It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

It is widely accepted that learning becomes more enduring and deeper if geometric concepts are presented in various orientations and dimensions in textbooks. The purpose of this study was to examine how geometric concepts are presented in the Turkish elementary mathematics curriculum and the textbooks in terms of sizes and orientations. For this…

In this article, the author describes the Lutterloh method of making dress patterns, which was developed in Germany in the 1930s. The underlying principle involves the modification of basic designs and it is claimed that it provides better fits for women of different sizes and shapes than do other commercially available patterns. The method is…

A discussion of what constitutes proof is given. Methods of teaching proof in a more intuitive and informal way than is usually done are suggested. (MK)

Number patterns discovered by third graders are described and discussed. (MK)

Magic circles, number puzzles somewhat more complex than magic squares, are described and discussed. (MK)

An activity is presented which provides a novel approach to number patterns, experience in following an unusual algorithmic procedure, and practice in systematic search techniques and basic facts. (MK)

The mathematics curriculum should be imbedded into the cultural environment of the student. Discussed is the mathematical educational potential of decorative motif. (PK)

Mathematical activities suitable for reproduction as worksheets are suggested. These activities are adaptations of the classic tower puzzle and are intended to help students discover patterns, make generalizations, and use the strategy of solving simpler problems in order to solve a more difficult one. (MK)

Worksheets for duplication are provided for this activity designed for students in grades 6-10. The objective of the activity is to have students discover generalizations about the patterns formed. (MK)

Describes the stages of a process of reflective thinking. Investigates how geometrical models can be used in learning and teaching mathematics in connection with the process. Identifies two models for children of age four to eight: constant path in the space of shapes and continuous path of varied polygonal shapes. (Author/YP)

Patterns generated by the set of natural or counting numbers are discussed. Included are quartic, odd, square, and triangular numbers. (MK)

A problem sometimes called Moser's circle problem where a circular region has to be partitioned with chords without any three chords intersecting at one point, is discussed. It is shown that Moser's circle problem makes the students to use a variety of mathematical tools to find correct solutions to problems and gives an opportunity to think about…

Two posters that can be used to provide experience in recognizing patterns in sequences of numbers are provided. Suggested number sequences for different grade levels are given. (MK)

The author suggests ideas intended to lead to independent study on topics including trigonometry, Pythagoras, algebra, transformational geometry, primes, and countability. The ideas are based on Islamic patterns devised using a square lattice of dots and repeated reflections. (PK)