In the current debate about the abstractness of children's early grammatical knowledge, Tomasello & Abbott-Smith (2002) have suggested that children might first develop 'weak' or 'partial' representations of abstract syntactic structures. This paper attempts to characterize these structures by comparing the development of constructions around verbs in Tomasello's (1992) case study of Travis, with those of 10 children (Stage I-II) in a year-length, longitudinal study. The results show some evidence that children's early knowledge of argument structure is verb-specific, but also some evidence that children can generalize knowledge about argument structure across verbs. One way to explain these findings is to argue that children are learning limited scope formulae around high frequency subjects and objects, which serve as building blocks for more abstract structures such as S+V and V+O. The implication is that children may have some verb-general knowledge of the transitive construction as early as Stage I, but that this knowledge is still far from being fully abstract knowledge.