Addresses the role that mathematical definitions can play in the middle grades mathematics classroom and focuses on the concept of angle as it was introduced to 6th grade students. Describes a traditional approach and an alternative approach to teaching the concept of angle. Illustrates students' concept images of angle. (KHR)

Assesses students' geometric thinking through an action research task that uses problems from the National Assessment of Educational Progress (NAEP). Improves students' conceptual understanding of geometric properties and measurement by exploring complex figures, perimeter, and area concepts. (YDS)

Use of prepartitioned models is proposed to help students construct a meaningful concept of fractions. Partitioning, geometric shapes as fractional models, concepts related to successful partitioning, and other benefits from partitioning experiences are discussed. Sample activities are suggested. (CW)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

Various methods for solving the problem of finding when the hour and minute hand of a watch have the same direction are explored. The relationship of these problems to the educational environment and the maturity of the student are discussed. (CW)

Describes PC Logo, an instructional tool that can be used for teaching and enhancing a student's knowledge of graphs and geometric concepts. (CCM)

Students at all levels benefit from a multi-faceted approach to learning abstract material. The most commonly used technique in teaching the pure theory of international trade is a combination of geometry and algebraic derivations. Numerical simulation can provide a valuable third support to these approaches. The author describes a simple…

In early 2004, Cabrilog released version "II plus" of their interactive geometry package. According to the author, "Cabri Geometry II plus" is clearly a much more useful package than the earlier version. However, unlike other sophisticated applications packages, the designers have avoided creating so many options that secondary students lose their…

Mathematical games provide wonderful opportunities to engage students in meaningful and rich mathematical investigations. This article describes three mathematical games suitable to be played by different groups of students, from young elementary school students, learning the basics of arithmetic and geometry, to older students making their first…

Hoping to develop in her students an understanding of mathematics as a way of thinking more than a way of doing, the author of this article describes how her students worked on a spatial reasoning problem stemming from an iteratively constructed sequence of cylinders. She presents an activity of making cylinders out of paper models, and for every…

"Nuggets" are suggestions with practical advice to help in communicating biology to students. They are shorter than the formal papers and have not been peer-reviewed, but may provide ideas for the classroom. This article presents inexpensive alternative methods for students to measure small volumes of liquids in school biology laboratories.

It is over 25 years since Wood, Bruner and Ross (1976, "Journal of Child Psychology and Psychiatry," 17, 89-100) introduced the idea of "scaffolding" to represent the way children's learning can be supported. Despite problems, this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing…

The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently…

The growing concern of teachers to improve their theoretical classes together with the revolution in content and methods brought about by the New Information Technologies combine to offer students a new more attractive, efficient and agreeable form of learning. The case of Descriptive Geometry (DG) is particularly special, since the main purpose…