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Large scale studies have documented socioeconomic (SES) and racial/ethnic disparities in children’s standardized math achievement at kindergarten entry. These early math skills predict future mathematics achievement and career success. However, limited research has been conducted using large sample sizes to understand how SES and race/ethnicity are related to children's numerical skills at even younger ages. The current study aims to investigate sociodemographic variability in three fundamental areas of early numeracy: non-verbal numerosity discrimination, rote counting, and cardinal number word knowledge. In addition, we will examine if the relations between numerical skills might be explained by their shared correlations to sociodemographic factors and if differences in numerical skills between sociodemographic groups can be explained by variability in working memory. Finally, we also investigate whether childcare attendance moderates early sociodemographic differences in numerical abilities. To achieve these goals, data from children aged 2;6 to 6;0 will be gathered from ~ 45 US sites, drawn from a larger multi-lab international project (ManyNumbers project). The findings of this research will enhance our understanding of early emerging variability in numerical skills and provide insights into developing responsive and inclusive educational practices that support diverse learning needs in the early years. 

Large language models (LLMs) have achieved impressive performance but face high computational costs and latency, limiting their deployment in resource-constrained settings. In contrast, small-scale LLMs (SLMs) are more efficient yet struggle to capture evolving real-world knowledge. Retrieval-augmented generation (RAG) helps by integrating external knowledge, but imperfect retrieval can introduce distracting noise that misleads SLMs. We propose {\name}, a robust RAG framework for SLMs via Margin-aware Preference Optimization. {\name} employs multi-turn prompting for detailed reasoning, rejection sampling for high-quality explanations, and contrastive preference selection to refine responses by maximizing the likelihood gap between preferred and non-preferred outputs.