This article focuses on spontaneous and progressive knowledge building in ''the arithmetic of the child.'' The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical interviews. Theoretical models elucidate behavior patterns and the corresponding mental structures underlying them. The individual interviews of the pupils were video recorded. The results show that the activated behavior patterns, which are responses to well-adapted contexts presented by the researcher, are compatible with findings in Swedish compulsory schools. Six of the pupils' mental structures in the study are numerical. A substantial implication for special education is the harmonization of the content in teaching with the children's own ways of operating, which implies a triadic teaching process. (Contains 3 tables.)