## 6 Discussion
### Engagement Level and Collaboration Patterns  
As we mentioned earlier, immersive systems can effectively affect the degree of engagement of users. We can observe from the overall engagement scores that the three groups obtained a similar level of engagement. This result does not provide support for our H2. If we look closely into the mean ratings of each category, Single participants gave lower ratings on challenge, exploration, and discovery. By inference, we can say that there are perceived and actual benefits of having a partner to work with. However, the Singles group provided a significantly higher score than Non-Shared one on control, which partially supports H2. By inference, we can say that even though participants in the Non-Shared group had control over their exploration, just having a partner interacting alongside made the participants feel less in control of this process. They might feel to have less freedom and were somewhat influenced or even 'bothered' by what their partner was doing or saying. This was especially the case for the Shared group. Between the two collaborative groups, participants in the Non-Shared group felt that shared interaction could be especially beneficial for joint discoveries and explorations. These participants also felt very focused on the visualizations and tasks because the shared view made it easier for them to know what their partner was doing. This could have helped enhance their level of attention on how the visualizations were changing in response to their partner's interactions. In addition, the shared view could have supported a more fluid collaborative experience (than the non-shared view). According to the video recordings, we observed that participants in the shared condition tended to divide the tasks between them, and they did so very quickly and more often. We also noticed that the shared control facilitated more communication between each pair. Participants in the Non-Shared group tended to do explorations independently and did not often share ideas, despite having the possibility to glance at their partner's workspace (by simply turning their heads). Therefore, participants in the non-shared condition operated the visual elements more frequently when solving the tasks. In the shared condition, it was evident that these participants discussed more and interacted with each other more. They were observed making demonstrations to each other, commenting on their partner's interactions, and sharing their insights to arrive at a solution together. In addition, for the Non-Shared participants, when they wanted to discuss the task, they had to walk over to show what they are doing or gesture to each other. Face-to-face communication was more necessary in this case. However, for the Shared group users, they did not need much body movement for sharing ideas. For example, when one user was interacting with one of the solids, the partner just needed to look at his/her own workspace. It was also quite interesting that participants in the Shared condition tended to show what would qualify as leadership and being more proactive. In previous studies, researchers have shown that while being placed in an immersive virtual environment, participants tended to become leaders and take more proactive roles, but the same participants may not exhibit this quality in the real world [18]. Our finding could further extend these results to the cases of public and private workspaces. A public workspace within a virtual environment seemed to have fostered proactiveness and assertiveness. Not everything was positive in the shared condition. These participants gave lower ratings on Creativity. Our analysis of the video captures and interviews with the participants pointed to one main reason for this low rating, and that was when conflicts showed up. We noticed that when sharing the controls, both participants wanted to access the same visual objects at the same time. In such cases, one participant must make a compromise and wait until his/her partner has finished the interactions.