Levels in Conceptualizing and Solving Addition and Subtraction Compare Word Problems

Abstract

This article presents an analysis of conceptual and linguistic complexities of matching situations expressed as word problems and describes possible ways of conceptualizing and solving such problems. Data from first and second graders suggest a progression of four levels in conceptualizing and solving these problems. In the first-Relational-level, children can answer "Who has more/less?" but not "How much more/less?" In the second-Language Cue-level, children are more likely to solve problems with action, Equalizing language ("If he gets 2 more cats, he will have as many cats as dogs") than with static, Compare language ("He has 2 more dogs than cats"). They are especially likely to solve problems in which finding the unknown compared quantity is directed by keywords in the relational sentence. At the third-Understand Matching Situations-level, children find Inconsistent problems (those in which the relational sentence is opposite to the needed solution action) considerably more difficult than other types. Children overwhelmingly solve problems in which one compared quantity is unknown by using an Equalizing approach in which the Extra quantity is added to or taken from the other known quantity. They predominantly solve problems in which the difference between two known compared quantities is unknown by using a Matching conception in which the Small quantity is taken from the Big quantity. At the fourth-Solve Inconsistent-level, children come to be able to solve Inconsistent problems, primarily by using Equalizing conceptions in which the relation given in the relational sentence is reversed.