tical basis for this new approach. She writes that various theories of instruction draw from cognitive psychology by focusing on models of learning, typical development, and individual differences in children. How children think and learn is addressed buy developmental psychology, information processing theory, and theories of affective development. Developmental stage theory specifically suggests that learning across and within domains occurs in a series of incremental, overlapping, and integrated stages, and different theorists suggest the interaction of various elements in contributing to learning. Underlying this theoretical model are ideas concerning the nature of children's basic intellectual structures, the stages through which the structures develop, and the process of stage transition. Some theories are age-specific and follow Piaget in seeing learning in discrete stages. The theory offered by Case, for instance, sees children as capable of learning from 1 month, and he depicts the cognitive structures, or schemes, underlying learning with representing a current state (problem representation), representing a state that has a higher affective value (objectives), and representing a sequence of operations that take individuals from one state to another (strategies). Case identifies four major age related stages of executive development (sensorimotor, relational, dimensional, and vectorial operations).
Montague emphasizes the value of metagonition in mathematical problem solving, stating that metacognitive ability enables learners to adjust to varying task demands and contexts. Montague states that "metacognition facilitates the selection and allocation of techniques and strategies for successful task completion." Lack of metacognitive abilty affects developemnt for those with learning disabiltiies and appears to affect the development and use of effective strategies for representing problems and executing solutions.<...