@article{HartmannMastFischer2015,
  author    = {Hartmann, Matthias and Mast, Fred W. and Fischer, Martin H.},
  title     = {Spatial biases during mental arithmetic: evidence from eye movements on a blank screen},
  series = {Frontiers in psychology},
  volume    = {6},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2015.00012},
  pages     = {8},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{HartmannLaubrockFischer2018,
  author    = {Hartmann, Matthias and Laubrock, Jochen and Fischer, Martin H.},
  title     = {The visual number world},
  series = {The quarterly journal of experimental psychology},
  volume    = {71},
  journal   = {The quarterly journal of experimental psychology},
  number    = {1},
  publisher = {Sage Publ.},
  address   = {London},
  issn      = {1747-0218},
  doi       = {10.1080/17470218.2016.1240812},
  pages     = {28 -- 36},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{HartmannFischerMast2019,
  author    = {Hartmann, Matthias and Fischer, Martin H. and Mast, Fred Walter},
  title     = {Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition},
  series = {The quarterly journal of experimental psychology},
  volume    = {72},
  journal   = {The quarterly journal of experimental psychology},
  number    = {7},
  publisher = {Sage Publ.},
  address   = {London},
  issn      = {1747-0218},
  doi       = {10.1177/1747021818809254},
  pages     = {1732 -- 1740},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@unpublished{HartmannFischer2014,
  author    = {Hartmann, Matthias and Fischer, Martin H.},
  title     = {Pupillometry: The eyes shed fresh light on the mind},
  series = {Current biology},
  volume    = {24},
  journal   = {Current biology},
  number    = {7},
  publisher = {Cell Press},
  address   = {Cambridge},
  issn      = {0960-9822},
  doi       = {10.1016/j.cub.2014.02.028},
  pages     = {R281 -- R282},
  year      = {2014},
  language  = {en}
}
@article{FischerHartmann2014,
  author    = {Fischer, Martin H. and Hartmann, Matthias},
  title     = {Pushing forward in embodied cognition: may we mouse the mathematical mind?},
  series = {Frontiers in psychology},
  volume    = {5},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2014.01315},
  pages     = {4},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}