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This study is aimed at the mechanisms used by students with an intellectual disability in the counting process. The assessment of the counting process is carried out through experimental tests inspired by the basic principles of Gelman and Gallistel, namely one-to-one, stable order, cardinality, abstraction and order irrelevance. This is a comparative study of participants with a developmental age of between 4 and 5 years, in two populations: a group of students with intellectual disability attending special education (SEN) schools, with chronological ages of between 8 and 12 years, whose developmental age was determined by the Cambrodi Dimensional Method, and another group of students without intellectual disability attending mainstream schools (MS). The data do not show significant differences between the one-to-one and stable order principles with respect to the variables MS and SEN, while significant differences are demonstrated for the principles of cardinality, abstraction and order irrelevance. (Contains 8 tables and 6 figures.)