**Title:**Understanding of Transitivity and Symmetry of Equality among High School Students

# MAT Thesis

**Abstract:**Effective algebraic thinking relies on a relational understanding of the equality sign, that is, that its purpose is to indicate that the values represented by the expressions on either side are the same (McNeil et al., 2006). Students used to arithmetic thinking tend to see the equality sign operationally, that is, that its purpose is to indicate that operations on the left are to be performed and the result placed to the right (Baroody & Ginsburg, 1983). This study examines two foundational concepts in equality, transitivity and symmetry, which rely on relational rather than operational understanding. Additionally, this study explores the extent to which mathematical notation itself (as opposed to underlying understanding of concepts) drives misunderstanding. The sample set is twenty-nine middle and high school girls at an alternative school in Metropolitan Detroit.