TY - JOUR A1 - Hartmann, Matthias A1 - Laubrock, Jochen A1 - Fischer, Martin H. T1 - The visual number world BT - a dynamic approach to study the mathematical mind JF - The quarterly journal of experimental psychology N2 - In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the visual number world-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements. KW - Eye movements KW - Mental arithmetic KW - Mental number line KW - Visual world paradigm Y1 - 2018 U6 - https://doi.org/10.1080/17470218.2016.1240812 SN - 1747-0218 SN - 1747-0226 VL - 71 IS - 1 SP - 28 EP - 36 PB - Sage Publ. CY - London ER - TY - JOUR A1 - Göbel, Silke M. A1 - McCrink, Koleen A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Observation of directional storybook reading influences young children’s counting direction JF - Journal of experimental child psychology N2 - Even before formal schooling, children map numbers onto space in a directional manner. The origin of this preliterate spatial–numerical association is still debated. We investigated the role of enculturation for shaping the directionality of the association between numbers and space, focusing on counting behavior in 3- to 5-year-old preliterate children. Two studies provide evidence that, after observing reading from storybooks (left-to-right or right-to-left reading) children change their counting direction in line with the direction of observed reading. Just observing visuospatial directional movements had no such effect on counting direction. Complementarily, we document that book illustrations, prevalent in children’s cultures, exhibit directionality that conforms to the direction of a culture’s written language. We propose that shared book reading activates spatiotemporal representations of order in young children, which in turn affect their spatial representation of numbers. KW - Counting direction KW - Cross-cultural KW - Mental number line KW - Reading KW - Spatial-numerical association KW - Preschool children Y1 - 2017 U6 - https://doi.org/10.1016/j.jecp.2017.08.001 SN - 0022-0965 SN - 1096-0457 VL - 166 SP - 49 EP - 66 PB - Elsevier CY - New York ER - TY - JOUR A1 - Reike, Dennis A1 - Schwarz, Wolfgang T1 - Categorizing digits and the mental number line JF - Attention, perception, & psychophysics : AP&P ; a journal of the Psychonomic Society, Inc. N2 - Following the classical work of Moyer and Landauer (1967), experimental studies investigating the way in which humans process and compare symbolic numerical information regularly used one of two experimental designs. In selection tasks, two numbers are presented, and the task of the participant is to select (for example) the larger one. In classification tasks, a single number is presented, and the participant decides if it is smaller or larger than a predefined standard. Many findings obtained with these paradigms fit in well with the notion of a mental analog representation, or an Approximate Number System (ANS; e.g., Piazza 2010). The ANS is often conceptualized metaphorically as a mental number line, and data from both paradigms are well accounted for by diffusion models based on the stochastic accumulation of noisy partial numerical information over time. The present study investigated a categorization paradigm in which participants decided if a number presented falls into a numerically defined central category. We show that number categorization yields a highly regular, yet considerably more complex pattern of decision times and error rates as compared to the simple monotone relations obtained in traditional selection and classification tasks. We also show that (and how) standard diffusion models of number comparison can be adapted so as to account for mean and standard deviations of all RTs and for error rates in considerable quantitative detail. We conclude that just as traditional number comparison, the more complex process of categorizing numbers conforms well with basic notions of the ANS. KW - Categorization KW - Numerical distance effect KW - Mental number line KW - Diffusion models Y1 - 2019 U6 - https://doi.org/10.3758/s13414-019-01676-w SN - 1943-3921 SN - 1943-393X VL - 81 IS - 3 SP - 614 EP - 620 PB - Springer CY - New York ER - TY - JOUR A1 - Hartmann, Matthias A1 - Fischer, Martin H. A1 - Mast, Fred Walter T1 - Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition JF - The quarterly journal of experimental psychology N2 - A growing body of research shows that the human brain acts differently when performing a task together with another person than when performing the same task alone. In this study, we investigated the influence of a co-actor on numerical cognition using a joint random number generation (RNG) task. We found that participants generated relatively smaller numbers when they were located to the left (vs. right) of a co-actor (Experiment 1), as if the two individuals shared a mental number line and predominantly selected numbers corresponding to their relative body position. Moreover, the mere presence of another person on the left or right side or the processing of numbers from loudspeaker on the left or right side had no influence on the magnitude of generated numbers (Experiment 2), suggesting that a bias in RNG only emerged during interpersonal interactions. Interestingly, the effect of relative body position on RNG was driven by participants with high trait empathic concern towards others, pointing towards a mediating role of feelings of sympathy for joint compatibility effects. Finally, the spatial bias emerged only after the co-actors swapped their spatial position, suggesting that joint spatial representations are constructed only after the spatial reference frame became salient. In contrast to previous studies, our findings cannot be explained by action co-representation because the consecutive production of numbers does not involve conflict at the motor response level. Our results therefore suggest that spatial reference coding, rather than motor mirroring, can determine joint compatibility effects. Our results demonstrate how physical properties of interpersonal situations, such as the relative body position, shape seemingly abstract cognition. KW - Mental number line KW - random number generation KW - joint action KW - joint Simon effect KW - empathy KW - Interpersonal Reactivity Index Y1 - 2019 U6 - https://doi.org/10.1177/1747021818809254 SN - 1747-0218 SN - 1747-0226 VL - 72 IS - 7 SP - 1732 EP - 1740 PB - Sage Publ. CY - London 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 - Winter, Bodo A1 - Matlock, Teenie A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Mental number space in three dimensions JF - Neuroscience & biobehavioral reviews : official journal of the International Behavioral Neuroscience Society N2 - A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated. (C) 2015 Elsevier Ltd. All rights reserved. KW - Embodiment KW - Intra-parietal sulcus KW - Mental number line KW - Metaphor KW - Neglect KW - Spatial cognition KW - SNARC Y1 - 2015 U6 - https://doi.org/10.1016/j.neubiorev.2015.09.005 SN - 0149-7634 SN - 1873-7528 VL - 57 SP - 209 EP - 219 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Random walks on the mental number line JF - Experimental brain research KW - Mental number line KW - RNG KW - SNARC KW - Spatial bias KW - Walking Y1 - 2014 U6 - https://doi.org/10.1007/s00221-013-3718-7 SN - 0014-4819 SN - 1432-1106 VL - 232 IS - 1 SP - 43 EP - 49 PB - Springer CY - New York ER - TY - JOUR A1 - Pinhas, Michal A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Heed the signs: Operation signs have spatial associations JF - The quarterly journal of experimental psychology N2 - Mental arithmetic shows systematic spatial biases. The association between numbers and space is well documented, but it is unknown whether arithmetic operation signs also have spatial associations and whether or not they contribute to spatial biases found in arithmetic. Adult participants classified plus and minus signs with left and right button presses under two counterbalanced response rules. Results from two experiments showed that spatially congruent responses (i.e., right-side responses for the plus sign and left-side responses for the minus sign) were responded to faster than spatially incongruent ones (i.e., left-side responses for the plus sign and right-side responses for the minus sign). We also report correlations between this novel operation sign spatial association (OSSA) effect and other spatial biases in number processing. In a control experiment with no explicit processing requirements for the operation signs there were no sign-related spatial biases. Overall, the results suggest that (a) arithmetic operation signs can evoke spatial associations (OSSA), (b) experience with arithmetic operations probably underlies the OSSA, and (c) the OSSA only partially contributes to spatial biases in arithmetic. KW - Mental arithmetic KW - Mental number line KW - Operational momentum KW - Pointing KW - Spatial-numerical association of response codes effect Y1 - 2014 U6 - https://doi.org/10.1080/17470218.2014.892516 SN - 1747-0218 SN - 1747-0226 VL - 67 IS - 8 SP - 1527 EP - 1540 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Schwarz, Wolfgang A1 - Eiselt, Anne-Kathrin T1 - Numerical distance effects in visual search JF - Attention, perception, & psychophysics : AP&P ; a journal of the Psychonomic Society, Inc. N2 - We present three experiments in which observers searched for a target digit among distractor digits in displays in which the mean numerical target-distractor distance was varied. Search speed and accuracy increased with numerical distance in both target-present and target-absent trials (Exp. 1A). In Experiment 1B, the target 5 was replaced with the letter S. The results suggest that the findings of Experiment 1A do not simply reflect the fact that digits that were numerically closer to the target coincidentally also shared more physical features with it. In Experiment 2, the numerical distance effect increased with set size in both target-present and target-absent trials. These findings are consistent with the view that increasing numerical target-distractor distance affords faster nontarget rejection and target identification times. Recent neurobiological findings (e.g., Nieder, 2011) on the neuronal coding of numerosity have reported a width of tuning curves of numerosity-selective neurons that suggests graded, distance-dependent coactivation of the representations of adjacent numbers, which in visual search would make it harder to reject numerically closer distractors as nontargets. KW - Numerical distance effect KW - Visual search KW - Category effect KW - Mental number line KW - Numerical magnitude Y1 - 2012 U6 - https://doi.org/10.3758/s13414-012-0342-8 SN - 1943-3921 VL - 74 IS - 6 SP - 1098 EP - 1103 PB - Springer CY - New York 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 -