@article{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 = {Frontiers in Psychology},
  journal   = {Frontiers in Psychology},
  publisher = {Frontiers},
  address   = {Lausanne, Schweiz},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2022.943191},
  pages     = {1 -- 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}
}
@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}
}
@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{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}
}
@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}
}