Executive function (EF) is considered a set of interrelated cognitive processes, including inhibitory control, working memory, and attentional shifting, that are connected to the development of the prefrontal cortex and contribute to children's problem solving skills and self regulatory behavior (Best & Miller, 2010; Garon, Bryson, & Smith, 2008). EF skills are argued to be foundational for children to thrive in academic domains (Morrison, Cameron Ponitz, & McClelland, 2010), particularly for mathematics (Blair, Ursache, Greenberg, Veron-Feagans, & The Family Life Project Investigators, 2015). Consistent with this theory, EF measures are consistently found to correlate with children's mathematics achievement (Bull & Lee, 2014; Friso-van den Bos, van der Ven, Kroesbergen, & van Luit, 2013), and predict growth in mathematics using a variety of samples and analytic strategies (Blair et al., 2015; Fuhs, Nesbitt, Farran, & Dong, 2014; McClelland et al., 2014). The current study attempts to answer two complementary research questions to better understand associations between executive function (EF) and mathematics in early childhood. First, the study examines whether children's mathematics scores are better predicted by a single EF factor or specific EF components (i.e., inhibitory control, working memory, attentional shifting). Given that EF tasks have been found to tap a single underlying EF factor in early childhood (e.g., Wiebe et al., 2008), the authors hypothesize that the EF factor will account for most of the task-specific EF associations with mathematics. Second, the study examines if associations between EF and mathematics are a function of time-general inter-individual differences or time-specific variation (i.e., cross-lagged effects). Large associations between EF and mathematics have been found (e.g., Fuhs et al., 2014); however, these estimates may be upwardly biased due to persistent interindividual differences not fully statistically controlled in cross-lagged panel models (Hamaker et al., 2015). Prior work on children's mathematics achievement suggests that the factors that affect achievement similarly across development contribute more to the longitudinal stability of individual differences in children's mathematics achievement than the direct effects of children's previous achievement on their later learning (Bailey, Watts, Littlefield, & Geary, 2014). Thus, the authors hypothesize that the associations between EF and mathematics will be larger for the time general factors than for cross-lagged, time-specific factors. Tables and figures are appended.