@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}
}
@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{FischerShaki2014,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Spatial associations in numerical cognition-From single digits to arithmetic},
  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       = {10.1080/17470218.2014.927515},
  pages     = {1461 -- 1483},
  year      = {2014},
  abstract  = {The literature on spatial associations during number processing is dominated by the SNARC (spatial-numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the "original" speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies.},
  language  = {en}
}