The MOOCs (Massive Open Online Courses) forum carries rich discussion data that contains multi-level cognition-related behavior patterns, which brings the potential for an in-depth investigation into the development trend of the group and individual cognitive presence in discourse interaction. This paper describes a study conducted in the context of an introductory astronomy course on the Chinese MOOCs platform, examining the relationship between discussion pacings (i.e., instructor-paced or learner-paced discussion), cognitive presence, and learning achievements. Using content analysis, lag sequential analysis, logistic regression, and grouped regression approaches, the study analysed the online discussion data collected from the Astronomy Talk course involving 2603 participants who contributed 24,018 posts. The findings of the study demonstrated the significant cognitive sequential patterns, and revealed the significant differences in the distribution of cognitive presence with different discussion pacings and learning achievement groups, respectively. Moreover, we found that the high-achieving learners were mostly in the exploration, integration, and resolution phase, and learner-paced discussion had a greater moderating effect on the relationship between cognitive presence and learning achievements. Based on the findings and discussion, suggestions for improving the learners' cognitive presence and learning achievements in the MOOC environment are discussed.