Limited evidence exists on how teachers contribute to student learning gains in early childhood education. This study draws on the Dynamic Model of Educational Effectiveness (DMEE) and investigates the impact of teacher factors on pre-primary students’ mathematics achievement. It also examines whether the five proposed dimensions—frequency, quality, focus, stage, and differentiation—can clarify the conditions under which these factors influence learning. Using a stage sampling procedure, 463 students and 27 teachers from Greek pre-primary schools were selected. Mathematics achievement was assessed at the beginning and end of the school year, while external observations measured the DMEE factors. Analysis of observation data using multi-trait multilevel models provided support for the construct validity of the measurement framework. Teacher factors explained variation in student achievement gains in mathematics. The added value of using a multidimensional approach to measure the functioning of the teacher factor was identified. Implications of the findings are drawn.