**Published online first in:**
*Educational Evaluation and Policy Analysis*
**June 25, 2014**
Paul L. Morgan, The Pennsylvania State University

George Farkas, University of California, Irvine

Steve Maczuga, The Pennsylvania State University

*Abstract*
We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by first-grade teachers in the United States and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement—three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in the first-grade classrooms were associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted effect sizes [ESs] = .05–.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and studentcentered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ESs = .03–.04). First-grade teachers in the United States may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.