@misc{MiklashevskyFischerLindemann2022,
  author    = {Miklashevsky, Alex and Fischer, Martin H. and Lindemann, Oliver},
  title     = {Spatial-numerical associations without a motor response? Grip force says 'Yes'},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {810},
  issn      = {1866-8364},
  doi       = {10.25932/publishup-57832},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-578324},
  pages     = {12},
  year      = {2022},
  abstract  = {In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).},
  language  = {en}
}
@article{MiklashevskyFischerLindemann2022,
  author    = {Miklashevsky, Alex and Fischer, Martin H. and Lindemann, Oliver},
  title     = {Spatial-numerical associations without a motor response? Grip force says 'Yes'},
  series = {Acta Psychologica},
  volume    = {231},
  journal   = {Acta Psychologica},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1873-6297},
  doi       = {10.1016/j.actpsy.2022.103791},
  pages     = {1 -- 17},
  year      = {2022},
  abstract  = {In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).},
  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{GoebelMcCrinkFischeretal.2018,
  author    = {G{\"o}bel, Silke M. and McCrink, Koleen and Fischer, Martin H. and Shaki, Samuel},
  title     = {Observation of directional storybook reading influences young children's counting direction},
  series = {Journal of experimental child psychology},
  volume    = {166},
  journal   = {Journal of experimental child psychology},
  publisher = {Elsevier},
  address   = {New York},
  issn      = {0022-0965},
  doi       = {10.1016/j.jecp.2017.08.001},
  pages     = {49 -- 66},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{LonnemannMuellerBuettneretal.2018,
  author    = {Lonnemann, Jan and M{\"u}ller, Christian and B{\"u}ttner, Gerhard and Hasselhorn, Marcus},
  title     = {The influence of visual-spatial skills on the association between processing of nonsymbolic numerical magnitude and number word sequence skills},
  series = {Journal of experimental child psychology},
  volume    = {178},
  journal   = {Journal of experimental child psychology},
  publisher = {Elsevier},
  address   = {New York},
  issn      = {0022-0965},
  doi       = {10.1016/j.jecp.2018.09.018},
  pages     = {184 -- 197},
  year      = {2018},
  abstract  = {Nonsymbolic numerical magnitude processing skills are assumed to be fundamental to mathematical learning. Recent findings suggest that visual-spatial skills account for associations between children's performance in visually presented nonsymbolic numerical magnitude comparison tasks and their performance in visually presented arithmetic tasks. The aim of the current study was to examine whether associations between children's performance in visually presented tasks assessing nonsymbolic numerical magnitude processing skills and their performance in tasks assessing early mathematical skills, which do not involve visual stimulation, may also be mediated by visual-spatial skills. This line of reasoning is based on the assumption that children make use of mental visualization processes when working on tasks assessing early mathematical skills, such as knowledge of the sequence of number words, even when these tasks do not involve visual stimulation. We assessed 4- to 6-year-old children's performance in a nonsymbolic numerical magnitude comparison task, in tasks concerning knowledge of the sequence of number words, and in a developmental test to assess visual-spatial skills. Children's nonsymbolic numerical magnitude processing skills were found to be associated with their number word sequence skills. This association was fully mediated by interindividual differences in visual-spatial skills. The effect size of this mediation effect was small. We assume that the ability to construct mental visualizations constitutes the key factor underlying this mediation effect.},
  language  = {en}
}
@article{ReikeSchwarz2019,
  author    = {Reike, Dennis and Schwarz, Wolfgang},
  title     = {Categorizing digits and the mental number line},
  series = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  volume    = {81},
  journal   = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  number    = {3},
  publisher = {Springer},
  address   = {New York},
  issn      = {1943-3921},
  doi       = {10.3758/s13414-019-01676-w},
  pages     = {614 -- 620},
  year      = {2019},
  abstract  = {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.},
  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}
}
@article{ShakiSeryFischer2015,
  author    = {Shaki, Samuel and Sery, Noa and Fischer, Martin H.},
  title     = {1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic},
  series = {Journal of cognitive psychology},
  volume    = {27},
  journal   = {Journal of cognitive psychology},
  number    = {4},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {2044-5911},
  doi       = {10.1080/20445911.2014.973414},
  pages     = {471 -- 477},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{PinhasShakiFischer2015,
  author    = {Pinhas, Michal and Shaki, Samuel and Fischer, Martin H.},
  title     = {Addition goes where the big numbers are: evidence for a reversed operational momentum effect},
  series = {Psychonomic bulletin \& review : a journal of the Psychonomic Society},
  volume    = {22},
  journal   = {Psychonomic bulletin \& review : a journal of the Psychonomic Society},
  number    = {4},
  publisher = {Springer},
  address   = {New York},
  issn      = {1069-9384},
  doi       = {10.3758/s13423-014-0786-z},
  pages     = {993 -- 1000},
  year      = {2015},
  abstract  = {Number processing evokes spatial biases, both when dealing with single digits and in more complex mental calculations. Here we investigated whether these two biases have a common origin, by examining their flexibility. Participants pointed to the locations of arithmetic results on a visually presented line with an inverted, right-to-left number arrangement. We found directionally opposite spatial biases for mental arithmetic and for a parity task administered both before and after the arithmetic task. We discuss implications of this dissociation in our results for the task-dependent cognitive representation of numbers.},
  language  = {en}
}
@misc{WinterMatlockShakietal.2015,
  author    = {Winter, Bodo and Matlock, Teenie and Shaki, Samuel and Fischer, Martin H.},
  title     = {Mental number space in three dimensions},
  series = {Neuroscience \& biobehavioral reviews : official journal of the International Behavioral Neuroscience Society},
  volume    = {57},
  journal   = {Neuroscience \& biobehavioral reviews : official journal of the International Behavioral Neuroscience Society},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0149-7634},
  doi       = {10.1016/j.neubiorev.2015.09.005},
  pages     = {209 -- 219},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{ShakiFischer2014,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Random walks on the mental number line},
  series = {Experimental brain research},
  volume    = {232},
  journal   = {Experimental brain research},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {0014-4819},
  doi       = {10.1007/s00221-013-3718-7},
  pages     = {43 -- 49},
  year      = {2014},
  language  = {en}
}
@article{PinhasShakiFischer2014,
  author    = {Pinhas, Michal and Shaki, Samuel and Fischer, Martin H.},
  title     = {Heed the signs: Operation signs have spatial associations},
  series = {The quarterly journal of experimental psychology},
  volume    = {67},
  journal   = {The quarterly journal of experimental psychology},
  number    = {8},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-0218},
  doi       = {10.1080/17470218.2014.892516},
  pages     = {1527 -- 1540},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@article{HartmannMartarelliMastetal.2014,
  author    = {Hartmann, Matthias and Martarelli, Corinna S. and Mast, Fred W. and Stocker, Kurt},
  title     = {Eye movements during mental time travel follow a diagonal line},
  series = {Consciousness and cognition},
  volume    = {30},
  journal   = {Consciousness and cognition},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {1053-8100},
  doi       = {10.1016/j.concog.2014.09.007},
  pages     = {201 -- 209},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@article{SchwarzEiselt2012,
  author    = {Schwarz, Wolfgang and Eiselt, Anne-Kathrin},
  title     = {Numerical distance effects in visual search},
  series = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  volume    = {74},
  journal   = {Attention, perception, \& psychophysics : AP\&P ; a journal of the Psychonomic Society, Inc.},
  number    = {6},
  publisher = {Springer},
  address   = {New York},
  issn      = {1943-3921},
  doi       = {10.3758/s13414-012-0342-8},
  pages     = {1098 -- 1103},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{ShakiFischer2013,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Your neighbors define your value a study of spatial bias in number comparison},
  series = {Acta psychologica : international journal of psychonomics},
  volume    = {142},
  journal   = {Acta psychologica : international journal of psychonomics},
  number    = {3},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0001-6918},
  doi       = {10.1016/j.actpsy.2013.01.004},
  pages     = {308 -- 313},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}
@article{FischerRielloGiordanoetal.2013,
  author    = {Fischer, Martin H. and Riello, Marianna and Giordano, Bruno L. and Rusconi, Elena},
  title     = {Singing numbers ... in cognitive space - a dual-task study of the link between pitch, space, and numbers},
  series = {Topics in cognitive science},
  volume    = {5},
  journal   = {Topics in cognitive science},
  number    = {2},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {1756-8757},
  doi       = {10.1111/tops.12017},
  pages     = {354 -- 366},
  year      = {2013},
  abstract  = {We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the spatial association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension.},
  language  = {en}
}