Second and fifth graders’ changes in strategies for integer addition

Research on integer addition often attributes students’ performance to their grade level while ignoring the role of prior whole number knowledge in influencing their learning difficulties. To explore whether these difficulties are related to their grade level or persistence in using rules based on their whole-number experiences, we first paired three second-grade students with three fifth-grade students who had similar integer addition strategies on their pretest. Then, we compared their strategy changes and performance after small-group sessions and whole-class activities around integer addition (i.e., instructional intervention). Although all pairs gained from the pretest to posttest, one fifth grader still relied on the rule of addition as getting a larger absolute value, suggesting her prior prolonged whole number addition experience impeded her progress compared to her second-grade pair. In fact, after whole-class activities, the second-grade pairs demonstrated better overall gains than the fifth-grade pairs. We extended our exploration to a larger group of 32 fifth graders and 18 second graders. Although fifth graders had higher performance on both the pretest and posttest, second graders made a significantly larger gain on two-addend integer addition problems than fifth graders. We argue that to make a more meaningful comparison across grade levels, researchers need to explore students’ strategy changes based on their prior knowledge. Our study findings suggest that some integer addition strategies, based on prolonged whole number addition experience, may hinder students’ further understanding of integer addition and contribute to learning difficulties.