Emphasizes, and illustrates with examples, the importance of taking classroom time to rectify incorrect student thinking by immediately undoing, or unraveling, students' misconceptions, errors, or misapplications. When this process is cultivated without a judgmental attitude on the part of the teacher, students' confidence is inspired and…

Indicates that utilizing calculators to introduce algebraic concepts in a prealgebra course provides students with a solid foundation for the study of college mathematics. Pedagogical criteria emphasized the difference between exact and approximate results, appropriate use of the calculator in problem solving, the role of estimation in…

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Presents a series of activities developed from the "Arithmetic Teacher's" regular feature entitled "Problem Solving: Tips for Teachers" to help students develop skills in each of the four steps of Polya's problem-solving process: (1) Understanding the Problem; (2) Making a Plan; (3) Carrying Out the Plan; and (4) Reflecting…

Presents three stories from mathematics history that can be integrated into classroom teaching: (1) the account of how Eratosthenes measured the circumference of the earth to discuss the concept of units in measurement, (2) ideas from Archimedes, Vite, and Descartes to introduce pi, and (3) the discovery of the Cardanic formula as an example of…

Introduces a cultural perspective in the teaching of mathematics. Describes the mathematical practices of African peoples and of the indigenous peoples of the Americas in relationship with numbers and numeration, design and pattern, architecture, and games of chance and skill. (MDH)

Utilizing geometric topics as examples, this article describes the uses of concept maps specific to the evaluation of teaching outcomes, the monitoring of student progress, and the introduction of learning activities, particularly the initiation of classroom discourse to encourage students to articulate their own ideas and to appreciate the ideas…

Describes the American Indians in Mathematics (AIM) project developed by Montana State University's Center for Native American Studies and Mathematics Department. The AIM summer program uses new technologies and teaching methods and focused mentoring to create learning communities in classrooms, schools, and reservations. Discusses AIM's…

Mathematical fiction writing as a learning tool is discussed utilizing an actual example of a student's fictional text related to the field of geometry. Commentary about this example and how it relates to other areas of mathematics can provide teachers with insight into students' schema for organization and internalization of mathematical…

Three male students (ages 13-15) with behavior disorders/emotional disturbances were taught to self-monitor in 3 successive academic areas: reading, mathematics, and spelling. Students made gains in academic accuracy, productivity, and on-task behavior; and improvements were observed across all subject areas. (Author/JDD)

Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…

Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…