The theory of unary and binary operations are discussed and illustrated with examples from school mathematics. Presentations of selected inverse operations are made and attention is drawn to certain "typical" problems that occur during instruction and learning of these concepts. (MP)

Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)

A computer program named BUGGY is described. The program is designed to duplicate "traditional" student mathematical mistakes; pupils are to identify the nature of the errors the computer makes. (MP)