Finger–digit compatibility in Arabic numeral processing

Abstract

Finger–digit response compatibility was tested by asking participants to identify Arabic digits by pressing 1 of 10 keys with all 10 fingers. The direction of the finger–digit mapping was varied by manipulating the global direction of the hand–digit mapping as well as the direction of the finger–digit mapping within each hand (in each case, from small to large digits, or the reverse). The hypothesis of a left-to-right mental number line predicted that a complete left-to-right mapping should be easier whereas the hypothesis of a representation based on finger counting predicted that a counting-congruent mapping should be easier. The results show that when all 10 fingers are used to answer, a mapping congruent with the prototypical finger-counting strategy reported by the participants leads to better performance than does a mapping congruent with a left-to-right oriented mental number line, both in palm-down and palm-up postures of the hands, and they demonstrate that finger-counting strategies influence the way that numerical information is mentally represented and processed.

We thank W. Fias and B. Reynvoet for their helpful comments on an earlier draft of this paper. This work was supported by the Neuromath Research and Training Network from the European Community (Grant # HPRN–CT–2000–00076) and Grant 01/06–267 from the Communauté Française de Belgique–Actions de Recherche Concertées (Belgium). MP is Research Associate at the Fonds National pour la Recherche Scientifique (Belgium).

Notes

¹ This has been shown, for example, in Iranians (Dehaene et al., 1993). This suggests a relationship between the direction of writing and the direction of the SNARC effect. Note that there was no evidence of a complete reversal of the spatial–numerical association as a function of the direction of writing. However, in Iranian immigrants, the slope of the SNARC effect was a function of the time spent away from Iran: The longer the Iranian participants had stayed in a left-to-right writing system, the more the slope of their SNARC effect was similar to that of occidental participants.

² Informal testing after the experiment confirmed that at least 82% of the participants used the typical Italian association when counting with their fingers. This aspect was formally assessed in Experiment 2.

³ All the analyses were also run without discarding 0, and the results were virtually the same.

⁴ Zero was reentered in these analyses to test its possible best associations.

⁵ The ANOVAs for the digits 3, 5, and 0 did not reach the corrected p level (observed p levels = .048, .046, and .043, respectively); significant differences were revealed in any event by the t tests.

⁶ The ANOVAs for the left index and middle fingers and thumb did not reach the corrected p level (observed p levels = .048, .763, and .281, respectively); significant differences were revealed in any case by the t tests.

⁷ Once the experiment was finished, the participants were asked to place their hands palm down on their knees. After having adopted this position, they were asked to show “how they count from 1 to 10 on their fingers”. All participants spontaneously turned their palms up and used the prototypical Italian finger-counting.

⁸ The magnitude effect observed in this study (about 100 ms) is much larger than that usually observed (about 30 ms classically). Although this difference may reflect some critical hand-switching cost related to finger counting that would support our view, it is probably due to our specific experimental set-up using 10 possible answers whereas more classic experiments generally used only two different responses. Indeed, in choice decision situations RL increases with the number of possible responses—a phenomenon known as Hick's information-theory law—such that the mean choice response latency is equal to K log₂ N, where K is a constant and N the number of possible responses (Hick, 1952). For example, if the absolute processing time is, say, 400 ms for small digits and 430 ms for large digits, the difference will be 30 ms with two responses (log₂ 2 = 1; mean small = 400 ms, mean large = 430 ms) but it will be about 100 ms with 10 responses (log₂ 10 = 3.32; mean small = 1,328 ms, mean large = 1,428 ms; these mean RLs actually correspond to those observed before the motor correction). It is, however, worth noting that this does not weaken our current interpretations that are based on direct comparisons between mappings within our experiment.