ABSTRACT
This chapter describes a conceptual orientation toward what is going on in complex quantitative situations, and shows how teachers can help students make mathematical sense of those situations. It argues for better curricular balance between teaching and learning about number/operation and quantity/quantitative reasoning. Algebraic reasoning is characterized by its generality and by the role that symbolic expressions play in stating general relationships, comparing and manipulating them, and facilitating many numerical evaluations. The basic idea is to move out of the situation and its constituent quantities and into the world of symbolic expressions and equations. Algebraic notation and methods are powerful tools for stating, analyzing, and manipulating general relationships, but without ideas of substantial generality to express, students will find little sense in and little use for algebra. An emphasis on the quantitative aspects of situations reorients students' mathematical focus in some important ways, affecting both the development of their arithmetic reasoning and their future prospects in algebra.
