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 - GEN A1 - Fischer, Martin H. A1 - Sixtus, Elena A1 - Göbel, Silke M. T1 - Commentary BT - a pointer about grasping numbers T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe N2 - kein Abstract vorhanden T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 420 KW - numerical cognition KW - embodied cognition KW - gestures KW - numeracy training KW - mathematical cognition Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406260 IS - 420 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 - 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 - 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 - INPR A1 - Fischer, Martin H. A1 - Sixtus, Elena A1 - Göbel, Silke M. T1 - Commentary: A pointer about grasping numbers T2 - Frontiers in psychology KW - numerical cognition KW - embodied cognition KW - gestures KW - numeracy training KW - mathematical cognition Y1 - 2015 U6 - https://doi.org/10.3389/fpsyg.2015.00227 VL - 6 PB - Frontiers Research Foundation CY - Lausanne 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 - JOUR A1 - Shaki, Samuel A1 - Sery, Noa A1 - Fischer, Martin H. T1 - 1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic JF - Journal of cognitive psychology N2 - Over the past decade or so, a large number of studies have revealed that conceptual meaning is sensitive to situational context. More recently, similar contextual influences have been documented in the domain of number knowledge. Here we show such context dependency in a length production task. Adult participants saw single digit addition problems of the form n1 + n2 and produced the sum by changing bi-directionally the length of a horizontally extended line, using radially arranged buttons. We found that longer lines were produced when n1 < n2 compared to n1 > n2 and that unit size increased with result size. Thus, the mathematical axioms of commutativity and identity do not seem to hold in mental addition. We discuss implications of these observations for our understanding of cognitive mechanisms involved in mental arithmetic and for situated cognition generally. KW - Operand order effect KW - Situated cognition KW - Mental number line KW - SNARC KW - Operational momentum Y1 - 2015 U6 - https://doi.org/10.1080/20445911.2014.973414 SN - 2044-5911 SN - 2044-592X VL - 27 IS - 4 SP - 471 EP - 477 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Wasner, Mirjam A1 - Möller, Korbinian A1 - Fischer, Martin H. A1 - Nuerk, Hans-Christoph T1 - Related but not the same: Ordinality, cardinality and 1-to-1 correspondence in finger-based numerical representations JF - Journal of cognitive psychology N2 - Finger-based numerical representations have gained increasing research interest. However, their description and assessment often refer to different numerical principles of ordinality, cardinality and 1-to-1 correspondence. Our aim was to investigate similarities and differences between these principles in finger-based numerical representations. Sixty-eight healthy adults performed ordinal finger counting, cardinal finger montring (showing the number of gestures) and finger-to-number mapping with twisted arms and fingers. We found that counting gestures and montring postures were identical for Number 10 but differed to varying degrees for other numbers. Interestingly, there was no systematic relation between finger-to-number mapping and ordinal finger counting habits. These data question the assumption of a unitary embodied finger-based numerical representation, but suggest that different finger-based representations co-exist and can be recruited flexibly depending on the numerical aspects to be conveyed. KW - Finger-based numerical representations KW - Finger counting KW - 1-to-1 Correspondence KW - Cardinality KW - Ordinality Y1 - 2015 U6 - https://doi.org/10.1080/20445911.2014.964719 SN - 2044-5911 SN - 2044-592X VL - 27 IS - 4 SP - 426 EP - 441 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - INPR A1 - Lindemann, Oliver A1 - Fischer, Martin H. T1 - Embodied number processing T2 - Journal of cognitive psychology Y1 - 2015 U6 - https://doi.org/10.1080/20445911.2015.1032295 SN - 2044-5911 SN - 2044-592X VL - 27 IS - 4 SP - 381 EP - 387 PB - Routledge, Taylor & Francis Group CY - Abingdon ER -