The general purposes of a model are discussed, then seven papers are presented which demonstrate several different facets of the problems associated with constructing and using models of mathematics learning. In the first paper, the task addressed concerns how to incorporate developmental psychology into perceptions of what is happening in the mind of the child; in the next paper, children's approaches to problem solving are examined when the given information includes more than is necessary to solve the problem. In two other papers, the mathematics that provides the goals for instruction is considered. In the fifth paper, a model for learning mathematics that is similar to the traditional models used in the physical sciences is presented; the use of clinical interviews in building an adequate model of learning mathematics is discussed in the next paper; and in the final paper, several major principles in a Piagetian-oriented model are examined. The mathematical areas covered by the models include problem solving, geometry, arithmetic computation, counting, and numeration. (DT)