Student cognition in response to intuitive and counterintuitive stimuli in the school science curriculum is not well understood. To address this issue, this study examines high school students' cognitive responses to three counterintuitive physics problems. Our analysis reveals that student success in arriving at counter-intuitive physical responses is related to the depth of their interpretation of problem statements. When students were able to see the deep structure of a problem (i.e. recognize underlying physical principles and concepts applicable to a problem situation), they were more likely to arrive at the scientifically accepted response, despite its counter-intuitive nature. Our findings suggest that students' difficulties in solving counterintuitive problems can be due to the emergence of a superficial focus when reading problem statements. They also raise the possibility of student development of disciplinary intuition based on accepted scientific knowledge ('physics intuition').