The classical twin method -- comprising comparisons of monozygotic (MZ) and dizygotic (DZ) twins -- in the domain of cognitive abilities and attainments has led to wide acceptance of results suggesting a large amount of additive genetic variance, with far-reaching implications both for the nature of future studies on the causes of cognitive variance and for intervention policies, as in education. However, this interpretation is only valid if the method observes a number of conditions, which have to hold. Here, we show that the most crucial of these, namely, the equal environments assumption (EEA), may not hold. Consequently, differences in twin correlations might be at least partly explained by treatment effects from parents, teachers, peers, and so on. In addition, well-known interactions at various levels confound the model of simple additive effects on which the classical twin method is predicated and results are interpreted. For example, at a socio-cognitive level, DZ twins may respond to treatments differently from MZ twins. This interaction may further explain MZ?DZ correlation differences. There is abundant evidence for such interactive effects in published twin data. We suggest that there is a need for a more thorough examination of these problems.