Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

Imaginal perspective switches are often considered to be difficult, because they call for additional cognitive transformations of object coordinates (transformation hypothesis). Recent research suggests that problems can also result from conflicts between incompatible sensorimotor and cognitive object location codes during response specification…