This study examined how intellectual openness affected the extent to which students engaged in the processes of critical thinking in computer-supported collaborative argumentation (CSCA). This study found: a) indications of differences in the number of personal rebuttals posted in reply to direct challenges between more versus less open students (ES = +0.33); b) significant differences in number of personal rebuttals posted between the less versus more open students among the males (ES = +1.32), but not among the females (ES = -0.19); and c) no difference in the way students responded to challenges. These findings identify how specific traits and gender can potentially affect performance in CSCA and suggest new process-oriented strategies and tools for analyzing and structuring discussions to promote critical inquiry. (Contains 1 table and 5 figures.)