This paper presents textual tinkerability, a new concept for fostering early literacy skills during parent-child reading. Textual tinkerability maps storytelling gestures to changes in animation and text to assist reading exploration and demonstration of the link between text, spoken word, and concept. TinkRBooks are flexible tablet-based storybooks that allow readers to actively explore concepts in text using textual tinkerability. When reading TinkRBooks, both parents and children can alter text (character attributes and parts of speech) by manipulating story elements (props and characters) as they read. We demonstrate how textual tinkerability encourages more dialog, print referencing and dialogic questioning between parent-child dyads in shared reading as compared to paper books. In addition, our study reports observations of storytelling performance behaviors that foster playful and socially intimate shared reading behaviors that are closely mapped to the teaching and learning of emergent literacy skills.