This paper shows how touch-screen devices, of which Tubby is a fictional (although highly plausible) example, can contribute to young children’s math learning and to research on it. Children can engage intensely with Tubby in the classroom and at home. Teachers use Tubby, displayed on a smartboard, for whole-class instruction and for work with small groups. The child brings Tubby home to share with parents and do homework. Tubby can help children to explore, construct, practice, and develop skills and understanding. Tubby offers engaging math storybooks, which both teachers and parents enjoy reading with the child. Researchers can contribute to the creation of Tubby and can use the tablet to investigate the efficacy of Tubby’s instruction. Tubby can also be used to conduct macrogenetic research on the development of mathematical thinking. Research of this type will require use of complex statistical techniques as well as qualitative methods, such as case studies. Tubby facilitates the design and implementation of experiments on Tubby’s affordances. Researchers can also examine the use of Tubby for formative assessment. The tablet can provide detailed descriptions of children’s engagement in the various activities. Tubby can also be used for summative research that provides a valuable portrait of the child’s learning over the course of the year. This information could largely eliminate the use of high-stakes achievement testing and traditional achievement tests.