ABSTRACT
A common instructional practice in mathematics is to present students with word problems that describe various real-life situations involving apples, cars, workers, and many other characters. Such problems are used both to exemplify certain properties of abstract mathematical concepts, and to provide situations that can be meaningfully modeled by the abstract rules of mathematics (Nesher, 1989). In both roles, students are invited to relate mathematical concepts and rules with their semantic knowledge. For example, they are told that addition is like a procedure for combining sets of marbles, that the operation of division is analogous to partition of a set of cookies among children, and that linear functions capture the properties of constant change in temperature. However, because many aspects of the situations described in the problems cannot or should not be mapped onto mathematical concepts and rules, teachers warn students not to treat the analogies literally. For example, students are told that addition is not specific to combining marbles, that division is not confined to sharing cookies, and that linear functions cannot capture many essential properties of temperature.
