The following effects were revealed by two studies on the mathematical advancement in elementary schools: Elementary school pupils make long-term profits from a training of quantity-number competencies, which result in a transfer of basic arithmetic skills. In contrast, students of special education schools only gain short term benefits from such training and no transfer effect can be shown.These differences in training effects could be the result of individual differences of the scholars or of differences schooling. In order to study this query in more detail, children with comparable individual conditions, but from different school systems (elementary school or special education school), of two different studies with comparable design were chosen. By these means, the following four conditions could be compared: 1) elementary school pupils, having received training of quantity-number competencies (N = 6); 2) elementary school pupils, having obtained general training of inductive reasoning (N = 6); 3) scholars of special education schools, having obtained training of quantity-number competencies (N = 6), and 4) pupils of special education schools, having received general training of inductive reasoning (N = 6). The results showed that both mathematical training groups increase their quantity-number competencies on a short-term basis. However, only for the elementary school pupils these effects are stable over time. In addition, only those scholars succeed in transferring the trained quantity-number competencies to arithmetic abilities. Possible reasons for these findings are discussed.