Cross-sectional studies such as TIMSS can reveal associations between teaching practices and student achievement that are against expectations with the theory of Educational Effectiveness Research. Therefore, this paper extends TIMSS 2019 study into a follow-up approach examining what is the contribution of TIMSS educational assessment in Teacher Effectiveness Research. Therefore, students in 4th grade who participated in TIMSS 2019 were followed next academic year in Cyprus. At the same time, two different theoretical frameworks were considered for examining the effect of teaching quality on student cognitive outcomes. Multilevel modeling techniques were performed for the analyses of the study. TIMSS predictive validity of student mathematics achievement was supported claiming that a follow-up study using TIMSS data is possible.