Connecting Research to Teaching: Linking Task Characteristics to the Development of Symbol Sense

“Let x equal the number of miles.” How many explanations of solutions to word problems begin with a similar statement? As teachers, we frequently encourage students to state what their variables represent when they begin to solve a problem. However, we frequently see students who get lost in the notation and seem to have little or no means for finding their way out—or worse, students may not realize that they are lost. Lisa, a calculus student working on the Alpha and Beta travel task shown in figure 1, confidently began work on the task, used algebraic notation to represent quantities within the task, and arrived at a solution. In addition, Lisa was very comfortable with her answer. Lisa's work, as discussed in the next paragraph, was not correct and actually reveals a problem in her interpretation of notational expressions. We use this example to lead into a discussion of symbol sense, our goals for students, and how tasks can be used to help meet those goals. Readers may wish to try the tasks shown in figures 1, 3, 5, 7, and 9 before reading further.