TY - JOUR A1 - Lindner, Nadja A1 - Moeller, Korbinian A1 - Hildebrandt, Frauke A1 - Hasselhorn, Marcus A1 - Lonnemann, Jan T1 - Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding JF - Frontiers in Psychology N2 - Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude. KW - spatial language KW - frames of reference KW - numerical development KW - mental number line KW - preschool children Y1 - 2022 U6 - https://doi.org/10.3389/fpsyg.2022.943191 SN - 1664-1078 SP - 1 EP - 13 PB - Frontiers CY - Lausanne, Schweiz ER - TY - GEN A1 - Lindner, Nadja A1 - Moeller, Korbinian A1 - Hildebrandt, Frauke A1 - Hasselhorn, Marcus A1 - Lonnemann, Jan T1 - Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding T2 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe N2 - Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 815 KW - spatial language KW - frames of reference KW - numerical development KW - mental number line KW - preschool children Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-581270 SN - 1866-8364 IS - 815 ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Competing Biases in Mental Arithmetic BT - When Division Is More and Multiplication Is Less JF - Frontiers in human neuroscience N2 - Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such “operational momentum” (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic. KW - heuristics and biases KW - numerical cognition KW - mental arithmetic KW - mental number line KW - operational momentum Y1 - 2017 U6 - https://doi.org/10.3389/fnhum.2017.00037 SN - 1662-5161 VL - 11 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Competing Biases in Mental Arithmetic BT - When Division Is More and Multiplication Is Less N2 - Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such “operational momentum” (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 312 KW - heuristics and biases KW - mental arithmetic KW - mental number line KW - numerical cognition KW - operational momentum Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-103492 ER - TY - JOUR A1 - Shaki, Samuel A1 - Pinhas, Michal A1 - Fischer, Martin H. T1 - Heuristics and biases in mental arithmetic BT - revisiting and reversing operational momentum JF - Thinking & Reasoning N2 - Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. KW - Heuristics KW - mental arithmetic KW - mental number line KW - operational momentum KW - problem-solving Y1 - 2017 U6 - https://doi.org/10.1080/13546783.2017.1348987 SN - 1354-6783 SN - 1464-0708 VL - 24 IS - 2 SP - 138 EP - 156 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Multiple spatial mappings in numerical cognition JF - Journal of experimental psychology : Human perception and performance N2 - A recent cross-cultural comparison (Shaki, Fischer, & Petrusic, 2009) suggested that spatially consistent processing habits for words and numbers are a necessary condition for the spatial representation of numbers (Spatial-Numerical Association of Response Codes; SNARC effect). Here we reexamine the SNARC in Israelis who read text from right to left but numbers from left to right. We show that, despite these spatially inconsistent processing habits, a SNARC effect still emerges when the response dimension is spatially orthogonal to the conflicting processing dimension. These results clarify the cognitive conditions for spatial-numerical mappings. KW - mental number line KW - reading habits KW - SNARC Y1 - 2012 U6 - https://doi.org/10.1037/a0027562 SN - 0096-1523 VL - 38 IS - 3 SP - 804 EP - 809 PB - American Psychological Association CY - Washington ER - TY - GEN A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Newborn chicks need no number tricks BT - Commentary: Number-space mapping in the newborn chick resembles humans' mental number line T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe N2 - kein Abstract T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 414 KW - mental number line KW - innate number sense KW - numerical cognition KW - spatial cognition KW - spatial numerical associations Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406425 IS - 414 ER - TY - INPR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Newborn chicks need no number tricks. Commentary: Number-space mapping in the newborn chick resembles humans' mental number line T2 - Frontiers in human neuroscienc KW - mental number line KW - innate number sense KW - numerical cognition KW - spatial cognition KW - spatial numerical associations Y1 - 2015 U6 - https://doi.org/10.3389/fnhum.2015.00451 SN - 1662-5161 VL - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Number concepts: abstract and embodied JF - Philosophical transactions of the Royal Society of London : B, Biological sciences N2 - Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind. KW - embodied cognition KW - mental arithmetic KW - mental number line KW - numerical cognition KW - SNARC effect Y1 - 2018 U6 - https://doi.org/10.1098/rstb.2017.0125 SN - 0962-8436 SN - 1471-2970 VL - 373 IS - 1752 PB - Royal Society CY - London ER - TY - INPR A1 - Kucian, Karin A1 - Plangger, Fabienne A1 - O'Gorman, Ruth A1 - von Aster, Michael G. T1 - Operational momentum effect in children with and without developmental dyscalculia T2 - Frontiers in psychology KW - developmental dyscalculia KW - operational momentum KW - children KW - learning disability KW - numerical cognition KW - mental number line KW - symbolic calculation KW - attention Y1 - 2013 U6 - https://doi.org/10.3389/fpsyg.2013.00847 SN - 1664-1078 VL - 4 IS - 45 PB - Frontiers Research Foundation CY - Lausanne ER - TY - INPR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Removing spatial responses reveals spatial concepts even in a culture with mixed reading habits T2 - Frontiers in human neuroscienc KW - cross-cultural KW - random number generation KW - mental number line KW - embodied numerical cognition KW - automatic processing Y1 - 2014 U6 - https://doi.org/10.3389/fnhum.2014.00966 SN - 1662-5161 VL - 8 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Jeglinski-Mende, Melinda A. A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Rezension zu: Varma, Sashank ; Schwartz, Daniel L.: The mental representation of integers : an abstract-to-concrete shift in the understanding of mathematical concepts. - Cognition. - 121 (2011), 3. - S. 363 - 385 T2 - Frontiers in psychology KW - cognitive development KW - mental number line KW - negative numbers KW - embodied cognition KW - abstract concepts Y1 - 2018 U6 - https://doi.org/10.3389/fpsyg.2018.00209 SN - 1664-1078 VL - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Hartmann, Matthias A1 - Mast, Fred W. A1 - Fischer, Martin H. T1 - Spatial biases during mental arithmetic BT - evidence from eye movements on a blank screen T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe N2 - While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the "mental number line"), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8-3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 426 KW - mental arithmetic KW - eye movements KW - mental number line KW - operational momentum KW - embodied cognition KW - grounded cognition Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406504 IS - 426 ER - TY - JOUR A1 - Hartmann, Matthias A1 - Mast, Fred W. A1 - Fischer, Martin H. T1 - Spatial biases during mental arithmetic: evidence from eye movements on a blank screen JF - Frontiers in psychology N2 - While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the "mental number line"), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8-3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space. KW - mental arithmetic KW - eye movements KW - mental number line KW - operational momentum KW - embodied cognition KW - grounded cognition Y1 - 2015 U6 - https://doi.org/10.3389/fpsyg.2015.00012 SN - 1664-1078 VL - 6 PB - Frontiers Research Foundation CY - Lausanne ER - 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 - INPR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Two steps to space for numbers T2 - Frontiers in psychology KW - spatial-nunmerical association KW - SNARC KW - mental number line KW - numerical cognition KW - spatial cognition Y1 - 2015 U6 - https://doi.org/10.3389/fpsyg.2015.00612 SN - 1664-1078 VL - 6 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Two steps to space for numbers T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 412 KW - spatial-nunmerical association KW - SNARC KW - mental number line KW - numerical cognition KW - spatial cognition Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406522 IS - 412 ER -