Time for Learning Integers: Changes in Second and Fifth Graders' Integer Understanding

Mahtob Aqazade, Purdue University


Young children demonstrate the capacity to learn about integers and operate with them. Yet, children begin to learn whole number concepts in kindergarten and are not introduced to negative numbers until sixth or seventh grade. During this time, students solidify ideas about numbers and the operation of addition based on whole number experiences. This study explores 16 second-grade and 17 fifth-grade students’ conceptualization of integers. After completing a pretest, students engaged in two small group sessions to analyze sets of contrasting integer addition problems, participated in a whole-class lesson on integer addition, and then took a posttest. The type of comparison problems (First session: Positive + Positive vs. Positive + Negative and Second session: Negative + Negative vs. Positive + Negative) were used in the intervention sessions to support students in characterizing directional movements with the operation of signed numbers. Students could have noticed, regardless of the starting number, adding a positive number always corresponds to a movement towards positive direction and adding a negative number always results in a movement in a negative direction. The findings revealed that students from both grades improved significantly from pretest to posttest in integer arithmetic and comparison items. Even though the fifth graders’ average score on the pretest arithmetic items was higher than the second graders’ average score, their average score on the posttest arithmetic items was lower. In fact, there was a significant test by grade interaction indicating that second graders made higher gains from pretest to posttest than fifth graders. These findings suggest that second graders could benefit from a contrasting cases intervention by focusing more on the role of the operation while fifth graders’ stronger preconceptions, along with the longer cultivation of the whole number concept, may have limited their ability to refine their conceptions of negative numbers when using this type of comparison.




Newton, Purdue University.

Subject Area

Mathematics education

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