ABSTRACT
In this chapter, we attempt to provide an overview of the main arguments presented in the book and offer some recommendations for mathematics instruction. One of the major issues in mathematics education is the need for children to see connections and relationships between mathematical ideas and to apply this understanding to the solution of new problems. Young children bring to school a substantial body of knowledge about number and informal problem-solving processes and can successfully solve a range of problems by directly representing or modelling the actions or relationships described in the problem (Carpenter et al., 1993; Fuson, 1992a, 1992b; Ginsburg & Baron, 1993; Resnick, 1992). However, as children progress through the grade levels, for many of them their perception of mathematics as a meaningful domain appears to deteriorate and they have difficulty linking what they already know and understand to the symbols and rules they use (Fuson, 1992a, 1992b; Greeno, 1989; Onslow, 1991; Wearne & Hiebert, 1985). This is clearly evident by the middle grades (Wearne & Hiebert, 1988b).
