In this paper, we illustrate the merit of applying insights from Cognitive Linguistics to pedagogical grammar. We do so by examining English prepositions, long assumed to be one of the most difficult areas of acquisition for second language learners. The approach to the semantics of English prepositions we present is that developed in Evans and Tyler (2004a, b, In prep.) and Tyler and Evans (2001a, 2003). This account offers the following insights: 1) the concepts encoded by prepositions are image-schematic in nature and thus have an embodied basis. In other words, prepositions are not appropriately modelled as constituting linguistic propositions or semantic feature bundles (the received view in formal linguistics); 2) an English preposition encodes an abstract mental idealization of a spatial relation, derived from more specific spatial scenes. This forms the primary meaning component of a semantic network; 3) the idealized spatial relation, also encodes a functional element, which derives from the way spatial relations are salient and relevant for human function and interaction with the physical environment and 4) the additional senses in the semantic network have been extended in systematic, constrained ways. We discuss two key principles of extension: ways of viewing a spatial scene and experiential correlation. We demonstrate the usefulness of a Cognitive Linguistics approach by examining a few aspects of the lexicalization patterns exhibited by in and the four English prepositions of verticality, over, above, under and below. These prepositions provide good evidence that prepositional meanings are extended from the spatial to abstract domains in ways that are regular and constrained. We conclude that a Cognitive Linguistics approach to prepositions provides a more accurate, systematic account that, in turn, offers the basis for a more coherent, learnable presentation of this hitherto seemingly arbitrary aspect of English grammar. (Vyvyan Evans and Andrea Tyler)