## ABSTRACT

This chapter presents classroom episodes from grades one to six that illustrate a shift from thinking in terms of specific arithmetic statements to exploring more general assertions. These examples can be used to analyze the kinds of mathematical thinking involved, to consider the conditions that allow such reasoning to take place, and to determine connections between the mathematics of the K–8 curriculum and the formal algebra program. The episodes have been drawn from two sources. The first is a set of narratives about classroom events written by participants in the SummerMath for Teachers Program. The second source is data collected in Teaching to the Big Ideas, a 4-year teacher development project conducted collaboratively by the Education Development Center, TERC, and SummerMath for Teachers. The first set of episodes illustrates children's interest in considering operations as objects of study in themselves.