A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

This paper describes a model of student attainment of mathematical concepts and its development. In this model three types of activities (developmental, connecting, and abstract) are considered as an overlay on the three ways of representing mathematical concepts (physical/visual, oral, and symbolic). Each activity type involves some means of…