Conceptions of Expressions and Equations in Early Algebra: A Learning Trajectory

Abstract

This article describes a learning trajectory on expressions and equations based on the sixth grade Common Core Mathematics Standards (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Author, 2009) was conducted. A conjectured hypothetical learning trajectory (Simon, 1995; Clements & Sarama, 2004) was developed based on a review of research. The tasks were adapted and modified during the teaching experiment based on student sense making to support student learning. The realized trajectory that emerged and the design decisions that were made were documented. The data was analyzed using Corbin and Strauss' (2008) Constant Comparative method and Creswell's (2007) data analysis spiral. The findings reveal that student understanding of the changing meaning of variables within a problem context played a central role in student development of conceptual understanding of expressions and equations. Implications for classroom instruction and curriculum development are discussed.