Third grade teachers' mathematics instructional quality, mathematical knowledge for teaching, and mathematics teaching efficacy: A quantitative and qualitative analysis

The purpose of this study was to examine third grade teachers': (a) mathematics instructional quality, (b) mathematical knowledge for teaching, and (c) mathematics teaching efficacy. Using a mixed methods sequential explanatory design with participant selection, the study consisted of two phases.;First, in the quantitative phase, a latent profile analysis (LPA) was conducted to determine the predominant profiles among a sample of 103 third-grade teachers. Three profiles of teachers emerged from the analysis. The first profile (51%) scored above the means (relative to the sample) on mathematics instructional quality, mathematical knowledge for teaching, and mathematics teaching efficacy; the second profile (41%) scored below average on the three constructs, and the third profile (8%) was comparable to the first profile with the exception of below average mathematics instructional quality.;Based upon the results of the LPA, eight participants were selected for the qualitative phase. Teachers' videotaped mathematics lessons (3--4 per teacher) were analyzed to determine the characteristics of mathematics instruction for each profile. Seven themes arose which were operationalized differently across the three profiles. The seven themes were: (1) procedures with connections or problem solving; (2) focus on a mathematical concept; (3) time on-task; (4) appropriate use of representations; (5) multidimensional discourse; (6) mathematical accuracy of instruction; and (7) promotion of accurate student conceptions.;The findings from the quantitative and qualitative phases complement each other to provide important information about the characteristics and needs of elementary school teachers regarding mathematics instruction. Implications for mathematics educators in professional development and teacher education programs are addressed.