@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}
}
@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}
}
@misc{LindnerMoellerHildebrandtetal.2022,
  author    = {Lindner, Nadja and Moeller, Korbinian and Hildebrandt, Frauke and Hasselhorn, Marcus and Lonnemann, Jan},
  title     = {Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {815},
  issn      = {1866-8364},
  doi       = {10.25932/publishup-58127},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-581270},
  pages     = {13},
  year      = {2022},
  abstract  = {Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old's spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children's absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children's spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children's SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers' relative understanding of numerical magnitude.},
  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}
}
@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}
}