The role of intermediary representations in solving lever balance problems with different target representations and problem complexities.

Introduction: Intermediary representations are widely regarded as potentially useful supports in physics problem solving, although their association with performance may vary across task characteristics. This study examined how intermediary representation use was associated with performance on lever balance problems and how this association varied across target representation types and problem complexity types. Methods: A total of 130 ninth grade students solved 12 problems representing three target representation types and four problem complexity types. Problem solving success was analyzed using a generalized linear mixed effects model. Results: Intermediary representation use was associated with higher overall problem solving success. However, this association was strongest for mathematical and tabular target representations and more limited for diagrammatic target representations. The magnitude of the association also varied across problem complexity types. Larger differences were observed for problems requiring the coordination of force magnitude with pivot location or lever arm length, whereas smaller or nonsignificant differences were observed for problems involving force magnitude only or force magnitude and direction. Discussion: These findings suggest that intermediary representation use may be most strongly associated with successful performance when problems require manageable relational coordination and translation into mathematical or tabular forms.