Argues the importance of teaching fractions and discusses examples of fundamental problems in students' conceptualization of common fractions and decimal fractions. (SS)

Examples are presented in which students are able to answer test items requiring manipulation of numbers for such topics as reducing fractions, but lack understanding of the operation. In addition to paper-and-pencil test, interviews are recommended for evaluating a student's understanding. (JP)

Some students can perform operations on fractions when using physical materials, but are unable to transfer this ability to operations with symbolic expressions. They seem to view the manipulative and paper-and-pencil problems as different and are not surprised to get different answers. (SD)

Reviews the author's research on students' conceptions of mathematics and suggests ways to overcome or prevent misconceptions. (MP)

Results of interviews with students regarding their conceptual understanding of fractions are discussed. Fewer than 10 percent had acquired an adequate conceptual base. (MP)

Research on the conceptual notions of fractions held by students at various levels of schooling is discussed. A method of approach to instructing students on fractions that seems to hold considerable promise is also covered in detail. (MP)

This paper describes student performance and beliefs regarding fractions resulting from a five-phase approach toward developing mathematical intuition via physical materials. Interviews with students using this approach and with students using a conventional textbook approach indicated significant differences in problem-solving abilities and…

Reports results from a project designed to bring about student conceptual change by using multiple modeling and representation as well as links to other areas. Students developed rules as conveniences and meanings for symbols, were active in learning, made interpretations, and had confidence in their thinking. (MKR)