Refine
Year of publication
Document Type
Language
- English (46)
Is part of the Bibliography
- yes (46)
Keywords
- SNARC (14)
- mental number line (11)
- numerical cognition (11)
- embodied cognition (8)
- mental arithmetic (8)
- Mental number line (7)
- SNARC effect (7)
- operational momentum (7)
- Numerical cognition (4)
- Operational momentum (4)
- spatial cognition (4)
- Mental arithmetic (3)
- cognitive bias (3)
- hemispheric asymmetry (3)
- spatial-numerical associations (3)
- Cross-cultural (2)
- Pointing (2)
- Spatial bias (2)
- Spatial cognition (2)
- addition (2)
- heuristics and biases (2)
- innate number sense (2)
- mental number line (MNL) (2)
- negative numbers (2)
- newborns (2)
- problem solving (2)
- spatial frequency (SF) (2)
- spatial numerical associations (2)
- spatial-nunmerical association (2)
- subtraction (2)
- temporal frequency (2)
- AHAB (1)
- Conceptual congruency effect (1)
- Counting (1)
- Counting direction (1)
- Distance effect (1)
- Embodied cognition (1)
- Embodiment (1)
- Go/no-go task (1)
- Heuristics (1)
- Heuristics and biases (1)
- IAT (1)
- Implicit association task (1)
- Intra-parietal sulcus (1)
- Magnitude comparison (1)
- Mental Number (1)
- Metaphor (1)
- Music cognition (1)
- Neglect (1)
- Number-space association (1)
- Numerical (1)
- Operand order effect (1)
- Pitch (1)
- Preschool children (1)
- RNG (1)
- Reading (1)
- Reading direction (1)
- SMARC (1)
- Semantic (1)
- Situated cognition (1)
- Social co-representation (1)
- Sound recognition (1)
- Spatial-numerical association (1)
- Spatial-numerical association of response codes (1)
- Spatial-numerical association of response codes effect (1)
- Walking (1)
- abstract concepts (1)
- associations (1)
- asymmetry (1)
- automatic processing (1)
- cognition (1)
- cognitive development (1)
- congruity effect (1)
- counting direction (1)
- cross-cultural (1)
- effect (1)
- embodied numerical cognition (1)
- frequency tuning (1)
- global (1)
- habits (1)
- local (1)
- magnitude association (1)
- numbers (1)
- problem-solving (1)
- random number generation (1)
- reading habits (1)
- spaces (1)
- spatial (1)
- spatial frequencies (1)
- spatial vision (1)
- temporal frequencies (1)
- tie problems (1)
Institute
There has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765-2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research.
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.
1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic
(2015)
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.
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.
Western adults associate small numbers with left space and large numbers with right space. Where does this pervasive spatial-numerical association come from? In this study, we first recorded directional counting preferences in adults with different reading experiences (left to right, right to left, mixed, and illiterate) and observed a clear relationship between reading and counting directions. We then recorded directional counting preferences in pre-schoolers and elementary school children from three of these reading cultures (left to right, right to left, and mixed). Culture-specific counting biases existed before reading acquisition in children as young as 3 years and were subsequently modified by early reading experience. Together, our results suggest that both directional counting and scanning activities contribute to number-space associations.
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.
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.
Spatial-numerical associations (SNAs) have been studied extensively in the past two decades, always requiring either explicit magnitude processing or explicit spatial-directional processing. This means that the typical finding of an association of small numbers with left or bottom space and of larger numbers with right or top space could be due to these requirements and not the conceptual representation of numbers. The present study compares explicit and implicit magnitude processing in an implicit spatial-directional task and identifies SNAs as artefacts of either explicit magnitude processing or explicit spatial-directional processing; they do not reveal spatial conceptual links. This finding requires revision of current accounts of the relationship between numbers and space.