Research shows that collaborative work promotes student learning and improves social skills, but teachers are still exploring how to best support problem-solving in a small group context, particularly in the science classroom. This study builds on prior research to characterise teacher interactions with small groups in secondary science and analyses how those interactions affect a collectively constructed space -- the triple problem solving space (TPSS) -- in which group members collectively understand a task (content/cognitive dimension), manage social interactions (social/relational dimension), and co-construct the emotional life of the group (affective dimension). Results of two biology teachers' interactions with students in small groups working on inquiry and engineering design activities show that most interactions were administrative and had little influence on the group's TPSS. Teacher interactions that engaged students in monitoring their problem-solving process, however, did have the capacity to increase cognitive work of the group, which subsequently impacted the students' group affect and social dimension. These findings suggest that interactions focused on cognitive processes have the potential to support all aspects of a group's TPSS. Though this research is only a first step in understanding the impact of teacher interactions on small group work, implications for teaching practices are discussed.