@article{Fischer2018,
  author    = {Fischer, Martin H.},
  title     = {Why Numbers Are Embodied Concepts},
  series = {Frontiers in Psychology},
  volume    = {8},
  journal   = {Frontiers in Psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2017.02347},
  pages     = {1 -- 3},
  year      = {2018},
  language  = {en}
}
@misc{Fischer2018,
  author    = {Fischer, Martin H.},
  title     = {Why Numbers Are Embodied Concepts},
  series = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {440},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-412097},
  pages     = {3},
  year      = {2018},
  language  = {en}
}
@misc{FischerBrugger2011,
  author    = {Fischer, Martin H. and Brugger, Peter},
  title     = {When digits help digits spatial-numerical associations point to finger counting as prime example of embodied cognition},
  series = {Frontiers in psychology},
  volume    = {2},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2011.00260},
  pages     = {7},
  year      = {2011},
  abstract  = {Spatial numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific, and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Implications of this "manumerical cognition" stance for the distinction between grounded, embodied, and situated cognition are discussed.},
  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@unpublished{FischerShaki2015,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}
}
@article{MiklashevskyLindemannFischer2021,
  author    = {Miklashevsky, Alex and Lindemann, Oliver and Fischer, Martin H.},
  title     = {The force of numbers},
  series = {Frontiers in human neuroscience / Frontiers Research Foundation},
  volume    = {14},
  journal   = {Frontiers in human neuroscience / Frontiers Research Foundation},
  publisher = {Frontiers Media},
  address   = {Lausanne},
  issn      = {1662-5161},
  doi       = {10.3389/fnhum.2020.590508},
  pages     = {16},
  year      = {2021},
  abstract  = {The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100-140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.},
  language  = {en}
}
@phdthesis{Sixtus2018,
  author    = {Sixtus, Elena},
  title     = {Subtle fingers - tangible numbers: The influence of finger counting experience on mental number representations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-420115},
  school      = {Universit{\"a}t Potsdam},
  pages     = {vi, 138},
  year      = {2018},
  abstract  = {Numbers are omnipresent in daily life. They vary in display format and in their meaning so that it does not seem self-evident that our brains process them more or less easily and flexibly. The present thesis addresses mental number representations in general, and specifically the impact of finger counting on mental number representations. Finger postures that result from finger counting experience are one of many ways to convey numerical information. They are, however, probably the one where the numerical content becomes most tangible. By investigating the role of fingers in adults' mental number representations the four presented studies also tested the Embodied Cognition hypothesis which predicts that bodily experience (e.g., finger counting) during concept acquisition (e.g., number concepts) stays an immanent part of these concepts. The studies focussed on different aspects of finger counting experience. First, consistency and further details of spontaneously used finger configurations were investigated when participants repeatedly produced finger postures according to specific numbers (Study 1). Furthermore, finger counting postures (Study 2), different finger configurations (Study 2 and 4), finger movements (Study 3), and tactile finger perception (Study 4) were investigated regarding their capability to affect number processing. Results indicated that active production of finger counting postures and single finger movements as well as passive perception of tactile stimulation of specific fingers co-activated associated number knowledge and facilitated responses towards corresponding magnitudes and number symbols. Overall, finger counting experience was reflected in specific effects in mental number processing of adult participants. This indicates that finger counting experience is an immanent part of mental number representations. Findings are discussed in the light of a novel model. The MASC (Model of Analogue and Symbolic Codes) combines and extends two established models of number and magnitude processing. Especially a symbolic motor code is introduced as an essential part of the model. It comprises canonical finger postures (i.e., postures that are habitually used to represent numbers) and finger-number associations. The present findings indicate that finger counting functions both as a sensorimotor magnitude and as a symbolic representational format and that it thereby directly mediates between physical and symbolic size. The implications are relevant both for basic research regarding mental number representations and for pedagogic practices regarding the effectiveness of finger counting as a means to acquire a fundamental grasp of numbers.},
  language  = {en}
}
@article{FischerShaki2018,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic},
  series = {Frontiers in psychology},
  volume    = {9},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2018.02453},
  pages     = {9},
  year      = {2018},
  abstract  = {Even simple mental arithmetic is fraught with cognitive biases. For example, adding repeated numbers (so-called tie problems, e.g., 2 + 2) not only has a speed and accuracy advantage over adding different numbers (e.g., 1 + 3) but may also lead to under-representation of the result relative to a standard value (Charras et al., 2012, 2014). Does the tie advantage merely reflect easier encoding or retrieval compared to non-ties, or also a distorted result representation? To answer this question, 47 healthy adults performed two tasks, both of which indicated under-representation of tie results: In a result-to-position pointing task (Experiment 1) we measured the spatial mapping of numbers and found a left-bias for tie compared to non-tie problems. In a result-to-line-length production task (Experiment 2) we measured the underlying magnitude representation directly and obtained shorter lines for tie-compared to non-tie problems. These observations suggest that the processing benefit of tie problems comes at the cost of representational reduction of result meaning. This conclusion is discussed in the context of a recent model of arithmetic heuristics and biases.},
  language  = {en}
}
@article{FischerHartmann2014,
  author    = {Fischer, Martin H. and Hartmann, Matthias},
  title     = {Pushing forward in embodied cognition: may we mouse the mathematical mind?},
  series = {Frontiers in psychology},
  volume    = {5},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2014.01315},
  pages     = {4},
  year      = {2014},
  abstract  = {Freely available software has popularized "mousetracking" to study cognitive processing; this involves the on-line recording of cursor positions while participants move a computer mouse to indicate their choice. Movement trajectories of the cursor can then be reconstructed off-line to assess the efficiency of responding in time and across space. Here we focus on the process of selecting among alternative numerical responses. Several studies have recently measured the mathematical mind with cursor movements while people decided about number magnitude or parity, computed sums or differences, or simply located numbers on a number line. After some general methodological considerations about mouse tracking we discuss several conceptual concerns that become particularly evident when "mousing" the mathematical mind.},
  language  = {en}
}
@unpublished{KucianPlanggerO'Gormanetal.2013,
  author    = {Kucian, Karin and Plangger, Fabienne and O'Gorman, Ruth and von Aster, Michael G.},
  title     = {Operational momentum effect in children with and without developmental dyscalculia},
  series = {Frontiers in psychology},
  volume    = {4},
  journal   = {Frontiers in psychology},
  number    = {45},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2013.00847},
  pages     = {3},
  year      = {2013},
  language  = {en}
}