A study was conducted to examine the learning of mathematical concepts by English dominant and Spanish dominant primary school children. The concepts considered were number, numeration, and computational procedures. Using the case study method, a three step procedure was designed to study individual math objectives: (1) objectives were first identified in the curriculum; (2) these objectives were then included in a teacher survey for ratings on item difficulty as perceived by the teachers; and (3) students were observed while learning the identified math objectives. Among the findings of the study were: (1) field independence tends to be associated with achievement in mathematics, while field sensitivity tends to be associated with lower levels of achievement; (2) field independent students tend to perform better on the precise thinking exercises, demonstrating a higher ability to use and apply rules; (3) the ages of children within a grade do not seem to be related to achievement; (4) children's language skills have not completely developed by the first grade, and there are specific usages that occur in math teaching which cause children difficulty; and (5) bilingual Hispanic students tend to perform at higher levels than do English or Spanish monolingual students. (Author/APM)