New forms of tangible and spatial child computer interaction and supporting technologies can be designed to leverage the way children develop intelligence in the world. In order to design playful learning tangibles designers must understand how children interact with and understand the representations embedded in tangible systems. In this short work in progress paper the author summarizes relevant theory from cognitive developmental psychology which may provide grounding for the design of tangibles to support children's learning. Keywords Tangible interaction, embedded interaction, cognitive development, dynamic systems, learning, children. ACM Classification Keywords H.5.2. [Information Interfaces and Presentation]: User interfaces, H.5.1 [Multimedia Information Systems]: Artificial, augmented and virtual realities.