Contrast polarity affects verification of addition and subtraction problems via conceptual mapping

The extent to which processing of abstract numerical concepts depends on perceptual representations is still an open question. In four experiments, we examined the association between contrast polarity and mental arithmetic, as well as its possible source. Undergraduate psychology students verified the correctness of single-digit arithmetic problems such as 2 + 5 = 7 or 9 - 6 = 5. Problems appeared either in white or black on a grey background, thus creating positive or negative contrast polarity, respectively. When the correct response was Yes (No), participants were faster (slower) in verifying positive than negative addition problems and in verifying negative than positive subtraction problems. Experiment 2 confirmed that the same result also held for written word problems (e.g., SEVEN + SIX = THIRTEEN). However, Experiment 3 found that the effect of contrast polarity observed in Experiments 1 and 2 disappeared in a blocked design where arithmetic operation was a between-participant factor. In addition, Experiment 4 revealed that the effect of contrast polarity does not generalise to multiplication and division. Overall, available evidence suggests that participants spontaneously associate the abstract relation between addition and subtraction (more-less) with a similar relation between contrast polarities (bright-dark).

Symbol grounding of number words in the subitization range

In three experiments, we explored whether number words are grounded in a nonsymbolic representation of numerosity. We used a sentence-picture verification task, where participants are required to check whether the concept given in a sentence corresponds to the subsequently presented object. We concurrently manipulated numerical congruency by orthogonally varying the number word attached to the concept and the quantity of objects. The number words and numerosities varied from one to four in Experiment 1 and from six to nine in Experiment 2. In Experiment 3, we employed number words six and eight with the constraint that, in the incongruent condition, a constant number-to-numerosity ratio of 2:1 was used. In Experiment 1, we found that participants were faster and more efficient when concept-object matches were accompanied by numerical congruency relative to incongruency. On the other hand, no such difference was observed in Experiments 2 and 3 for numbers falling outside of the subitization range. The results are consistent with the hypothesis that number words from one to four are grounded in a nonsymbolic representation of the size of small sets.