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 - 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 - Hartmann, Matthias A1 - Mast, Fred W. A1 - Fischer, Martin H. T1 - Counting is a spatial process: evidence from eye movements JF - Psychological research : an international journal of perception, attention, memory, and action N2 - Spatial-numerical associations (small numbers-left/lower space and large numbers-right/upper space) are regularly found in simple number categorization tasks. These associations were taken as evidence for a spatially oriented mental number line. However, the role of spatial-numerical associations during more complex number processing, such as counting or mental arithmetic is less clear. Here, we investigated whether counting is associated with a movement along the mental number line. Participants counted aloud upward or downward in steps of 3 for 45 s while looking at a blank screen. Gaze position during upward counting shifted rightward and upward, while the pattern for downward counting was less clear. Our results, therefore, confirm the hypothesis of a movement along the mental number line for addition. We conclude that space is not only used to represent number magnitudes but also to actively operate on numbers in more complex tasks such as counting, and that the eyes reflect this spatial mental operation. Y1 - 2016 U6 - https://doi.org/10.1007/s00426-015-0722-5 SN - 0340-0727 SN - 1430-2772 VL - 80 SP - 399 EP - 409 PB - Springer CY - Heidelberg 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 - JOUR A1 - Hartmann, Matthias A1 - Martarelli, Corinna S. A1 - Mast, Fred W. A1 - Stocker, Kurt T1 - Eye movements during mental time travel follow a diagonal line JF - Consciousness and cognition N2 - Recent research showed that past events are associated with the back and left side, whereas future events are associated with the front and right side of space. These spatial-temporal associations have an impact on our sensorimotor system: thinking about one's past and future leads to subtle body sways in the sagittal dimension of space (Miles, Nind, & Macrae, 2010). In this study we investigated whether mental time travel leads to sensorimotor correlates in the horizontal dimension of space. Participants were asked to mentally displace themselves into the past or future while measuring their spontaneous eye movements on a blank screen. Eye gaze was directed more rightward and upward when thinking about the future than when thinking about the past. Our results provide further insight into the spatial nature of temporal thoughts, and show that not only body, but also eye movements follow a (diagonal) "time line" during mental time travel. (C) 2014 Elsevier Inc. All rights reserved. KW - Mental time travel KW - Eye movements KW - Mental time line KW - Spatial-temporal association KW - Future KW - Past KW - Embodied cognition KW - Metaphors KW - Mental number line Y1 - 2014 U6 - https://doi.org/10.1016/j.concog.2014.09.007 SN - 1053-8100 SN - 1090-2376 VL - 30 SP - 201 EP - 209 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Fischer, Martin H. A1 - Hartmann, Matthias T1 - Pushing forward in embodied cognition: may we mouse the mathematical mind? JF - Frontiers in psychology N2 - Freely available software has popularized "mousetracking" to study cognitive processing; this involves the on-line recording of cursor positions while participants move a computer mouse to indicate their choice. Movement trajectories of the cursor can then be reconstructed off-line to assess the efficiency of responding in time and across space. Here we focus on the process of selecting among alternative numerical responses. Several studies have recently measured the mathematical mind with cursor movements while people decided about number magnitude or parity, computed sums or differences, or simply located numbers on a number line. After some general methodological considerations about mouse tracking we discuss several conceptual concerns that become particularly evident when "mousing" the mathematical mind. KW - mousetracking KW - numerical cognition KW - SNARC effect KW - trajectories KW - on-line processing Y1 - 2014 U6 - https://doi.org/10.3389/fpsyg.2014.01315 SN - 1664-1078 VL - 5 PB - Frontiers Research Foundation CY - Lausanne ER -