@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}
}