Children's Strategies: Opportunities to Teach Inverse Relations

• In Event: 46.086 - Roundtable Session 16
  In Roundtable Session: 46.086-5 - Investigations Into Elementary Students' Mathematical Thinking

Abstract

Prior studies reported overwhelming evidence of elementary students’ lack of formal understanding of inverse relations. Given that understanding is not an all-or-nothing phenomenon, this study explores kindergarten- to third-grade students’ (n=281) existing strategies when solving inverse problems about addition and subtraction. Findings show that although the correctness of students’ responses to contextual and non-contextual tasks increased over grades, their explanations did not share this pattern. Overall, students at all grades performed poorly at explanations. Yet, there was a clear middle status from none to full understanding. In particular, our findings reveal detailed levels of students’ part-whole-schema along with varied abilities to identify the unknown quantity, which may shed light on classroom instructions that seek the development of students’ inverse understanding.

Authors

• Meixia Ding, Temple University

• Abbey Auxter, Temple University