We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same procedural levels as those without disabilities though they have difficulties in reaching the most abstract level (numerical facts). The use of fingers or concrete representations (balls) appears as a fundamental process among these students. As for errors, these vary widely depending on the students, and can be attributed mostly to an incomplete knowledge of the decimal number system. (Contains 8 tables and 15 figures.)