This paper presents a cognitive model of goal formulation in designing that is triggered by surprise. Cognitive system approaches to design synthesis focus on generating alternative designs in response to design goals or requirements. Few existing systems provide models for how goals change during designing, a hallmark of creative design in humans. In this paper we present models of surprise and reformulation as metacognitive processes that transform design goals in order to explore surprising regions of a design search space. The model provides a system with specific goals for exploratory behaviour, whereas previous systems have modelled exploration and novelty-seeking abstractly. We use observed designs to construct a probabilistic model that represents expectations about the design domain, and then reason about the unexpectedness of new designs with that model. We implement our model in the domain of culinary creativity, and demonstrate how the cognitive behaviors of surprise and problem reformulation can be incorporated into design reasoning.