Numerical abstractness and elementary arithmetic

Conceptual Integration of Arithmetic Operations With Real-World Knowledge: Evidence From Event-Related Potentials

Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials (ERPs)-N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving task, when participants generated labeled answers to semantically aligned and misaligned arithmetic problems (e.g., 6 roses + 2 tulips = ? vs. 6 roses + 2 vases = ?), the second object label in misaligned problems yielded an N400 effect for addition (but not division) problems. In a verification task, when participants judged arithmetically correct but semantically misaligned problem sentences to be "unacceptable," the second object label in misaligned sentences elicited a P600 effect. Thus, depending on task constraints, misaligned problems can show either of two ERP signatures of conceptual disruption. These results show that well-educated adults can integrate mathematical and semantic relations on the rapid timescale of within-domain ERP effects by a process akin to analogical mapping.

Semantic alignment and number comparison

Are the quantity representations activated by Arabic digits influenced by semantic context? We developed a novel paradigm to examine semantic alignment effects (e.g., Bassok et al. in J Exp Psychol Learn Mem Cogn 34:343-352, 2008) in number comparison. A horizontal word pair (either less more or few many) appeared for 480 ms to prime either relative magnitude (less more) or quantity (few many). Then a horizontal pair of single digits that were either successors (near) or differed by at least four (far) appeared above the word pair. Participants indicated verbally whether or not the word and digit pairs were congruent with respect to left-to-right ascending or descending relative magnitude. The RT advantage for far number pairs compared to near pairs (the distance effect) was greater with magnitude primes (81 ms) than quantity primes (17 ms), demonstrating a semantic alignment effect. This effect disappeared in Experiment 2 in which participants received identical stimuli but named the larger of the two digits and were free to ignore the primes. Nonetheless, mean RT in Experiment 2 was faster with prime and target pairs both ascending or both descending, but only with quantity primes. This prime-dependent order-congruity effect suggests that semantic alignment with respect to numerical order affected number comparison in Experiment 2. The results thereby demonstrate that number comparison exhibits task-dependent semantic alignment effects and recruits distinct numerical representations as a function of semantic context (e.g., Cohen Kadosh and Walsh in Behav Brain Sci 32:313-373, 2009).