The author shows how simple models based on mutual interactions between children and their environments explain not only smooth evolutions but also sudden jumps, temporal regressions, cycles and chaotic change in cognitive and language development. A central concept of the system is non-linearity - small causes can have big effects and variables may be sensitive to threshold effects. Using this dynamics systems model, the text demonstrates that the classic develomental models, such as Piaget's assimilation-accomodation model or Vygotsky's zone of proximal development, reveal hidden complexities. Models which explain orderly change and stability can also explain chaotic, unstable and unpredictable processes. The thesis is illustrated with examples from early language development, and social and personality development during adolescence. Mathematical equations and easy tutorials enable the reader to test the model in a spreadsheet format.