The goal of the present study was to investigate the electrophysiological correlates of second-language (L2) morphosyntactic processing in highly proficient late learners of an L2 with long exposure to the L2 environment. ERPs were collected from 22 English-Spanish late learners while they read sentences in which morphosyntactic features of the L2 present or not present in the first language (number and gender agreement, respectively) were manipulated at two different sentence positions-within and across phrases. The results for a control group of age-matched native-speaker Spanish participants included an ERP pattern of LAN-type early negativity followed by P600 effect in response to both agreement violations and for both sentence positions. The late L2 learner results included a similar pattern, consisting of early negativity followed by P600, in the first sentence position (within-phrase agreement violations) but only P600 effects in the second sentence position (across-phrase agreement violation), as well as significant amplitude and onset latency differences between the gender and the number violation effects in both sentence positions. These results reveal that highly proficient learners can show electrophysiological correlates during L2 processing that are qualitatively similar to those of native speakers, but the results also indicate the contribution of factors such as age of acquisition and transfer processes from first language to L2.

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A sophisticated and flexible understanding of the equals sign is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator, and the equals sign as signalling the same value on both sides of the equation. We argue here that as well as these two conceptions, the notion of substitution is also an important part of a sophisticated understanding of mathematical equivalence. We provide evidence from a cross-cultural study in which English and Chinese children were asked to rate the "cleverness" of operational, sameness and substitutive definitions of the equals sign. A Principle Components Analysis revealed the substitutive items were distinct from the sameness items. Furthermore, Chinese children rated the substitutive items as 'very clever', whereas the English children rated them as 'not so clever', suggesting that the notion of substitution develops differently across the two countries. Implications for developmental models of children's understanding of equivalence are discussed.