This report presents results of several extensive empirical studies. Prior to these studies it was believed that errors in procedural skills such as multi-digit subtraction could be accurately modelled with two mechanisms: bugs ("competence" phenomena reflecting mistaken beliefs about subtraction which are stable over time) and slips…

This manual is used with MATHBOXES, a computer program written for Apple II microcomputers to help children relate formal mathematical symbols for representing simple word problems to the informal strategies using physical objects that they naturally use to solve them. There is a substantial body of research that documents that young children are…

Research on structural learning theory is reviewed as a base for designing computer-assisted instruction programs. An intelligent "Rule Tutor" emphasizing diagnosis and remediation for whole number concepts is described. (MNS)