Path integration, the ability to maintain an estimate of one's location by continuously integrating self-motion cues, is a vital component of the brain's navigation system. We present a spiking neural network model of path integration derived from a starting assumption that the brain represents continuous variables, such as spatial coordinates, using Spatial Semantic Pointers (SSPs). SSPs are a representation for encoding continuous variables as high-dimensional vectors, and can also be used to create structured, hierarchical representations for neural cognitive modelling. Path integration can be performed by a recurrently-connected neural network using SSP representations. Unlike past work, we show that our model can be used to continuously update variables of any dimensionality. We demonstrate that symbol-like object representations can be bound to continuous SSP representations. Specifically, we incorporate a simple model of working memory to remember environment maps with such symbol-like representations situated in 2D space.