Until recently, the accepted view of algebra among many mathematics educators has been that it is too abstract and too difficult for children to learn before secondary school. This chapter argues against this viewpoint. We believe this view arose from the narrow way the subject has come to be construed in U.S. schools and the way children are viewed in relation to it. In the past two decades, much effort has been devoted by mathematics educators in the United States toward determining what algebra and algebraic thinking are and when children are capable of doing it (Carpenter, Franke, & Levi, 2003; Chazan, 1996; National Council of Teachers of Mathematics, 1998; Schifter, 1999). A separate, but related, strand of mathematics education research and curriculum development has investigated children’s understanding of the mathematics of change here and abroad (Barnes, 1992; DiSessa, Hammer, Sherin, & Kolpakowski, 1991; Krabbendam, 1982; Swan & Shell Centre Team, 1989).