Kiteracy is an educational kit designed to improve the literacy process of children with Down syndrome by enabling higher levels of interaction. The kit is based on two Spanish literacy methods: global and phonics. In this work, we present a qualitative study based on video-recorded sessions with twelve children from a Down syndrome institution. The study analyzes three forms of interactions: cardboard, multi-touch and tangible. The task carried out by special education teachers and children in the experimental sessions involved working in pairs (Teacherchild) and autonomous self-learning (child only). Through the sessions, we identified situations in which the teacher took the control in the cardboard version. In the multi-touch version, both the teacher and the child shared the control. However in the tangible version the child took the control. In the self-learning sessions, we observed that multi-touch and tangible interaction seems to offer an enjoyable time for children. Surveys and interviews with teachers revealed that tangible objects offered greater adaptability to create playful reading strategies.