Linear mapping of numbers onto space requires attention

Anobile, Giovanni; Cicchini, Guido Marco; Burr, David

doi:10.1016/j.cognition.2011.11.006

Cited by 104 publications

(124 citation statements)

References 34 publications

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“…However, the main finding of the current study is that different mechanisms underlie two wide-spread cognitive number processing tasks: the number comparison task and the number line estimation task. This finding is consistent with recent studies (e.g., Anobile et al, 2012;Barth & Paladino, 2011;Ebersbach, Frick, Luwel, Onghena, & Verschaffel, 2008;Verguts et al, 2005) which have argued in favour of alternative explanations to explain the results in number line estimation and comparison. As a result, we and others have argued in favour of alternative measures to investigate magnitude representation, such as priming (e.g., Defever, Sasanguie, Gebuis, & Reynvoet, 2011) and same-different judgments (e.g., Cohen Kadosh, Muggleton, Silvanto, & Walsh, 2010;Defever, Sasanguie, Vandewaetere, & Reynvoet, 2012;Van Opstal & Verguts, 2011).…”

Section: Discussionsupporting

confidence: 83%

“…According to these authors, the requirement of a proportion judgment in this task provides a better explanation than does the idea of a logarithmic-to-linear representational shift. In another study, Anobile, Cicchini and Burr (2012) showed that when adults are distracted by a concurrent task, they perform logarithmically on a non-symbolic number line estimation task. This finding led the authors to suggest that the non-linearity arises from an intrinsic logarithmic representation and that attentional resources play a very important role in making the shift to linear representations.…”

Section: Discussionmentioning

confidence: 99%

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Number Compasison and Number Line Estimation Rely on Different Mechanisms

Sasanguie

Reynvoet

2013

PSYCHOL BELG

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Section: Discussionsupporting

confidence: 83%

Section: Discussionmentioning

confidence: 99%

Number Compasison and Number Line Estimation Rely on Different Mechanisms

Sasanguie

Reynvoet

2013

PSYCHOL BELG

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“…We suspect that the final word will not come from experiments using number-line estimation alone. Moreover, manipulations based on perceptual analogues to number lines (e.g., Anobile, Cicchini, & Burr, 2012; al., 2008) may have only limited applicability, because their stimuli are mainly nonsymbolic. Rather, several numeracy tasks that combine these techniques may be needed to crossvalidate the findings.…”

Section: Discussionmentioning

confidence: 99%

Knowledge on the line: Manipulating beliefs about the magnitudes of symbolic numbers affects the linearity of line estimation tasks

Chesney

Matthews

2013

Psychon Bull Rev

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It has been suggested that differences in performance on number-line estimation tasks are indicative of fundamental differences in people's underlying representations of numerical magnitude. However, we were able to induce logarithmic-looking performance in adults for magnitude ranges over which they can typically perform linearly by manipulating their familiarity with the symbolic number formats that we used for the stimuli. This serves as an existence proof that individuals' performances on number-line estimation tasks do not necessarily reflect the functional form of their underlying numerical magnitude representations. Rather, performance differences may result from symbolic difficulties (i.e., number-to-symbol mappings), independently of the underlying functional form. We demonstrated that numberline estimates that are well fit by logarithmic functions need not be produced by logarithmic functions. These findings led us to question the validity of considering logarithmic-looking performance on number-line estimation tasks as being indicative that magnitudes are being represented logarithmically, particularly when symbolic understanding is in question.

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“…The greater involvement of attention control in counting tasks when, for instance, a person must compare the values of digits under time pressure, is confirmed by some experimental data (Anobile et al 2012). In such situations, an index of precision which the function X returns is sufficiently high for the sake of operating with linearly scaled mental number axes.…”

Section: Neurophysiological Datamentioning

confidence: 53%

Algebraic Models of Mental Number Axes: Part II

Krysztofiak

2015

Axiomathes

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The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are extensions of BASAN-structures. The constructed formal model unifies two competitive conceptions of cognitive arithmetic: namely, the conception of the mental number line and the conception of parallel individuation. The paper is the continuation of a paper entitled Representational structures of arithmetical thinking, in which rich empirical evidence supporting the model is presented. The main result achieved in the present paper may be philosophically interpreted as an attempt to formalize the Kantian conception of the pure idea of time, understood as the a priori form of human arithmetical thinking. In this way, our theory may be comprehended as a result of applying the hard method of logical reconstruction of fundamental epistemological categories.

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Linear mapping of numbers onto space requires attention

Cited by 104 publications

References 34 publications

Number Compasison and Number Line Estimation Rely on Different Mechanisms

Number Compasison and Number Line Estimation Rely on Different Mechanisms

Knowledge on the line: Manipulating beliefs about the magnitudes of symbolic numbers affects the linearity of line estimation tasks

Algebraic Models of Mental Number Axes: Part II

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