Metacognitive and Non-Metacognitive Processes in Arithmetic Performance: Can There Be More than One Meta-Level?

The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens' model of metacognition. According to the Nelson-Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more than two levels, cognitive processes from at least one level can be described as both meta- and object-level processes. The question arises whether it is possible that the very same cognitive processes are both controlled and controlling. The feasibility of owning the same cognitive processes-which are considered the same from an external point of view of assessment-as both meta- and object-level processes within the same individual opens the possibility of investigating the transition from meta-level to object-level. Modeling cognitive development by means of a series of such transitions calls forth an understanding of possible developmental phases in a given domain of learning. The developmental phases of arithmetic performance are described as a series of transitions from arithmetical facts to strategies of arithmetic word problem solving. For school learning and instruction, the role of metacognitive scaffolding as a powerful educational approach is emphasized.