Flexibility across and flexibility within: The domain of integer addition and subtraction

To better understand the role that flexibility plays in students’ success on integer addition and subtraction problems, we examined students’ flexibility when solving open number sentences. We define flexibility as the degree to which a learner uses more than one strategy to solve a single task when prompted, as well as the degree to which a learner changes strategies when solving a range of tasks to accommodate task differences. We introduce the categorizations of flexibility within and flexibility across to distinguish these two ways of operationalizing flexibility. We examined flexibility and performance within and among three groups of students — 2nd and 4th graders who had negative numbers in their numerical domains, 7th graders, and college-track 11th graders. Profiles of five students are shared to provide insight in relation to the quantitative findings.