What influence does the teacher exercise over their students' learning outcomes? This study investigates the impact of teacher quality on student learning outcomes in science halfway through the first year of high school. A multiple-measurement model estimates the potential impact of teacher influence on learning outcomes for 1,060 secondary school students (16-year-olds), as well as the influence on student engagement, motivation, and self-discipline. Teacher quality has a very weak effect on student learning outcomes. However, teacher quality seems to influence student motivation and self-discipline to a significantly larger extent. Further, there is an indirect effect of teacher quality on learning outcomes in science via student engagement, motivation, and self-discipline. Holding the science teacher accountable for pupils' learning outcomes is highly problematic. (Contains 4 tables, 1 figure and 7 footnotes.)