This paper reports the results of the second of a series of collaborative studies examining how children acquire the skills to represent and solve verbal addition and subtraction problems. The purpose of this study was to identify the cognitive processing capabilities of a group of Tasmanian (Australian) children. Fifteen cognitive tests were administered to 122 4- to 8-year-old children enrolled at Sandy Bay Infant School in Hobart, Tasmania. The data derived from the tests were examined in four ways. First, responses were scored and distributions for the population were prepared. From this data it was evident that five of the tests failed to differentiate the children. Second, the relationship of the scores for the 10 remaining tests were examined and this analysis revealed one primary factor reflecting quantitative skills, and another reflecting qualitative transformations. Third, since the primary factor accounted for most of the variance, the hierarchical order of the tests was examined. No evidence of such an order was found. Finally, the test scores for the 10 differentating tests were related to four memory (M-space) tests given earlier to the same population. The pattern of responses on the cognitive tests for six groups identified via a cluster analysis of the M-space data demonstrated systematic differences between five of the six groups. (Author/MP)