We consider the task of learning distributed representations for arithmetic word problems. We outline the characteristics of the domain of arithmetic word problems that make generic text embedding methods inadequate, necessitating a specialized representation learning method to facilitate the task of retrieval across a wide range of use cases within online learning platforms. Our contribution is two-fold; first, we propose several 'operators' that distil knowledge of the domain of arithmetic word problems and schemas into word problem transformations. Second, we propose a novel neural architecture that combines LSTMs with graph convolutional networks to leverage word problems and their operator-transformed versions to learn distributed representations for word problems. While our target is to ensure that the distributed representations are schema-aligned, we do not make use of schema labels in the learning process, thus yielding an unsupervised representation learning method. Through an evaluation on retrieval over a publicly available corpus of word problems, we illustrate that our framework is able to consistently improve upon contemporary generic text embeddings in terms of schema-alignment.