The authors discuss an application of Bion's conceptualisation of thinking and non-thinking states (K and -K links) to the treatment of a nine-year-old girl. The authors consider Bion's interrelated concepts such as K and -K, container/contained, maternal reverie, and the development of thinking through alpha function to be highly applicable to child treatment. The afore-mentioned conceptual elements are used to elucidate case material over two consecutive hours. A K link is established between therapist and patient, the fragility of which link is then demonstrated by its deterioration into a -K link. Complex issues about knowing and not knowing are central in this girl's clinical presentation. She was conceived through "in vitro" fertilisation (IVF), and subsequently diagnosed with cerebral palsy. The authors consider the emotional impact of this origin story and how the parents relate to it. The authors discuss how parents sometimes cope with perceived losses by wishing to shield or protect their children. This can have repercussions for children's efforts to know (K) and not to know (-K). The fear that emotional knowledge will be too painful to bear can interfere with "learning from experience". Bion's premise that the purpose of analysis is the growth of the mind is synonymous with the child analyst's goal of fostering development and understanding impediments to development. (Contains 6 notes.)