Dynamic structures of parent-child number talk: An application of categorical cross-recurrence quantification analysis and companion to Duong et al. (under review).

Social interactions, particularly parent-child conversations, play a critical role in children's early learning and pre-academic skill development. While these interactions are bidirectional, complex, and dynamic, much of the research in this area tends to separate speakers' talk and capture the frequency of words or utterances. Beyond the aggregation of talk exists rich information about conversational structures and processes, such as the extent to which speakers are aligned or reciprocate each other's talk. These measures can be derived using categorical cross-recurrence quantification analysis (CRQA), a method that quantifies the temporal structure and co-visitation of individual and sequential events, e.g., utterances between speakers. In this paper, we present an application of CRQA, following the protocol described in our tutorial paper (Duong et al., under review), to describe alignment in parent-child conversations about numbers and math (i.e., number talk). We used the 'crqa' package in R (Coco, Monster, Leonardi, Dale, & Wallot, 2021) and the code used in this application is available in the Supplemental Materials (and can be found here: https://github.com/s-duong/crqa-number-talk). Further, the CRQA measures derived from this application were compared to traditional frequency measures of talk, i.e., counts of utterances, in the prediction of children's math skills. Overall, we showed that (1) CRQA can be applied to existing transcription data to uncover theoretically-driven patterns of parent-child talk that are not captured by common frequency measures and (2) these CRQA measures offer additional, rich information about interactions beyond frequencies of talk and can be used to predict individual differences in children's math skills.