COMPUTER PRESENTATIONS OF STRUCTURE IN ALGEBRA

Typical errors found in previous studies of students’ errors in algebra suggest that students studying algebra frequently fail to realize that formulas in mathematical symbol systems have an intrinsic structure (Lewis, 1981; Matz, 1982; Sleeman, 1982, 1984, 1985). In algebra, expressions are structured explicitly by the use of parentheses, and implicitly by assuming conventions for the order in which we perform arithmetic operations. It is hypothesized that many of students’ errors in manipulating an algebraic expression are due to their inattention to the expression’s structure. To test this hypothesis, we built a program, called EXPRESSIONS, that presents expressions and equations in two formats: in usual (sentential) form and in the form of an expression tree. The figure to the right shows the screen after having entered the equation 4x-6=2(x-3) and then having multiplied both sides by 1 . The equation’s