TY - JOUR A1 - Hartmann, Matthias A1 - Laubrock, Jochen A1 - Fischer, Martin H. T1 - The visual number world BT - a dynamic approach to study the mathematical mind JF - The quarterly journal of experimental psychology N2 - In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the visual number world-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements. KW - Eye movements KW - Mental arithmetic KW - Mental number line KW - Visual world paradigm Y1 - 2018 U6 - https://doi.org/10.1080/17470218.2016.1240812 SN - 1747-0218 SN - 1747-0226 VL - 71 IS - 1 SP - 28 EP - 36 PB - Sage Publ. CY - London ER - TY - JOUR A1 - Wiemers, Michael A1 - Bekkering, Harold A1 - Lindemann, Oliver T1 - Spatial interferences in mental arithmetic: Evidence from the motion-arithmetic compatibility effect JF - The quarterly journal of experimental psychology N2 - Recent research on spatial number representations suggests that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of the problem-solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and the vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space. KW - Mental arithmetic KW - Numerical cognition KW - Spatial-numerical associations KW - Embodied cognition Y1 - 2014 U6 - https://doi.org/10.1080/17470218.2014.889180 SN - 1747-0218 SN - 1747-0226 VL - 67 IS - 8 SP - 1557 EP - 1570 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Spatial associations in numerical cognition-From single digits to arithmetic JF - The quarterly journal of experimental psychology N2 - The literature on spatial associations during number processing is dominated by the SNARC (spatial-numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the "original" speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies. KW - Embodied cognition KW - Mental arithmetic KW - Numerical cognition KW - Operational momentum KW - Spatial-numerical association of response codes KW - SNARC Y1 - 2014 U6 - https://doi.org/10.1080/17470218.2014.927515 SN - 1747-0218 SN - 1747-0226 VL - 67 IS - 8 SP - 1461 EP - 1483 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Pinhas, Michal A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Heed the signs: Operation signs have spatial associations JF - The quarterly journal of experimental psychology N2 - Mental arithmetic shows systematic spatial biases. The association between numbers and space is well documented, but it is unknown whether arithmetic operation signs also have spatial associations and whether or not they contribute to spatial biases found in arithmetic. Adult participants classified plus and minus signs with left and right button presses under two counterbalanced response rules. Results from two experiments showed that spatially congruent responses (i.e., right-side responses for the plus sign and left-side responses for the minus sign) were responded to faster than spatially incongruent ones (i.e., left-side responses for the plus sign and right-side responses for the minus sign). We also report correlations between this novel operation sign spatial association (OSSA) effect and other spatial biases in number processing. In a control experiment with no explicit processing requirements for the operation signs there were no sign-related spatial biases. Overall, the results suggest that (a) arithmetic operation signs can evoke spatial associations (OSSA), (b) experience with arithmetic operations probably underlies the OSSA, and (c) the OSSA only partially contributes to spatial biases in arithmetic. KW - Mental arithmetic KW - Mental number line KW - Operational momentum KW - Pointing KW - Spatial-numerical association of response codes effect Y1 - 2014 U6 - https://doi.org/10.1080/17470218.2014.892516 SN - 1747-0218 SN - 1747-0226 VL - 67 IS - 8 SP - 1527 EP - 1540 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - D'Ascenzo, Stefania A1 - Lugli, Luisa A1 - Nicoletti, Roberto A1 - Fischer, Martin H. T1 - Assessing orienting of attention to understand the time course of mental calculation JF - Cognitive processing : international quarterly of cognitive science N2 - Number processing induces spatial attention shifts to the left or right side for small or large numbers, respectively. This spatial-numerical association (SNA) extends to mental calculation, such that subtractions and additions induce left or right biases, respectively. However, the time course of activating SNAs during mental calculation is unclear. Here, we addressed this issue by measuring visual position discrimination during auditory calculation. Thirty-four healthy adults listened in each trial to five successive elements of arithmetic facts (first operand, operator, second operand, equal and result) and verbally classified their correctness. After each element (except for the result), a fixation dot moved equally often to either the left or right side and participants pressed left or right buttons to discriminate its movement direction (four times per trial). First and second operand magnitude (small/large), operation (addition/subtraction), result correctness (right/wrong) and movement direction (left/right) were balanced across 128 trials. Manual reaction times of dot movement discriminations were considered in relation to previous arithmetic elements. We found no evidence of early attentional shifts after first operand and operator presentation. Discrimination performance was modulated consistent with SNAs after the second operand, suggesting that attentional shifts occur once there is access to all elements necessary to complete an arithmetic operation. Such late-occurring attention shifts may reflect a combination of multiple element-specific biases and confirm their functional role in mental calculation. KW - Attention KW - Mental arithmetic KW - Numerical cognition KW - Spatial-numerical KW - associations Y1 - 2020 U6 - https://doi.org/10.1007/s10339-020-00970-y SN - 1612-4782 SN - 1612-4790 VL - 21 IS - 4 SP - 493 EP - 500 PB - Springer CY - Heidelberg ; Berlin ER - TY - JOUR A1 - Pinhas, Michal A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Addition goes where the big numbers are: evidence for a reversed operational momentum effect JF - Psychonomic bulletin & review : a journal of the Psychonomic Society N2 - Number processing evokes spatial biases, both when dealing with single digits and in more complex mental calculations. Here we investigated whether these two biases have a common origin, by examining their flexibility. Participants pointed to the locations of arithmetic results on a visually presented line with an inverted, right-to-left number arrangement. We found directionally opposite spatial biases for mental arithmetic and for a parity task administered both before and after the arithmetic task. We discuss implications of this dissociation in our results for the task-dependent cognitive representation of numbers. KW - Mental arithmetic KW - Mental number line KW - Operational momentum KW - Pointing KW - SNARC Y1 - 2015 U6 - https://doi.org/10.3758/s13423-014-0786-z SN - 1069-9384 SN - 1531-5320 VL - 22 IS - 4 SP - 993 EP - 1000 PB - Springer CY - New York ER -