The topic of teacher credentials and student performance is revisited in an international setting using the TIMSS-99 data. The lack of consistent positive link between credentials and performance can be explained via three routes: measurement problem of ''teacher quality'' input, measurement problem of ''student outcomes'', and the production function form that is assumed to link the input and the output. Although there is a small literature focusing on student outcome measurement problems, suggesting the use of cognitive achievements rather than test scores, in most cases those cognitive measures are nothing but math and science scores. This study contributes to the literature by borrowing from the measurement and psychometrics theories to decompose single scores into three categories of cognitive abilities. The hypothesis is that teachers may play a crucial role in the development of some student cognitive skills while not in the others. Using a ''rule-space'' model, this article identifies three cognitive skills: the process skill, the reading skill and the mathematical think skill. The study finds that: (1) in general teacher credentials have no effect on any type of cognitive skill development as well as on the test score, and (2) the within-teacher variance of student performance is much larger than between-teacher variance in Japan and Korea, whereas the reverse is true in the US and the Netherlands. The phenomenon of ''private tutoring'' is quoted as an explanation of this pattern.