-5 - -5 Is Like 5 - 5 = 0: Analogical Reasoning With Integers

• In Event: Poster Session 20
  In Poster Session: Mathematical Reasoning and Proof Across Grades

Abstract

How do children begin to reason about negative numbers? Using a pre-test, instruction, post-test design, this study investigates the role of analogies in 61 first-graders’ journeys to make sense of integer addition and subtraction. The results indicate that as students learn more about negative numbers, the analogies they use to interpret integer arithmetic problems shift from drawing on the problems’ surface features to the deep structure of problems. With a greater focus on the problems’ structures, student can begin to reason about the changing meaning of addition and subtraction when negatives are involved. Students’ reasoning provides important aspects for further investigation and points to possible discussion topics that teachers can use to challenge students’ thinking about integers.

Author

• Laura Bofferding, Purdue University