The major focus of this study is to trace the cognitive development of students throughout a mathematics course and to seek the qualitative differences between those of different levels of achievement. The aspect of the project described here concerns the use of concept maps constructed by the students at intervals during the course. From these maps, schematic diagrams were constructed which strip the concept maps of detail and show only how they are successively built by keeping some old elements, reorganizing, and introducing new elements. The more successful student added new elements to old in a structure that gradually increased in complexity and richness. The less successful had little constructive growth, building new maps on each occasion. (Contains 19 references.) (Author/MM)