The Three Basic Dimensions model, theorizes three mediators for the effect of teaching quality dimensions on student outcomes. However, the proposed mediating paths and their effects have largely not been empirically tested. This study investigated the mediating role of depth of-processing, time-on-task, and need satisfaction between student-perceived teaching quality and student mathematics achievement and interest, expanding the TBD model to include mediation paths suggested by theories of motivation, cognition, and effort. Data from the TALIS Video Study for Germany, comprising 958 secondary school students in 41 classrooms, were used to run multilevel longitudinal and correlational mediation analyses. The results only found mediation effects at the student level; there were no mediating effects at the classroom level. Not all of the hypothesized relationships thought to exist between the mediators and achievement and interest outcomes were confirmed. The conceptual sequence of the variables, the choice of correlational vs. longitudinal evidence, and the level of analysis were all shown to have an impact on the results. The study thus confirms some of the assumptions of the TBD model, identifies new paths between teaching quality and student outcomes, and provides suggestions for how to proceed with further investigation of a model which should be expanded and more thoroughly empirically tested.