Cognitive and non-cognitive influences on the mathematical learning of children attending four community schools in different provinces of Papua New Guinea and an international primary school in Lae were investigated. Altogether, 446 pupils, most in grades 2, 4, or 6, were given pencil-and-paper group tests; 253 pupils were also given individual tests of visual memory and memory space. Forty-four boys were selected for intensive study and given a battery of individual tests, including equipment-based tests of mathematical problem solving; conservation of number, length, and quantity; and spatial abilities. Memory span measures were also obtained. Whenever necessary, individual testing was carried out in the child's vernacular. Each of the 44 boys was interviewed, with an attempt made to glean his attitude toward school mathematics and influences affecting the ways he learned it. Analysis revealed that the patterns of abilities of National (native Papua New Guinean students) and Expatriate (students of the Lae International Primary School) children were similar. However, Expatriate children clearly outperformed National children on pencil-and-paper group tests. Evidence is presented to show that the difference in performance level is largely a function of language and home background factors. Instruments are included in the appendixes. (Author/MNS)