Cognitive models explain knowledge quality or school achievement mainly in connection with pupil competences and variables of home and school environment. In the first part of the paper we closely examine the findings ofmultiple secondary analyses made on the results gathered in the international comparative TIMSS research on achievements in natural science and mathematics. The authors of this research establish that in all countries (25 countries participated), except in the Netherlands, grater proportion of interpersonal variability can be accounted for by inter-pupil rather than inter-school differences Furthermore, they conclude that measured "pupil" and"school" variables explain a relatively small proportion of total variability in pupils' achievements. Findings such as these led us to closely examine pupil variables in terms of their psychological characteristics and the quality of home environment. The results of the Slovene research are shownin the second part of the paper. Results show (the sample consisted of pupils in the 3rd year of primary school) that we can explain 39% of differences in pupils' achievements in the national knowledge assessment of the Slovene language and 29% of interpersonal variability in the mathematical knowledge measured at the national level. If we try to explain the differencesin the knowledge of the Slovene language, the best predictors are pupils' language competences, their intellectual abilities and maternal education, whereas in explaining the differences in achievements in the national assessment of mathematical knowledge the greatest predictive validityis shown by pupils' language competences, their intellectual abilities and paternal education.