Fabbri, Marco
(2008)
Componenti spaziali della rappresentazione cognitiva della grandezza del numero, [Dissertation thesis], Alma Mater Studiorum Università di Bologna.
Dottorato di ricerca in
Psicologia generale e clinica, 20 Ciclo. DOI 10.6092/unibo/amsdottorato/1013.
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Abstract
The humans process the numbers in a similar way to animals. There are countless
studies in which similar performance between animals and humans (adults and/or children)
are reported. Three models have been developed to explain the cognitive mechanisms
underlying the number processing. The triple-code model (Dehaene, 1992) posits an mental
number line as preferred way to represent magnitude. The mental number line has three
particular effects: the distance, the magnitude and the SNARC effects. The SNARC effect
shows a spatial association between number and space representations. In other words, the
small numbers are related to left space while large numbers are related to right space.
Recently a vertical SNARC effect has been found (Ito & Hatta, 2004; Schwarz & Keus,
2004), reflecting a space-related bottom-to-up representation of numbers. The magnitude
representations horizontally and vertically could influence the subject performance in explicit
and implicit digit tasks. The goal of this research project aimed to investigate the spatial
components of number representation using different experimental designs and tasks. The
experiment 1 focused on horizontal and vertical number representations in a within- and
between-subjects designs in a parity and magnitude comparative tasks, presenting positive or
negative Arabic digits (1-9 without 5). The experiment 1A replied the SNARC and distance
effects in both spatial arrangements. The experiment 1B showed an horizontal reversed
SNARC effect in both tasks while a vertical reversed SNARC effect was found only in
comparative task. In the experiment 1C two groups of subjects performed both tasks in two
different instruction-responding hand assignments with positive numbers. The results did not
show any significant differences between two assignments, even if the vertical number line
seemed to be more flexible respect to horizontal one. On the whole the experiment 1 seemed
to demonstrate a contextual (i.e. task set) influences of the nature of the SNARC effect. The
experiment 2 focused on the effect of horizontal and vertical number representations on
spatial biases in a paper-and-pencil bisecting tasks. In the experiment 2A the participants were
requested to bisect physical and number (2 or 9) lines horizontally and vertically. The findings
demonstrated that digit 9 strings tended to generate a more rightward bias comparing with
digit 2 strings horizontally. However in vertical condition the digit 2 strings generated a more
upperward bias respect to digit 9 strings, suggesting a top-to-bottom number line. In the
experiment 2B the participants were asked to bisect lines flanked by numbers (i.e. 1 or 7) in
four spatial arrangements: horizontal, vertical, right-diagonal and left-diagonal lines. Four
number conditions were created according to congruent or incongruent number line
representation: 1-1, 1-7, 7-1 and 7-7. The main results showed a more reliable rightward bias
in horizontal congruent condition (1-7) respect to incongruent condition (7-1). Vertically the
incongruent condition (1-7) determined a significant bias towards bottom side of line respect
to congruent condition (7-1). The experiment 2 suggested a more rigid horizontal number line
while in vertical condition the number representation could be more flexible. In the
experiment 3 we adopted the materials of experiment 2B in order to find a number line effect
on temporal (motor) performance. The participants were presented horizontal, vertical, rightdiagonal
and left-diagonal lines flanked by the same digits (i.e. 1-1 or 7-7) or by different
digits (i.e. 1-7 or 7-1). The digits were spatially congruent or incongruent with their respective
hypothesized mental representations. Participants were instructed to touch the lines either
close to the large digit, or close to the small digit, or to bisected the lines. Number processing
influenced movement execution more than movement planning. Number congruency
influenced spatial biases mostly along the horizontal but also along the vertical dimension.
These results support a two-dimensional magnitude representation. Finally, the experiment 4
addressed the visuo-spatial manipulation of number representations for accessing and retrieval
arithmetic facts. The participants were requested to perform a number-matching and an
addition verification tasks. The findings showed an interference effect between sum-nodes
and neutral-nodes only with an horizontal presentation of digit-cues, in number-matching
tasks. In the addition verification task, the performance was similar for horizontal and vertical
presentations of arithmetic problems. In conclusion the data seemed to show an automatic
activation of horizontal number line also used to retrieval arithmetic facts. The horizontal
number line seemed to be more rigid and the preferred way to order number from left-to-right.
A possible explanation could be the left-to-right direction for reading and writing. The vertical
number line seemed to be more flexible and more dependent from the tasks, reflecting
perhaps several example in the environment representing numbers either from bottom-to-top
or from top-to-bottom. However the bottom-to-top number line seemed to be activated by
explicit task demands.
Abstract
The humans process the numbers in a similar way to animals. There are countless
studies in which similar performance between animals and humans (adults and/or children)
are reported. Three models have been developed to explain the cognitive mechanisms
underlying the number processing. The triple-code model (Dehaene, 1992) posits an mental
number line as preferred way to represent magnitude. The mental number line has three
particular effects: the distance, the magnitude and the SNARC effects. The SNARC effect
shows a spatial association between number and space representations. In other words, the
small numbers are related to left space while large numbers are related to right space.
Recently a vertical SNARC effect has been found (Ito & Hatta, 2004; Schwarz & Keus,
2004), reflecting a space-related bottom-to-up representation of numbers. The magnitude
representations horizontally and vertically could influence the subject performance in explicit
and implicit digit tasks. The goal of this research project aimed to investigate the spatial
components of number representation using different experimental designs and tasks. The
experiment 1 focused on horizontal and vertical number representations in a within- and
between-subjects designs in a parity and magnitude comparative tasks, presenting positive or
negative Arabic digits (1-9 without 5). The experiment 1A replied the SNARC and distance
effects in both spatial arrangements. The experiment 1B showed an horizontal reversed
SNARC effect in both tasks while a vertical reversed SNARC effect was found only in
comparative task. In the experiment 1C two groups of subjects performed both tasks in two
different instruction-responding hand assignments with positive numbers. The results did not
show any significant differences between two assignments, even if the vertical number line
seemed to be more flexible respect to horizontal one. On the whole the experiment 1 seemed
to demonstrate a contextual (i.e. task set) influences of the nature of the SNARC effect. The
experiment 2 focused on the effect of horizontal and vertical number representations on
spatial biases in a paper-and-pencil bisecting tasks. In the experiment 2A the participants were
requested to bisect physical and number (2 or 9) lines horizontally and vertically. The findings
demonstrated that digit 9 strings tended to generate a more rightward bias comparing with
digit 2 strings horizontally. However in vertical condition the digit 2 strings generated a more
upperward bias respect to digit 9 strings, suggesting a top-to-bottom number line. In the
experiment 2B the participants were asked to bisect lines flanked by numbers (i.e. 1 or 7) in
four spatial arrangements: horizontal, vertical, right-diagonal and left-diagonal lines. Four
number conditions were created according to congruent or incongruent number line
representation: 1-1, 1-7, 7-1 and 7-7. The main results showed a more reliable rightward bias
in horizontal congruent condition (1-7) respect to incongruent condition (7-1). Vertically the
incongruent condition (1-7) determined a significant bias towards bottom side of line respect
to congruent condition (7-1). The experiment 2 suggested a more rigid horizontal number line
while in vertical condition the number representation could be more flexible. In the
experiment 3 we adopted the materials of experiment 2B in order to find a number line effect
on temporal (motor) performance. The participants were presented horizontal, vertical, rightdiagonal
and left-diagonal lines flanked by the same digits (i.e. 1-1 or 7-7) or by different
digits (i.e. 1-7 or 7-1). The digits were spatially congruent or incongruent with their respective
hypothesized mental representations. Participants were instructed to touch the lines either
close to the large digit, or close to the small digit, or to bisected the lines. Number processing
influenced movement execution more than movement planning. Number congruency
influenced spatial biases mostly along the horizontal but also along the vertical dimension.
These results support a two-dimensional magnitude representation. Finally, the experiment 4
addressed the visuo-spatial manipulation of number representations for accessing and retrieval
arithmetic facts. The participants were requested to perform a number-matching and an
addition verification tasks. The findings showed an interference effect between sum-nodes
and neutral-nodes only with an horizontal presentation of digit-cues, in number-matching
tasks. In the addition verification task, the performance was similar for horizontal and vertical
presentations of arithmetic problems. In conclusion the data seemed to show an automatic
activation of horizontal number line also used to retrieval arithmetic facts. The horizontal
number line seemed to be more rigid and the preferred way to order number from left-to-right.
A possible explanation could be the left-to-right direction for reading and writing. The vertical
number line seemed to be more flexible and more dependent from the tasks, reflecting
perhaps several example in the environment representing numbers either from bottom-to-top
or from top-to-bottom. However the bottom-to-top number line seemed to be activated by
explicit task demands.
Tipologia del documento
Tesi di dottorato
Autore
Fabbri, Marco
Supervisore
Dottorato di ricerca
Ciclo
20
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
linea numerica mentale effetto snarc spazio
URN:NBN
DOI
10.6092/unibo/amsdottorato/1013
Data di discussione
28 Aprile 2008
URI
Altri metadati
Tipologia del documento
Tesi di dottorato
Autore
Fabbri, Marco
Supervisore
Dottorato di ricerca
Ciclo
20
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
linea numerica mentale effetto snarc spazio
URN:NBN
DOI
10.6092/unibo/amsdottorato/1013
Data di discussione
28 Aprile 2008
URI
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