This book presents research on the subject of early arithmetic conducted in a Swedish compulsory school. The research is based on the epistemology of radical constructivism and the methodology "multiple interviews" and "the process of supervision". The problem was investigated by comparing children's early arithmetical knowledge-building in the compulsory school (CS), in CS's remedial teaching (REM) and in the school for intellectually disabled (SID). In an intervention study, twenty children of various ages in SID and REM participated, as well as their teachers. The aim was to adjust the teaching content to harmonize with the children's ways of operating and longitudinally investigate the children's progress, as well as to facilitate teachers' model-building of their children's various ways of operating and needs for learning.