ABSTRACT
By the time children get to school, they have already displayed enormous powers for making sense of the worlds they inhabit: the material world of things, the mental world of images, the symbolic world of labels and words, and the social world of practices. The claims made in this chapter are that the central problem of teaching is to get learners to make use of those powers and to develop them, and that algebraic thinking is what happens when those powers are used in the context of number and relationships. The chapter begins with a quick summary of some of the most important powers possessed by all children who can walk and talk. The use of these powers is briefly illustrated in the domain of arithmetic, before illustrating how algebra emerges from the use of these powers, ending with consideration of what those unaccustomed to making use of learners' powers might put forward as objections or obstacles to this perspective.
