Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.

Abstract
Four computer-based training strategies for geometrical problem solving in the domain of computer numerically controlled machinery programming were studied with regard to their effects on training performance, transfer performance, and cognitive load. A low- and a high-variabili ty conventional condition, in which conventional practice problems had to be solved (followed by worked examples), were compared with a low- and a high-variability worked condition, in which worked examples had to be studied. Results showed that students who studied worked examples gained most from high-variability examples, invested less time and mental effort in practice, and attained better and less effort-demanding transfer performance than students who first attempted to solve conventional problems and then studied work examples. In complex cognitive domains such as mathematics, phys- ics, or computer programming, problem solutions can often be characterized by a hierarchical goal structure. The goal of these solutions can be attained only by successfully attaining all subgoals. Learning and performance of complex cogni- tive tasks are typically constrained by limited processing ca- pacity. The more complex a task, that is, the more subgoals (that can be performed in alternative ways) it contains, the higher the processing demands are, and the more likely it is to exceed the concurrent processing and response capabilities of novices. Failure to learn these tasks may be attributed to the inadequate allocation of attention and the related high or excessive "cognitive load" (Sweller, 1988). Cognitive load can be considered to be a multidimensional construct that represents the load that performing a particular task imposes on the cognitive system of a particular learner (Paas & Van Merrienboer, in press-b). The construct can be conceived to consist of causal factors and assessment factors corresponding to factors that affect cognitive load and factors that are affected by cognitive load, respectively. The causal factors include the task environment characteristics, subject characteristics, and the interactions between task environ- ment and subject characteristics. Task characteristics include such factors as task structure, task novelty, type of reward