Findings from five related studies carried out in Tasmania, Australia in 1979-80 are summarized. The first study attempted to determine the memory capacity of a cross-sectional population of children aged 4-7, while the second study was designed to portray differences on a variety of mathematically related developmental tasks for the same population. Data from these two studies were used to form six groups differing in cognitive capacity, and the remaining three studies each used a sample of students from these groups. The third study examined the performance and strategies used to solve a structured set of verbal addition and subtraction problems. The fourth study involved repeated assessment of performance on a set of items measuring objectives related to addition and subtraction. In the last study, the children and their teachers were observed to see how addition and subtraction were taught and whether instruction varied because of the children's cognitive capacity. Differences in capacity were reflected in performance, but instruction did not vary. The capacity of children for processing information, the procedures students have invented to solve a variety of problems, and the way in which instruction is carried out in schools did not appear to be related to each other. (Author/MNS)