“…Some caregiver characteristics that could affect caregiver-child engagement in the HME and the relation between the HME and children's mathematics outcomes include caregivers' mathematics abilities, self-concept, attitudes, stereotypes, anxieties, and values regarding mathematics, as well as beliefs about the importance of mathematics for their child's development and learning (Blevins-Knabe et al, 2000;Borriello et al, 2020;Missall et al, 2015;Pan, Yang, Li, Liu, & Liu, 2018;Sari & Hunt, 2020;Sonnenschein et al, 2012;. Potential child characteristics that may also need to be accounted for include child abilities, interests, beliefs, attitudes, and anxieties surrounding mathematics (e.g., Cheung, Dulay, & McBride, 2020;Cheung, Yang, Dulay, & McBride, 2018;del Río et al, 2019del Río et al, , 2020Gunderson, Ramirez, Levine, & Beilock, 2012;Kleemans et al, 2012;LeFevre et al, 2009;Skwarchuk et al, 2014). Core questions that span a range of cognitive and affective characteristics of both caregivers and children are described, followed by key considerations for research on the HME in regard to these characteristics.…”