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…

A theoretical discussion of categorization, unit structures and structured units, and fractions as operators was introduced. The thinking of grade-three students (n=3) with regard to the meaning of fractions was investigated in two teaching episodes using the computer environments of SuperPaint and CopyCat. (Contains 14 references.) (MKR)