TY - THES A1 - Müller, Dana T1 - The representation of numbers in space : a journey along the mental number line T1 - Die Repräsentation von Zahlen im Raum : eine Reise entlang des mentalen Zahlenstrahls N2 - The present thesis deals with the mental representation of numbers in space. Generally it is assumed that numbers are mentally represented on a mental number line along which they ordered in a continuous and analogical manner. Dehaene, Bossini and Giraux (1993) found that the mental number line is spatially oriented from left­-to­-right. Using a parity­-judgment task they observed faster left-hand responses for smaller numbers and faster right-hand responses for larger numbers. This effect has been labelled as Spatial Numerical Association of Response Codes (SNARC) effect. The first study of the present thesis deals with the question whether the spatial orientation of the mental number line derives from the writing system participants are adapted to. According to a strong ontogenetic interpretation the SNARC effect should only obtain for effectors closely related to the comprehension and production of written language (hands and eyes). We asked participants to indicate the parity status of digits by pressing a pedal with their left or right foot. In contrast to the strong ontogenetic view we observed a pedal SNARC effect which did not differ from the manual SNARC effect. In the second study we evaluated whether the SNARC effect reflects an association of numbers and extracorporal space or an association of numbers and hands. To do so we varied the spatial arrangement of the response buttons (vertical vs. horizontal) and the instruction (hand­related vs. button­-related). For vertically arranged buttons and a button­related instruction we found a button-­related SNARC effect. In contrast, for a hand-­related instruction we obtained a hand­-related SNARC effect. For horizontally arranged buttons and a hand­related instruction, however, we found a button­related SNARC effect. The results of the first to studies were interpreted in terms of weak ontogenetic view. In the third study we aimed to examine the functional locus of the SNARC effect. We used the psychological refractory period paradigm. In the first experiment participants first indicated the pitch of a tone and then the parity status of a digit (locus­-of-­slack paradigma). In a second experiment the order of stimulus presentation and thus tasks changed (effect­-propagation paradigm). The results led us conclude that the SNARC effect arises while the response is centrally selected. In our fourth study we test for an association of numbers and time. We asked participants to compare two serially presented digits. Participants were faster to compare ascending digit pairs (e.g., 2-­3) than descending pairs (e.g., 3-­2). The pattern of our results was interpreted in terms of forward­associations (“1­-2-­3”) as formed by our ubiquitous cognitive routines to count of objects or events. N2 - Die vorliegende Arbeit beschäftigt sich mit der räumlichen Repräsentation von Zahlen. Generell wird angenommen, dass Zahlen in einer kontinuierlichen und analogen Art und Weise auf einem mentalen Zahlenstrahl repräsentiert werden. Dehaene, Bossini und Giraux (1993) zeigten, dass der mentale Zahlenstrahl eine räumliche Orientierung von links­-nach­-rechts aufweist. In einer Paritätsaufgabe fanden sie schnellere Links-hand­ Antworten auf kleine Zahlen und schnellere Rechts-hand Antworten auf große Zahlen. Dieser Effekt wurde Spatial Numerical Association of Response Codes (SNARC) Effekt genannt. In der ersten Studie der vorliegenden Arbeit ging es um den Einfluss der Schriftrichtung auf den SNARC Effekt. Eine strenge ontogenetische Sichtweise sagt vorher, dass der SNARC Effekt nur mit Effektoren, die unmittelbar in die Produktion und das Verstehen von Schriftsprache involviert sind, auftreten sollte (Hände und Augen). Um dies zu überprüfen, forderten wir Versuchspersonen auf, die Parität dargestellter Ziffern durch Tastendruck mit ihrem rechten oder linken Fuß anzuzeigen. Entgegen der strengen ontogenetischen Hypothese fanden wir den SNARC Effekt auch für Fußantworten, welcher sich in seiner Charakteristik nicht von dem manuellen SNARC Effekt unterschied. In der zweiten Studie gingen wir der Frage nach, ob dem SNARC Effekt eine Assoziation des nicht-­körperbezogenen Raumes und Zahlen oder der Hände und Zahlen zugrunde liegt. Um dies zu untersuchen, variierten wir die räumliche Orientierung der Tasten zueinander (vertikal vs. horizontal) als auch die Instruktionen (hand-­bezogen vs. knopf­-bezogen). Bei einer vertikalen Knopfanordnung und einer knopf-­bezogenen Instruktion fanden wir einen knopf­bezogenen SNARC Effekt. Bei einer hand-­bezogenen Instruktion fanden wir einen hand-­bezogenen SNARC Effekt. Mit horizontal angeordneten Knöpfen gab es unabhängig von der Instruktion einen knopf-­bezogenen SNARC Effekt. Die Ergebnisse dieser beiden ersten Studien wurden im Sinne einer schwachen ontogenetischen Sichtweise interpretiert. In der dritten Studie befassten wir uns mit dem funktionalen Ursprung des SNARC Effekts. Hierfür nutzten wir das Psychological Refractory Period (PRP) Paradigma. In einem ersten Experiment hörten Versuchspersonen zuerst einen Ton nach welchem eine Ziffer visuell präsentiert wurde (locus-­of-­slack Paradigma). In einem zweiten Experiment wurde die Reihenfolge der Stimuluspräsentation/Aufgaben umgedreht (effect­-propagation Paradigma). Unsere Ergebnisse lassen vermuten, dass der SNARC Effekt während der zentralen Antwortselektion generiert wird. In unserer vierten Studie überprüften wir, ob Zahlen auch mit Zeit assoziiert werden. Wir forderten Versuchspersonen auf zwei seriell dargebotene Zahlen miteinander zu vergleichen. Versuchspersonen waren schneller zeitlich aufsteigende Zahlen (z.B. erst 2 dann 3) als zeitlich abfolgenden Zahlen (z.B. erst 3 dann 2) miteinander zu vergleichen. Unsere Ergebnisse wurden im Sinne unseres vorwärtsgerichteten Mechanismus des Zählens („1-­2-­3“) interpretiert. KW - numerische Kognition KW - mentaler Zahlenstrahl KW - SNARC Effekt KW - Numerical cognition KW - mental number line KW - SNARC effect Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-12949 ER - TY - JOUR A1 - Fischer, Martin H. T1 - A hierarchical view of grounded, embodied, and situated numerical cognition JF - Cognitive processing : international quarterly of cognitive science N2 - There is much recent interest in the idea that we represent our knowledge together with the sensory and motor features that were activated during its acquisition. This paper reviews the evidence for such "embodiment" in the domain of numerical cognition, a traditional stronghold of abstract theories of knowledge representation. The focus is on spatial-numerical associations, such as the SNARC effect (small numbers are associated with left space, larger numbers with right space). Using empirical evidence from behavioral research, I first describe sensory and motor biases induced by SNARC, thus identifying numbers as embodied concepts. Next, I propose a hierarchical relationship between grounded, embodied, and situated aspects of number knowledge. This hierarchical conceptualization helps to understand the variety of SNARC-related findings and yields testable predictions about numerical cognition. I report several such tests, ranging from cross-cultural comparisons of horizontal and vertical SNARC effects (Shaki and Fischer in J Exp Psychol Hum Percept Perform 38(3): 804-809, 2012) to motor cortical activation studies in adults with left- and right-hand counting preferences (Tschentscher et al. in NeuroImage 59: 3139-3148, 2012). It is concluded that the diagnostic features for each level of the proposed hierarchical knowledge representation, together with the spatial associations of numbers, make the domain of numerical knowledge an ideal testing ground for embodied cognition research. KW - Embodied cognition KW - Grounded cognition KW - Numerical cognition KW - SNARC effect Y1 - 2012 U6 - https://doi.org/10.1007/s10339-012-0477-5 SN - 1612-4782 VL - 13 SP - S161 EP - S164 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. A1 - Goebel, Silke M. T1 - Direction counts A comparative study of spatially directional counting biases in cultures with different reading directions JF - Journal of experimental child psychology N2 - Western adults associate small numbers with left space and large numbers with right space. Where does this pervasive spatial-numerical association come from? In this study, we first recorded directional counting preferences in adults with different reading experiences (left to right, right to left, mixed, and illiterate) and observed a clear relationship between reading and counting directions. We then recorded directional counting preferences in pre-schoolers and elementary school children from three of these reading cultures (left to right, right to left, and mixed). Culture-specific counting biases existed before reading acquisition in children as young as 3 years and were subsequently modified by early reading experience. Together, our results suggest that both directional counting and scanning activities contribute to number-space associations. KW - Counting KW - Numerical cognition KW - Reading direction KW - Number-space association KW - Mental Number KW - Cross-cultural Y1 - 2012 U6 - https://doi.org/10.1016/j.jecp.2011.12.005 SN - 0022-0965 VL - 112 IS - 2 SP - 275 EP - 281 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Your neighbors define your value a study of spatial bias in number comparison JF - Acta psychologica : international journal of psychonomics N2 - Several chronometric biases in numerical cognition have informed our understanding of a mental number line (MNL). Complementing this approach, we investigated spatial performance in a magnitude comparison task. Participants located the larger or smaller number of a pair on a horizontal line representing the interval from 0 to 10. Experiments 1 and 2 used only number pairs one unit apart and found that digits were localized farther to the right with "select larger" instructions than with "select smaller" instructions. However, when numerical distance was varied (Experiment 3), digits were localized away from numerically near neighbors. This repulsion effect reveals context-specific distortions in number representation not previously noticed with chronometric measures. KW - Magnitude comparison KW - Mental number line KW - Numerical cognition KW - Spatial bias Y1 - 2013 U6 - https://doi.org/10.1016/j.actpsy.2013.01.004 SN - 0001-6918 VL - 142 IS - 3 SP - 308 EP - 313 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Spatial associations in numerical cognition-From single digits to arithmetic JF - The quarterly journal of experimental psychology N2 - The literature on spatial associations during number processing is dominated by the SNARC (spatial-numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the "original" speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies. KW - Embodied cognition KW - Mental arithmetic KW - Numerical cognition KW - Operational momentum KW - Spatial-numerical association of response codes KW - SNARC Y1 - 2014 U6 - https://doi.org/10.1080/17470218.2014.927515 SN - 1747-0218 SN - 1747-0226 VL - 67 IS - 8 SP - 1461 EP - 1483 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Wiemers, Michael A1 - Bekkering, Harold A1 - Lindemann, Oliver T1 - Spatial interferences in mental arithmetic: Evidence from the motion-arithmetic compatibility effect JF - The quarterly journal of experimental psychology N2 - Recent research on spatial number representations suggests that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of the problem-solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and the vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space. KW - Mental arithmetic KW - Numerical cognition KW - Spatial-numerical associations KW - Embodied cognition Y1 - 2014 U6 - https://doi.org/10.1080/17470218.2014.889180 SN - 1747-0218 SN - 1747-0226 VL - 67 IS - 8 SP - 1557 EP - 1570 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Sixtus, Elena A1 - Fischer, Martin H. A1 - Lindemann, Oliver T1 - Finger posing primes number comprehension JF - Cognitive processing : international quarterly of cognitive science N2 - Canonical finger postures, as used in counting, activate number knowledge, but the exact mechanism for this priming effect is unclear. Here we dissociated effects of visual versus motor priming of number concepts. In Experiment 1, participants were exposed either to pictures of canonical finger postures (visual priming) or actively produced the same finger postures (motor priming) and then used foot responses to rapidly classify auditory numbers (targets) as smaller or larger than 5. Classification times revealed that manually adopted but not visually perceived postures primed magnitude classifications. Experiment 2 obtained motor priming of number processing through finger postures also with vocal responses. Priming only occurred through canonical and not through non-canonical finger postures. Together, these results provide clear evidence for motor priming of number knowledge. Relative contributions of vision and action for embodied numerical cognition and the importance of canonicity of postures are discussed. KW - Embodied cognition KW - Finger counting KW - Numerical cognition KW - Priming Y1 - 2017 U6 - https://doi.org/10.1007/s10339-017-0804-y SN - 1612-4782 SN - 1612-4790 VL - 18 SP - 237 EP - 248 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Reike, Dennis A1 - Schwarz, Wolfgang T1 - Exploring the origin of the number-size congruency effect BT - sensitivity or response bias? JF - Attention, perception, & psychophysics : AP&P ; a journal of the Psychonomic Society, Inc. N2 - Physical size modulates the efficiency of digit comparison, depending on whether the relation of numerical magnitude and physical size is congruent or incongruent (Besner & Coltheart, Neuropsychologia, 17, 467–472, 1979), the number-size congruency effect (NSCE). In addition, Henik and Tzelgov (Memory & Cognition, 10, 389–395, 1982) first reported an NSCE for the reverse task of comparing the physical size of digits such that the numerical magnitude of digits modulated the time required to compare their physical sizes. Does the NSCE in physical comparisons simply reflect a number-mediated bias mechanism related to making decisions and selecting responses about the digit’s sizes? Alternatively, or in addition, the NSCE might indicate a true increase in the ability to discriminate small and large font sizes when these sizes are congruent with the digit’s symbolic numerical meaning, over and above response bias effects. We present a new research design that permits us to apply signal detection theory to a task that required observers to judge the physical size of digits. Our results clearly demonstrate that the NSCE cannot be reduced to mere response bias effects, and that genuine sensitivity gains for congruent number-size pairings contribute to the NSCE. KW - Numerical cognition KW - Number-size congruity effect KW - Signal detection theory Y1 - 2017 U6 - https://doi.org/10.3758/s13414-016-1267-4 SN - 1943-3921 SN - 1943-393X VL - 79 SP - 383 EP - 388 PB - Springer CY - New York ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Deconstructing spatial-numerical associations JF - Cognition : international journal of cognitive science N2 - Spatial-numerical associations (SNAs) have been studied extensively in the past two decades, always requiring either explicit magnitude processing or explicit spatial-directional processing. This means that the typical finding of an association of small numbers with left or bottom space and of larger numbers with right or top space could be due to these requirements and not the conceptual representation of numbers. The present study compares explicit and implicit magnitude processing in an implicit spatial-directional task and identifies SNAs as artefacts of either explicit magnitude processing or explicit spatial-directional processing; they do not reveal spatial conceptual links. This finding requires revision of current accounts of the relationship between numbers and space. KW - Go/no-go task KW - Implicit association task KW - Numerical cognition KW - SNARC effect Y1 - 2018 U6 - https://doi.org/10.1016/j.cognition.2018.02.022 SN - 0010-0277 SN - 1873-7838 VL - 175 SP - 109 EP - 113 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - D'Ascenzo, Stefania A1 - Lugli, Luisa A1 - Nicoletti, Roberto A1 - Fischer, Martin H. T1 - Assessing orienting of attention to understand the time course of mental calculation JF - Cognitive processing : international quarterly of cognitive science N2 - Number processing induces spatial attention shifts to the left or right side for small or large numbers, respectively. This spatial-numerical association (SNA) extends to mental calculation, such that subtractions and additions induce left or right biases, respectively. However, the time course of activating SNAs during mental calculation is unclear. Here, we addressed this issue by measuring visual position discrimination during auditory calculation. Thirty-four healthy adults listened in each trial to five successive elements of arithmetic facts (first operand, operator, second operand, equal and result) and verbally classified their correctness. After each element (except for the result), a fixation dot moved equally often to either the left or right side and participants pressed left or right buttons to discriminate its movement direction (four times per trial). First and second operand magnitude (small/large), operation (addition/subtraction), result correctness (right/wrong) and movement direction (left/right) were balanced across 128 trials. Manual reaction times of dot movement discriminations were considered in relation to previous arithmetic elements. We found no evidence of early attentional shifts after first operand and operator presentation. Discrimination performance was modulated consistent with SNAs after the second operand, suggesting that attentional shifts occur once there is access to all elements necessary to complete an arithmetic operation. Such late-occurring attention shifts may reflect a combination of multiple element-specific biases and confirm their functional role in mental calculation. KW - Attention KW - Mental arithmetic KW - Numerical cognition KW - Spatial-numerical KW - associations Y1 - 2020 U6 - https://doi.org/10.1007/s10339-020-00970-y SN - 1612-4782 SN - 1612-4790 VL - 21 IS - 4 SP - 493 EP - 500 PB - Springer CY - Heidelberg ; Berlin ER -