This study investigates when and how awareness of knowledge gaps (AKG) manifests by observing the problem-solving phase of the educational approach known as problem-solving followed by instruction (PS-I). By comprehensively exploring cognitive and metacognitive process of learners during this phase and categorizing students' judgements of knowledge structure in relation to AKG, it strengthens the underlying mechanisms of PS-I. With sixteen university students as participants, this study quantitatively and qualitatively analyzes conversations that take place during problem-solving activities. In the analysis, the authors suggest a total of ten cognitive and metacognitive events that occur and six judgements of knowledge structure in relation to AKG. The findings indicate that students spend most of their time solving the problem and seldom evaluate their thoughts; few express awareness of a knowledge gap. The authors discuss the relationships between the judgements of knowledge structure and consider when--and to what extent--students perceive their knowledge gaps. Lastly, the authors bring four learning behaviors (i.e., representing and reflecting on knowledge; recognizing and specifying knowledge gaps) with possible instructional strategies to promote each learning behavior.