Knowledge Change as a Function of Mathematics Experience: All Contexts are Not Created Equal

Abstract

This study investigated how understanding of the equal sign changes as a function of experience in mathematics and variations in context. Students with different levels of mathematics experience (elementary school, seventh grade, undergraduate, and graduate) were randomly assigned to view the equal sign in one of three contexts: (a) equal sign alone, =; (b) typical addition problem, 4 + 8 + 5 + 4 = __; or (c) equivalence problem, 4 + 8 + 5 = 4 + __. Students were asked to define the equal sign and to rate six fictitious students' definitions of the equal sign. Elementary school students interpreted the equal sign as an operational symbol meaning the answer or the total in all contexts, whereas undergraduate and graduate students viewed it as a relational symbol of equivalence in all contexts. Seventh-grade students interpreted the equal sign as an operational symbol in the alone and addition contexts but as a relational symbol of equivalence in the equivalence context. Results highlight that the shape of knowledge change depends on the context in which the knowledge is elicited. Furthermore, the context may influence whether newly emerging ideas are activated.