In this paper, we explore the early indicators of design fixation occurring during the concept development stage of children's design processes. This type of fixation, which we named: "concept fixation," causes a blind adherence to the current (possibly unfavourable) state of a design idea. Its occurrence hampers the creative thinking processes present in a design process, which in turn stagnates the development of initial design ideas into final designs. Until now, research on design fixation has mainly focussed on creative idea generation in the early phases of the design process through analysing (intermediate) design ideas and completed artefacts. However, children's fixation behaviours might be identified at an earlier moment through the conversations that take place in the classroom about their design ideas. To this end, we present a case study in which we explored early indicators of concept fixation of a group of 24 primary school children (ages 9-11) carrying out a co-design project. Fixation was observed through the manner in which the design teams responded to questions and comments from their peers and the client. Four categories of response behaviours indicating concept fixation emerged from the verbal data, namely: 'band-aids', 'already-in-there', 'question-not-relevant' and 'it's-not-possible'. We expect that the indicators will be helpful in identifying concept fixation during the design process, especially in an educational context. The process of identification of fixation, and reflecting on it, creates awareness. This is considered as an important step by professional designers towards guarding oneself from fixation episodes in future projects, and thus being more creative.