Background: The dynamic model of educational effectiveness (DMEE) is a comprehensive theoretical framework including factors that are important for school learning, based on consistent findings within educational effectiveness research. Purpose: This study investigates the impact of teacher and school factors of DMEE on mathematics and science achievement, and identifies factors with equalising qualities in terms of helping low-achieving student groups to catch up with their better-achieving peers. Sample: Data were retrieved from a large-scale, longitudinal project conducted in 571 classes in 334 schools in 6 European countries (Belgium/Flanders, Cyprus, Germany, Greece, Ireland and Slovenia). In each country, a sample of about 50 schools was drawn, and tests in mathematics and science were administered to all grade 4 students (N = 10,742) at the beginning and end of school-year 2010-2011. Design and methods: Data on teacher factors were collected through student questionnaires, and data on school factors were collected through teacher questionnaires. Two-level regression models were applied. Interaction effects between the factor and the group composition were estimated, while controlling for prior achievement. Results: Our results confirm the importance of most tested teacher factors (except for modelling and qualitative structuring) and all tested school factors of DMEE for effective math and science education. The majority of these factors appear to make an even greater difference for low-achieving student groups. Conclusions: Our results provide further validity to DMEE at classroom and school level, and indicate that most factors make a greater difference for low-achieving student groups. Thus, effective teaching is an important aspect for reducing the achievement gap. This illustrates the importance of placing the most effective teachers in schools with the highest percentage of underachieving students. Policy should encourage good teachers to teach in low-achieving schools by making these jobs more attractive, both financially and in terms of work conditions.