We take a socio-cultural approach to comparing how dual control of a new user interface paradigm--Separate Control of Shared Space (SCOSS)--and dual control of a single user interface can work to mediate the collaborative decision-making process between pairs of children carrying out a multiple categorisation word task on a shared computer. Qualitative analysis focuses on how the interface properties of SCOSS can encourage each child to participate in the task and to represent their own opinions as part of the process of reaching final joint agreement. We conclude by suggesting additional features to improve the content of collaborative conversations and by proposing other contexts that may benefit from this interface.