ABSTRACT
One of the major goals of mathematics education is that children see the connections and relationships between mathematical ideas and apply this understanding to the solution of new problems (Fuson, 1992; Hiebert, 1992; National Council of Teachers of Mathematics, 1989, 1991). If we accept that learning is an active construction process based on recognizing similarities between new and existing ideas (Baroody & Ginsburg, 1990; Davis, Maher, & Noddings, 1990; Duit, 1991), then it follows that children must develop meaningful and cohesive mental representations from the outset. Such representations must comprise the structural relations between ideas, not the superficial surface details, if children are to make the appropriate links to the new ideas (English & Halford, 1995; Gholson, Morgan, Dattel, & Pierce, 1990). In this chapter, I argue that the formation of these links involves a process of analogical reasoning, in which something new is understood by analogy with something that is known. Such reasoning appears to be one of the most important mechanisms underlying human thought and may be defined as a mapping of relations from one structure, the base or source, to another structure, the target (Gentner, 1983, 1989; Halford, 1993; Holyoak & Thagard, 1995).
