Reported are the results of an exploratory study that analyzed appropriate mathematical or "pre-mathematical" experiences for very young children of nursery school, kindergarten, or first-grade age. Among alternative approaches are the approach via sets, the approach via real numbers, and the approach via the physical act of counting. This study was based on the third approach, the physical act of counting. Included in the report is a discussion of learning, remarks about specific activities used with pupils, and a bibliography of related publications. (RP)