The authors conclude that the shape constancy task likely measures one's ability to overcome constructive perception processes that transform the retinal image into a final percept, and that this ability is necessary for the accurate rendering of objects.