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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.
A growing literature has suggested that processing of visual information presented near the hands is facilitated. In this study, we investigated whether the near-hands superiority effect also occurs with the hands moving. In two experiments, participants performed a cyclical bimanual movement task requiring concurrent visual identification of briefly presented letters. For both the static and dynamic hand conditions, the results showed improved letter recognition performance with the hands closer to the stimuli. The finding that the encoding advantage for near-hand stimuli also occurred with the hands moving suggests that the effect is regulated in real time, in accordance with the concept of a bimodal neural system that dynamically updates hand position in external space.
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.
Removing spatial responses reveals spatial concepts even in a culture with mixed reading habits
(2014)
Embodied number processing
(2015)
Finger-based numerical representations have gained increasing research interest. However, their description and assessment often refer to different numerical principles of ordinality, cardinality and 1-to-1 correspondence. Our aim was to investigate similarities and differences between these principles in finger-based numerical representations. Sixty-eight healthy adults performed ordinal finger counting, cardinal finger montring (showing the number of gestures) and finger-to-number mapping with twisted arms and fingers. We found that counting gestures and montring postures were identical for Number 10 but differed to varying degrees for other numbers. Interestingly, there was no systematic relation between finger-to-number mapping and ordinal finger counting habits. These data question the assumption of a unitary embodied finger-based numerical representation, but suggest that different finger-based representations co-exist and can be recruited flexibly depending on the numerical aspects to be conveyed.
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.