Task instructions modulate unit-decade binding in two-digit number representation.

Previous studies have found decomposed processes, as well as holistic processes, in the representation of two-digit numbers. The present study investigated the influence of task instruction on such processes. Participants completed both magnitude and parity tasks in one of three instructional conditions, where they were asked to either consider two-digit numbers as a whole or to focus on one specific digit. In two experiments, we found that when participants were asked to consider the two digits as an integrated number, they always exhibited a unit-decade compatibility effect, indicating a failure of selective attention on the digit relevant to the given task. However, the mere presence of the neighboring digit is not a sufficient condition for the compatibility effect: when participants were explicitly asked to process a specific digit, their success/failure to selectively ignore the irrelevant digit depended on task requirements. Further, computer mouse tracking indicated that the locus of the compatibility effect was related to late response-related processing. The results signify the deep involvement of top-down processes in unit-decade binding for two-digit number representation.

Reversing the Manual Digit Bias in Two-Digit Number Comparison.

Though recent work in numerical cognition has supported a strong tie between numerical and spatial representations (e.g., a mental number line), less is known about such ties in multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015) , we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

Response trajectories capture the continuous dynamics of the size congruity effect.

In a comparison task involving numbers, the size congruity effect refers to the general finding that responses are usually faster when there is a match between numerical size and physical size (e.g., 2-8) than when there is a mismatch (e.g., 2-8). In the present study, we used computer mouse tracking to test two competing models of the size congruity effect: an early interaction model, where interference occurs at an early representational stage, and a late interaction model, where interference occurs as dynamic competition between response options. In three experiments, we found that the curvature of responses for incongruent trials was greater than for congruent trials. In Experiment 2 we showed that this curvature effect was reliably modulated by the numerical distance between the two stimulus numbers, with large distance pairs exhibiting a larger curvature effect than small distance pairs. In Experiment 3 we demonstrated that the congruity effects persist into response execution. These findings indicate that incongruities between numerical and physical sizes are carried throughout the response process and result from competition between parallel and partially active response options, lending further support to a late interaction model of the size congruity effect.

It takes just one word to quash a SNARC.

Our directional reading habit seems to contribute to the widely reported association of small numbers with left space and larger numbers with right space (the spatial-numerical association of response codes, SNARC, effect). But how can this association be so flexible when reading habits are not? To address this question, we asked bilingual Russian-Hebrew readers to classify numbers by parity and alternated the number format from trial to trial between written words and Arabic digits. The number words were randomly printed in either Cyrillic or Hebrew script, thus inducing left-to-right or right-to-left reading, respectively. Classification performance indicated that the digits were spatially mapped when they followed a Russian word but not when they followed a Hebrew word. An auditory control experiment revealed left-to-right SNARC effects with different strengths in both languages. These results suggest that the SNARC effect reflects recent spatial experiences, cross-modal associations, and long-standing directional habits but not an attribute of the number concepts themselves.