Many researchers claim that children with Down syndrome learn to count mechanically. According to them, they do not have conceptual understanding of numbers. A proof of their claim is the fact that when a child with Down syndrome is interupted while counting he/she cannot continue from the last number, he/she has to start counting from the begging. According to other researchers, they learn to count by principles. This research reinforces the second view. According to our research children with Down syndrome cannot continue counting from the last number and start over again because of their Short-term Memory deficit. The early intervention designed for their memory development could be proved to be of major importance to their entire cognitive development.