@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} } @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{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} } @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{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} } @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{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{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{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} } @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} } @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} } @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} } @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} } @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{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} } @phdthesis{Mueller2006, author = {M{\"u}ller, Dana}, title = {The representation of numbers in space : a journey along the mental number line}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-12949}, school = {Universit{\"a}t Potsdam}, year = {2006}, abstract = {The present thesis deals with the mental representation of numbers in space. Generally it is assumed that numbers are mentally represented on a mental number line along which they ordered in a continuous and analogical manner. Dehaene, Bossini and Giraux (1993) found that the mental number line is spatially oriented from left­-to­-right. Using a parity­-judgment task they observed faster left-hand responses for smaller numbers and faster right-hand responses for larger numbers. This effect has been labelled as Spatial Numerical Association of Response Codes (SNARC) effect. The first study of the present thesis deals with the question whether the spatial orientation of the mental number line derives from the writing system participants are adapted to. According to a strong ontogenetic interpretation the SNARC effect should only obtain for effectors closely related to the comprehension and production of written language (hands and eyes). We asked participants to indicate the parity status of digits by pressing a pedal with their left or right foot. In contrast to the strong ontogenetic view we observed a pedal SNARC effect which did not differ from the manual SNARC effect. In the second study we evaluated whether the SNARC effect reflects an association of numbers and extracorporal space or an association of numbers and hands. To do so we varied the spatial arrangement of the response buttons (vertical vs. horizontal) and the instruction (hand­related vs. button­-related). For vertically arranged buttons and a button­related instruction we found a button-­related SNARC effect. In contrast, for a hand-­related instruction we obtained a hand­-related SNARC effect. For horizontally arranged buttons and a hand­related instruction, however, we found a button­related SNARC effect. The results of the first to studies were interpreted in terms of weak ontogenetic view. In the third study we aimed to examine the functional locus of the SNARC effect. We used the psychological refractory period paradigm. In the first experiment participants first indicated the pitch of a tone and then the parity status of a digit (locus­-of-­slack paradigma). In a second experiment the order of stimulus presentation and thus tasks changed (effect­-propagation paradigm). The results led us conclude that the SNARC effect arises while the response is centrally selected. In our fourth study we test for an association of numbers and time. We asked participants to compare two serially presented digits. Participants were faster to compare ascending digit pairs (e.g., 2-­3) than descending pairs (e.g., 3-­2). The pattern of our results was interpreted in terms of forward­associations ("1­-2-­3") as formed by our ubiquitous cognitive routines to count of objects or events.}, language = {en} }