Let H_n denote the space of symmetric functions, homogeneous of degree n. In this paper we introduce a new set of combinatorial objects called λ-brick tabloids and its variants, which we use to give combinatorial interpretations of the entries for twelve of the transition matrices between natural bases of H_n. Using these interpretations, it is possible to give purely combinatorial proofs of various identities between these connection matrices. Also as a consequence, the so called forgotten basis of Doubilet and Rota is shown to admit a natural combinatorial description in terms of brick tabloids and the monomial symmetric functions.