Levels in Conceptualizing and Solving Addition and Subtraction Compare Word Problems

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...

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