Group cognition is a cognitive science concept that studies how groups think, learn, and work. Most research investigates group cognition as a qualitative-oriented phenomenon. From a quantitative perspective, this research proposes a measure equation of group cognition, conducts empirical research during online collaborative problem-solving, and uses multiple quantitative methods to examine group cognition complemented with qualitative microanalysis. Specifically, social network analysis, behavioral pattern analysis, and quantitative content analysis are used to measure three groups' group cognition. Results show that only one group successfully develops group cognition through synergistic coordination of social, behavioral, and cognitive activities. Students in the other two groups either take separate responsibilities to cooperate or have unequal participations, which indicates an inadequacy of group cognition. The extent that three groups develop group cognition is consistent with the order of groups' final performance scores. Research analytical and pedagogical implications are provided to advance research and practice of group cognition.