Roles of External Representation in High School Student s Understanding of Algebraic Word Problem Solving

This study examined strategies high school students use to solve algebraic word problems, how they translate word problems into different mathematical representations, why students have difficulty solving algebraic word problems, and how their previous algebra experience in school influences their problem solving. Using three algebraic word problems, seven high school students were interviewed and interacted in a small group with think aloud technique. Findings from this study showed that most students understood the word problems (comprehend contexts) and devised plans to find the solutions. Specifically, the students currently taking algebra used equations to represent the problems. The students who took algebra in the past tried to create an equation but failed to remember. Instead, they used table, graph, or pictorial representation. The student who had not taken algebra in school drew a picture or made a table to solve the problems. The reasons students have difficulties solving the algebraic word problems are because 1) it is difficult for students to translate word problems into equations, 2) students believe that they have to create an equation for word problems, and 3) they are used to following cookbook procedures from their textbooks. Because of the difficulty of translation between the word problems and equation, a role of other external representations was examined. The students expressed a big gap between word problem and equation representation. However, the students were able to represent word problems in tables without any difficulty. Also tables helped students to create an equation. As a result, this study suggests that tables can act as an intermediate step between word problems and equations and help students understand the relationship between words and equations.