@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{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{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{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}
}
@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}
}