How Well Do You Need to Know It to Use It?

Abstract

There is currently a large body of literature about applying knowledge gained in class to real-life situations. However, comparatively little is known about how a student’s mastery of the material affects his or her ability to transfer this knowledge to unfamiliar settings. Our research seeks to illuminate the relationship between a student’s subject mastery level and his or her knowledge transfer to out-of-subject contexts. We use data from TIMSS mathematics (8 grade) and PISA mathematics to evaluate the link between subject mastery level – in this case, the mastery level of mathematics – and the transfer of learned math. Building off previous discussions of TIMSS and PISA test differences, we consider TIMSS performance as the mastery level of school mathematics, and PISA performance as the ability to transfer learned math to an out-of-subject context. The sample included 4,241 Russian students who took part in both the TIMSS 2011 and PISA 2012 cycles. In our study, we first divide the students into six groups according to their performance in the TIMSS. Then we identify the most difficult PISA test items based on the Rasch Model. Finally, we determine what percentage of the most difficult PISA items were answered correctly in every TIMSS group. This percentage served as a measure of the ability to successfully transfer knowledge. We found a positive relation between subject mastery level and the ability to transfer learned math to an out-of-subject context. The higher the mastery level of mathematics, the higher the probability that knowledge will be transferred. However, this link was not linear: only the highest mastery level contributed significantly to knowledge transfer. At other mastery levels, the rate of successful transfer differentiated only slightly. These results imply the importance of making certain that students have truly mastered curriculum before moving to new topics. Additionally, the non-linear nature of the link suggests that educators should begin rethinking how test results are interpreted.