TY - JOUR A1 - Mioni, Giovanna A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Heuristics and biases in the mental manipulation of magnitudes BT - Evidence from length and time production JF - Quarterly journal of experimental psychology / published in association with Experimental Psychology Society N2 - There is a debate about whether and why we overestimate addition and underestimate subtraction results (Operational Momentum or OM effect). Spatial-attentional accounts of OM compete with a model which postulates that OM reflects a weighted combination of multiple arithmetic heuristics and biases (AHAB). This study addressed this debate with the theoretically diagnostic distinction between zero problems (e.g., 3 + 0, 3 - 0) and non-zero problems (e.g., 2 + 1, 4 - 1) because AHAB, in contrast to all other accounts, uniquely predicts reverse OM for the latter problem type. In two tests (line-length production and time production), participants indeed produced shorter lines and under-estimated time intervals in non-zero additions compared with subtractions. This predicted interaction between operation and problem type extends OM to non-spatial magnitudes and highlights the strength of AHAB regarding different problem types and modalities during the mental manipulation of magnitudes. They also suggest that OM reflects methodological details, whereas reverse OM is the more representative behavioural signature of mental arithmetic. KW - Heuristics and biases KW - mental arithmetic KW - operational momentum KW - SNARC KW - effect Y1 - 2021 U6 - https://doi.org/10.1177/1747021820967663 SN - 1747-0218 SN - 1747-0226 VL - 74 IS - 3 SP - 536 EP - 547 PB - SAGE Publishing CY - Thousand Oaks, CA ER - TY - JOUR A1 - Fischer, Martin A1 - Winter, Bodo A1 - Felisatti, Arianna A1 - Myachykov, Andriy A1 - Jeglinski-Mende, Melinda A. A1 - Shaki, Samuel T1 - More Instructions Make Fewer Subtractions JF - Frontiers in Psychology N2 - Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; Öllinger et al., 2014). Problem solving can be defined as the search for possible changes in one's mind (Kahneman, 2003). In a recent study, Adams et al. (2021) assessed whether the predominant problem solving strategy when making changes involves adding or subtracting elements. In order to do this, they used several examples of simple problems, such as editing text or making visual patterns symmetrical, either in naturalistic settings or on-line. The essence of the authors' findings is a strong preference to add rather than subtract elements across a diverse range of problems, including the stabilizing of artifacts, creating symmetrical patterns, or editing texts. More specifically, they succeeded in demonstrating that “participants were less likely to identify advantageous subtractive changes when the task did not (vs. did) cue them to consider subtraction, when they had only one opportunity (vs. several) to recognize the shortcomings of an additive search strategy or when they were under a higher (vs. lower) cognitive load” (Adams et al., 2021, p. 258). Addition and subtraction are generally defined as de-contextualized mathematical operations using abstract symbols (Russell, 1903/1938). Nevertheless, understanding of both symbols and operations is informed by everyday activities, such as making or breaking objects (Lakoff and Núñez, 2000; Fischer and Shaki, 2018). The universal attribution of “addition bias” or “subtraction neglect” to problem solving activities is perhaps a convenient shorthand but it overlooks influential framing effects beyond those already acknowledged in the report and the accompanying commentary (Meyvis and Yoon, 2021). Most importantly, while Adams et al.'s study addresses an important issue, their very method of verbally instructing participants, together with lack of control over several known biases, might render their findings less than conclusive. Below, we discuss our concerns that emerged from the identified biases, namely those regarding the instructions and the experimental materials. Moreover, we refer to research from mathematical cognition that provides new insights into Adams et al.'s findings. KW - problem solving KW - addition KW - subtraction KW - cognitive bias KW - SNARC Y1 - 2021 U6 - https://doi.org/10.3389/fpsyg.2021.720616 SN - 1664-1078 VL - 12 SP - 1 EP - 3 PB - Frontiers Media SA CY - Lausanne, Schweiz ER - TY - GEN A1 - Fischer, Martin A1 - Winter, Bodo A1 - Felisatti, Arianna A1 - Myachykov, Andriy A1 - Jeglinski-Mende, Melinda A. A1 - Shaki, Samuel T1 - More Instructions Make Fewer Subtractions T2 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe N2 - Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; Öllinger et al., 2014). Problem solving can be defined as the search for possible changes in one's mind (Kahneman, 2003). In a recent study, Adams et al. (2021) assessed whether the predominant problem solving strategy when making changes involves adding or subtracting elements. In order to do this, they used several examples of simple problems, such as editing text or making visual patterns symmetrical, either in naturalistic settings or on-line. The essence of the authors' findings is a strong preference to add rather than subtract elements across a diverse range of problems, including the stabilizing of artifacts, creating symmetrical patterns, or editing texts. More specifically, they succeeded in demonstrating that “participants were less likely to identify advantageous subtractive changes when the task did not (vs. did) cue them to consider subtraction, when they had only one opportunity (vs. several) to recognize the shortcomings of an additive search strategy or when they were under a higher (vs. lower) cognitive load” (Adams et al., 2021, p. 258). Addition and subtraction are generally defined as de-contextualized mathematical operations using abstract symbols (Russell, 1903/1938). Nevertheless, understanding of both symbols and operations is informed by everyday activities, such as making or breaking objects (Lakoff and Núñez, 2000; Fischer and Shaki, 2018). The universal attribution of “addition bias” or “subtraction neglect” to problem solving activities is perhaps a convenient shorthand but it overlooks influential framing effects beyond those already acknowledged in the report and the accompanying commentary (Meyvis and Yoon, 2021). Most importantly, while Adams et al.'s study addresses an important issue, their very method of verbally instructing participants, together with lack of control over several known biases, might render their findings less than conclusive. Below, we discuss our concerns that emerged from the identified biases, namely those regarding the instructions and the experimental materials. Moreover, we refer to research from mathematical cognition that provides new insights into Adams et al.'s findings. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 763 KW - problem solving KW - addition KW - subtraction KW - cognitive bias KW - SNARC Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-550086 SN - 1866-8364 VL - 12 SP - 1 EP - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic JF - Frontiers in psychology N2 - 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. KW - AHAB KW - cognitive bias KW - mental arithmetic KW - numerical cognition KW - operational momentum KW - SNARC KW - tie problems Y1 - 2018 U6 - https://doi.org/10.3389/fpsyg.2018.02453 SN - 1664-1078 VL - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Felisatti, Arianna A1 - Laubrock, Jochen A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Commentary BT - A mental number line in human newborns T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 620 KW - spatial-numerical associations KW - SNARC KW - mental number line (MNL) KW - spatial frequency (SF) KW - temporal frequency KW - hemispheric asymmetry KW - newborns KW - embodied cognition Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-460413 SN - 1866-8364 IS - 620 ER - TY - JOUR A1 - Felisatti, Arianna A1 - Laubrock, Jochen A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Commentary BT - A mental number line in human newborns JF - Frontiers in Human Neuroscience KW - spatial-numerical associations KW - SNARC KW - mental number line (MNL) KW - spatial frequency (SF) KW - temporal frequency KW - hemispheric asymmetry KW - newborns KW - embodied cognition Y1 - 2020 U6 - https://doi.org/10.3389/fnhum.2020.00099 SN - 1662-5161 VL - 14 PB - Frontiers Research Foundation CY - Lausanne ER - TY - GEN A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Two steps to space for numbers T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 412 KW - spatial-nunmerical association KW - SNARC KW - mental number line KW - numerical cognition KW - spatial cognition Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406522 IS - 412 ER - TY - INPR A1 - Fischer, Martin H. A1 - Shaki, Samuel T1 - Two steps to space for numbers T2 - Frontiers in psychology KW - spatial-nunmerical association KW - SNARC KW - mental number line KW - numerical cognition KW - spatial cognition Y1 - 2015 U6 - https://doi.org/10.3389/fpsyg.2015.00612 SN - 1664-1078 VL - 6 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Shaki, Samuel A1 - Sery, Noa A1 - Fischer, Martin H. T1 - 1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic JF - Journal of cognitive psychology N2 - Over the past decade or so, a large number of studies have revealed that conceptual meaning is sensitive to situational context. More recently, similar contextual influences have been documented in the domain of number knowledge. Here we show such context dependency in a length production task. Adult participants saw single digit addition problems of the form n1 + n2 and produced the sum by changing bi-directionally the length of a horizontally extended line, using radially arranged buttons. We found that longer lines were produced when n1 < n2 compared to n1 > n2 and that unit size increased with result size. Thus, the mathematical axioms of commutativity and identity do not seem to hold in mental addition. We discuss implications of these observations for our understanding of cognitive mechanisms involved in mental arithmetic and for situated cognition generally. KW - Operand order effect KW - Situated cognition KW - Mental number line KW - SNARC KW - Operational momentum Y1 - 2015 U6 - https://doi.org/10.1080/20445911.2014.973414 SN - 2044-5911 SN - 2044-592X VL - 27 IS - 4 SP - 471 EP - 477 PB - Routledge, Taylor & Francis Group CY - Abingdon 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 - TY - JOUR A1 - Winter, Bodo A1 - Matlock, Teenie A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Mental number space in three dimensions JF - Neuroscience & biobehavioral reviews : official journal of the International Behavioral Neuroscience Society N2 - A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated. (C) 2015 Elsevier Ltd. All rights reserved. KW - Embodiment KW - Intra-parietal sulcus KW - Mental number line KW - Metaphor KW - Neglect KW - Spatial cognition KW - SNARC Y1 - 2015 U6 - https://doi.org/10.1016/j.neubiorev.2015.09.005 SN - 0149-7634 SN - 1873-7528 VL - 57 SP - 209 EP - 219 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Random walks on the mental number line JF - Experimental brain research KW - Mental number line KW - RNG KW - SNARC KW - Spatial bias KW - Walking Y1 - 2014 U6 - https://doi.org/10.1007/s00221-013-3718-7 SN - 0014-4819 SN - 1432-1106 VL - 232 IS - 1 SP - 43 EP - 49 PB - Springer CY - New York 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 - Shaki, Samuel A1 - Fischer, Martin H. T1 - Multiple spatial mappings in numerical cognition JF - Journal of experimental psychology : Human perception and performance N2 - 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. KW - mental number line KW - reading habits KW - SNARC Y1 - 2012 U6 - https://doi.org/10.1037/a0027562 SN - 0096-1523 VL - 38 IS - 3 SP - 804 EP - 809 PB - American Psychological Association CY - Washington ER -