Affordances of Graphical and Symbolic Representations in Algebraic Problem Solving

Successful algebraic problem solving entails adaptability of solution methods using different representations. Research suggests that students are more likely to choose symbolic solution methods over graphical ones even when graphical methods are more efficient. However, existing research has not addressed whether the efficiency of solution method varies depending on the nature of the problem solving task. This masters project addressed the question of whether symbolic and graphical solution methods provide different affordances with respect to computation and interpretation problems by presenting students with either symbolic or a graphical representation. Graphical representation was found to facilitate problem solving, particularly for interpretation problems. Participants experienced the most difficulty with interpretation problems that required the comparison of slopes when these problems were presented in symbolic format. Results suggest that this difficulty may be caused by symbolic representation biasing participants towards incorrect strategies. Participants rated graphical problems to be less difficult than symbolic problems, and the majority of participants reported a preference for graphical representation. These results set the stage for follow-up studies that will explore whether the nature of the problem solving task affects students’ choice of solution method.