Mathematical Relationship Formation

An investigation into the importance of mathematical relationship formation in word problem solving sought to identify ways in which mathematical reasoning and achievement can be improved. The investigation broke problem solving into a series of steps with the hopes of facilitating solution accuracy though a proposed cognitive model which emphasized the importance of relative set size identification and relationship formation in the problem solving process. Participants were presented with a series of one, two and three part word problems aimed at examining the importance of each step, while their eye movements were monitored in order to identify patterns in attentional allocation during the process. It was hypothesized that following the steps in the proposed cognitive model would result in higher problem solving accuracy and that high accuracy problem solvers would devote more attention to the relational statement of the problem than low accuracy problem solvers. Results supported the proposed cognitive model, suggesting that problem solving accuracy is facilitated through model application. Finally, eye movement analyses revealed that high and low accuracy problem solvers focus their attention in different places within the problem text; specifically high accuracy problem solvers attend more to the question than low accuracy problem solvers. Trends identified in this study can be applied to education in order to improve the math problem solving skill of students