Children develop rapidly during early childhood, and this includes their mathematics and executive function (EF) skills. Past research has focused on connections between early mathematics and EF, but more work was needed to fully understand these relations. In particular, past studies have generally used numeracy-based measures to assess early mathematics, although professional guidelines indicate a more comprehensive construct that includes geometry. The research herein addresses some of the gaps of previous work as it examines unique connections between early number, geometry, and EF. One hundred eighteen preschool children from urban and rural communities, being an average age of 53 months at the beginning of the preschool year, were assessed at both the beginning and end of the preschool year. Using the TEAM, a measure of early mathematics inclusive of number and geometry, and the Head Toes Knees Shoulders (HTKS), a measure of early EF with elements of working memory, inhibition, and cognitive shift, relationships between number, geometry, and EF were examined across the preschool year, using a cross-lagged panel model. Three-way ANOVAs were also used to examine differences based on demographic factors, specifically gender, maternal education, household income, and urbanicity (defined by USDA Rural-Urban Continuum Codes). Findings indicate demographic factors played a limited role; household income was significantly associated with number skills and urbanicity with EF skills at the beginning of the preschool year. No other significant relationships based on demographic variables were found. Number skills at Time 1 universally contributed to number, geometry, and EF performance at Time 2; geometry at Time 2 was universally influenced by number, geometry, and EF at Time 1. EF played a mixed role; Time 1 EF significantly predicted Time 2 geometry, and Time 2 EF was significantly predicted by Time 1 number skills. These findings suggest that geometry is an important area of early mathematics to consider, and the relationship between mathematics and EF may be more nuanced than previously understood
