The Relationship between Flexibility and Student Performance on Open Number Sentences with Integers.

To better understand the role that ways of reasoning play in students’ success on integer addition and subtraction problems, we examined the relationship between students’ flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups—39 2 and 4 graders who had negative numbers in their numerical domains, 40 7 graders, and 40 successful 11 graders—we found that flexibility and success were positively related. That is, the more flexibly students invoked ways of reasoning, the greater their success. These findings indicate that rather than searching for one particular model or approach to teaching integer operations, teachers should support multiple ways of reasoning and discuss features of problems that might make one way of reasoning more productive than another.