Format of Original
American Educational Research Association
2014 Annual Meeting of the American Educational Research Association
Past research has examined how elementary students interpret the equal sign and the concept of equality and established strong links between a robust understanding of equality and successful learning of algebraic concepts and skills. This paper focuses on middle and high school students’ conceptions of the equal sign and the concept of equality. Students’ written responses to groups of questions consistent with those used in studies with elementary students were analyzed for interpretations of the equal sign and the concept of equality. Data from 607 students, 248 middle and 359 high school, were examined using Matthews et al.’s (2012) map of the knowledge of the equal sign as a guide. The results revealed that middle and high school students alike have difficulty in articulating the meaning of the equal sign. Moreover, most middle and high school students do not have stable conceptions of the meaning of the equal sign and alternate their interpretations between operational and relational, depending on the problem. Similarly, students who interpret the equal sign as a symbol of sameness vary their interpretations of sameness between computational and relational, depending on the problem or group of problems. Implications for instruction are provided.