@article{ShakiFischer2017,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Competing Biases in Mental Arithmetic},
  series = {Frontiers in human neuroscience},
  volume    = {11},
  journal   = {Frontiers in human neuroscience},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2017.00037},
  year      = {2017},
  abstract  = {Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such "operational momentum" (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.},
  language  = {en}
}
@misc{ShakiFischer2017,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Competing Biases in Mental Arithmetic},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103492},
  pages     = {5},
  year      = {2017},
  abstract  = {Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such "operational momentum" (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.},
  language  = {en}
}
@article{ShakiPinhasFischer2017,
  author    = {Shaki, Samuel and Pinhas, Michal and Fischer, Martin H.},
  title     = {Heuristics and biases in mental arithmetic},
  series = {Thinking \& Reasoning},
  volume    = {24},
  journal   = {Thinking \& Reasoning},
  number    = {2},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1354-6783},
  doi       = {10.1080/13546783.2017.1348987},
  pages     = {138 -- 156},
  year      = {2017},
  abstract  = {Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving.},
  language  = {en}
}
@article{ShakiFischer2012,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Multiple spatial mappings in numerical cognition},
  series = {Journal of experimental psychology : Human perception and performance},
  volume    = {38},
  journal   = {Journal of experimental psychology : Human perception and performance},
  number    = {3},
  publisher = {American Psychological Association},
  address   = {Washington},
  issn      = {0096-1523},
  doi       = {10.1037/a0027562},
  pages     = {804 -- 809},
  year      = {2012},
  abstract  = {A recent cross-cultural comparison (Shaki, Fischer, \& Petrusic, 2009) suggested that spatially consistent processing habits for words and numbers are a necessary condition for the spatial representation of numbers (Spatial-Numerical Association of Response Codes; SNARC effect). Here we reexamine the SNARC in Israelis who read text from right to left but numbers from left to right. We show that, despite these spatially inconsistent processing habits, a SNARC effect still emerges when the response dimension is spatially orthogonal to the conflicting processing dimension. These results clarify the cognitive conditions for spatial-numerical mappings.},
  language  = {en}
}
@misc{ShakiFischer2015,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Newborn chicks need no number tricks},
  series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {414},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-406425},
  pages     = {3},
  year      = {2015},
  abstract  = {kein Abstract},
  language  = {en}
}
@unpublished{ShakiFischer2015,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Newborn chicks need no number tricks. Commentary: Number-space mapping in the newborn chick resembles humans' mental number line},
  series = {Frontiers in human neuroscienc},
  volume    = {9},
  journal   = {Frontiers in human neuroscienc},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2015.00451},
  pages     = {3},
  year      = {2015},
  language  = {en}
}
@misc{FischerShaki2018,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Number concepts: abstract and embodied},
  series = {Philosophical transactions of the Royal Society of London : B, Biological sciences},
  volume    = {373},
  journal   = {Philosophical transactions of the Royal Society of London : B, Biological sciences},
  number    = {1752},
  publisher = {Royal Society},
  address   = {London},
  issn      = {0962-8436},
  doi       = {10.1098/rstb.2017.0125},
  pages     = {8},
  year      = {2018},
  abstract  = {Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind.},
  language  = {en}
}
@unpublished{ShakiFischer2014,
  author    = {Shaki, Samuel and Fischer, Martin H.},
  title     = {Removing spatial responses reveals spatial concepts even in a culture with mixed reading habits},
  series = {Frontiers in human neuroscienc},
  volume    = {8},
  journal   = {Frontiers in human neuroscienc},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2014.00966},
  pages     = {2},
  year      = {2014},
  language  = {en}
}
@misc{JeglinskiMendeShakiFischer2018,
  author    = {Jeglinski-Mende, Melinda A. and Shaki, Samuel and Fischer, Martin H.},
  title     = {Rezension zu: Varma, Sashank ; Schwartz, Daniel L.: The mental representation of integers : an abstract-to-concrete shift in the understanding of mathematical concepts. - Cognition. - 121 (2011), 3. - S. 363 - 385},
  series = {Frontiers in psychology},
  volume    = {9},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2018.00209},
  pages     = {4},
  year      = {2018},
  language  = {en}
}
@misc{HartmannMastFischer2015,
  author    = {Hartmann, Matthias and Mast, Fred W. and Fischer, Martin H.},
  title     = {Spatial biases during mental arithmetic},
  series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {426},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-406504},
  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{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}
}
@unpublished{FischerShaki2015,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Two steps to space for numbers},
  series = {Frontiers in psychology},
  volume    = {6},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2015.00612},
  pages     = {3},
  year      = {2015},
  language  = {en}
}
@misc{FischerShaki2015,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Two steps to space for numbers},
  series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {412},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-406522},
  pages     = {3},
  year      = {2015},
  language  = {en}
}