Mental Brackets and Their Use by High School Students in Arithmetic and Algebra

Mental brackets constitute an idiosyncratic use of brackets sometimes used to evaluate arithmetic expressions and are closely connected with students' structure sense. The relevant literature describes the use of mental brackets focusing on primary school students and in the context of arithmetic. Using 181 high school students' solutions to seven tasks, this paper attempts to broaden the scope of mental brackets. It investigates high school students' mental brackets use and their presence in different mathematical domains. The findings show that high school students use mental brackets in the context of arithmetic while evaluating arithmetic expressions, and in the context of algebra, mainly when substituting numerical values in the variables. Moreover, the analysis provides further insights into the use of mental brackets. Sometimes they are applied to the whole expression (global mental brackets) and other times just to parts of it (local mental brackets).