ABSTRACT

A growing consensus has emerged over the necessity to reconceptualize the nature of algebra and algebraic reasoning and to provide students opportunity to engage in algebraic reasoning earlier in their education (Kaput, 1998; National Council of Teachers of Mathematics [NCTM], 1997, 1998). The artificial separation of arithmetic and algebra traditional in school mathematics curricula deprives students of powerful schemes for thinking about mathematics in the early grades and makes it more difficult for them to learn algebra in the later grades (Kieran, 1992; Matz, 1982). The solution, however, is not simply to push the current high school algebra curriculum down into the elementary school. Rather, we need to broaden the conception of the nature of school algebra such that the emphasis is not merely on the learning of rules for manipulating symbols or the skilled use of algebra procedures, but on the development of students' algebraic thinking.