Discussed is the behavior displayed by good problem solvers of feeling free to restructure, revise, or redefine a problem. Examples of student work are included. (MNS)

How the notion of limit can be developed through a meaningful approach is discussed. Selected portions of the high school calculus course are described, and errors on a test are analyzed. (MNS)

How physiological disciplines can contribute to the study of how people learn mathematics is considered. Manipulative and experiential learning, sequential versus hierarchical organization, declarative versus procedural knowledge, and short-term versus long-term memory are among the points discussed. (MNS)

Mathematics is considered a performing art. Examples illustrating this view are presented. Activities discussed are from the Madison Project materials and the mathematics program at University High School in Urbana, Illinois. Activities stress inventing strategies for attacking problems for elementary and secondary school mathematics. (RH)

Discusses a course taken at the University of Illinois (Champaign-Urbana) by undergraduates majoring in elementary education. The course attempts to combine theory and practice, emphasizing teaching methods which stress that learners make use of "mental representations" in assembling a working understanding of various components of their knowledge…

Compares the decisions facing teachers in current reform proposals to decisions made by teachers participating in the Madison Project in the 1960s. Discusses teaching methods utilized, lesson planning, and teacher/student interactions. Reports Madison Project teacher's responses to interview transcripts of the tutoring project at Berkeley,…

Discusses a new approach to mathematics education that moves away from methods that tell students what to do and toward methods that help students build mental representations of mathematical concepts. Contrasts the previous and emerging views and examines aspects of the new approach. (26 references) (MDH)

Presents two solutions of the Isis Problem, finding the dimensions of a rectangle for which the numerical values of the area and perimeter are equal, to hypothesize how the ancient Egyptians may have solved the problem without the benefits of more modern mathematics. (MDH)

Discusses why improvements in teaching mathematics are needed, including discussion of students, human development, knowledge and learning, structure of schools and instructional programs, and mathematics. Also discusses a need for two theories: (1) how young people form self-concepts and (2) classification of approaches to curricula and…

Attempts to distinguish between the lecture method and the constructivist approach, in general, and by citing classroom scenarios. The author cautions those whose writing seems to unintentionally endorse traditional lecture and drill and practice methods. (MKR)