Describes new approaches to mathematics education outlined in standards published by the National Council for Teachers of Mathematics. Highlights a new emphasis on interactive learning and real world applications in favor of rote memorization and drilling. Discusses the role of standards in educational reform efforts and suggests steps for change.…

Describes the use of simulation to introduce the bootstrapping technique of creating confidence intervals for the mean, median, and variance. These bootstrap confidence intervals are compared to the traditional confidence intervals for the purpose of analyzing accuracy of the technique. A Minitab program to produce confidence intervals is…

Presents two case studies from a book by Lusiane Weyl-Kailey in which she addresses the learning problems of 14-year-old boys from either a psychoanalytic perspective or a mathematical perspective, depending upon her diagnosis of the boys' problems. (MDH)

This paper describes an accelerative instructional program in algebra provided to a sixth-grade boy, highly able in mathematics, by parental home tutoring. The boy's high intrinsic motivation and teaching sensitive to his needs and abilities led to successful achievement. (DB)

Offers suggestions to make homework more beneficial to students and teachers. Discusses motivating students, planning assignments, grading, communicating teacher expectations, and maintaining consistency with respect to homework. (MDH)

Presents an activity to investigate the dimensions of the maximum rectangular area given a fixed perimeter using mathematical modeling and manipulative materials. Students collect and compare data, find patterns, graph data, write functions, and discuss the meaning of the related mathematical model. Provides three reproducible worksheets for the…

Shortcomings of mathematics curricula are described and research on the use of sameness analysis with learning-disabled and at-risk students is outlined. The paper then illustrates how to teach addition-subtraction and multiplication-division relationships and their interrelationships in the context of solving word problems in mathematics.…

Reported is a naturalistic study of the role of mathematical paradoxes in the preservice education of high school mathematics teachers. Findings indicate that the model of resolving paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions, and constructive…

Discussed is the notion of ethnomathematics as an epistemological approach to mathematics. The relationship between ethnomathematics and mathematics education is described. Suggestions regarding mathematical pedagogy are provided. (CW)

Issues regarding the construction of a national mathematics curriculum in Australia are presented and discussed. Included in the discussion are the status the framework will have, and its specificity, context, validity, and implementation. (CW)

Two geometry problems generated from a design problem involving a shuttle return mechanism in a weaving machine are presented. The solutions to these problems are detailed. (CW)

Parents can encourage their children to become better mathematical thinkers. The article describes how to assist children with problem solving and presents activities that develop specific skills (estimating, counting, sorting, volume, fractions, multiplication, money, story problems, patterning, averaging, computation, magic squares, plane…

Discusses four aspects of mathematics instruction envisioned by the "Professional Teaching Standards": choosing worthwhile mathematical tasks; orchestrating classroom discourse; creating a constructive environment for learning; and analyzing students' understanding and the contribution of teacher practice to student learning. Presents…

An activity designed as an introduction to High School geometry empowering students to see relationships and make geometric connections. A list of student generated relationships based on student constructed and manipulated diagrams is included. Discussion guidelines are suggested. (DE)

This article describes the ways in which a portfolio may be used in a mathematics classroom. It explains what a portfolio is, what goes into one, how one can be organized, and how one might be assessed. Examples of junior high school portfolios are included. (JAF)