The theory of community of inquiry (COI) is widely used to explain students’ experiences in online learning. However, it is rarely used to develop structured, evidence-based teaching strategies for managing communities of inquiry. To extend COI theory, this study proposes a dual-element construct of teaching presence and a problem-driven online small-group learning model. The study aims to understand the effects of teaching presence (combining facilitation and group reward) on social presence (peer interactions) and cognitive presence (cognitive learning outcomes). It incorporates leadership style in facilitation (transformational vs. transactional) and individual accountability in group reward to define strategies for the dual-element approach to teaching presence. A controlled experiment with a 2 × 2 factorial design was conducted on a text-based platform to observe the effects of facilitation style and individual accountability in group reward. Results showed that both the transformational (vs. transactional) facilitation style and individual accountability in group reward promoted peer interaction and cognitive learning outcomes. They also interacted positively to enhance peer interaction and cognitive learning outcomes. The nuanced effects of the different elements of the dual-element approach to teaching presence are discussed, along with theoretical and practical implications.