We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

In higher education the main subjects build on the knowledge acquired in high school. Research shows that students entering universities have acquired basic knowledge to different extents. It is very important to be able to apply mathematical knowledge directly. Students often treat practical knowledge separately from theoretical knowledge. They…

This article is concerned with an environmental education program designed to allow students, grades five through eight, to investigate important ecological relationships. The course has two phases, the awareness phase whereby students construct the Environmental-Ecological Web, and the involvement phase whereby they use it to investigate local…

Presents activities that explore step-cut dissections of whole rectangles. Provides students with the opportunity to discover patterns, which allows them to solve more and more complex problems that offer a context within which students can think about and use different mathematical concepts. (JRH)

Science centers can engage students; accommodate different learning styles and individual interests; help students become independent and confident learners; and encourage social skills among students. In this article, the author worked with third-grade students as they completed activities at learning centers during a week-long unit on simple…

This booklet is a collection of puzzles, investigations, and games. They are designed to be used with large objects such as tins or stones and diagrams marked on the ground. The children are to be encouraged to use an experimental, trial-and-error approach at first, and then develop methods of solution. (MNS)

This booklet is a collection of puzzles, games, and investigations. All that children need are some stones or shells, on some of which they must write numerals. For playing with the whole class, the game or puzzles may be marked out on the floor or in sand; in that case, larger objects such as small rocks and empty tins may be used. Children are…

Presents three investigations related to the game Bulgarian Solitaire. Investigations ask students to find and represent optimal solutions to the problem, to identify cyclical solution patterns for different numbers, and to respond to questions involving the number and nature of the cyclical solutions. An appendix provides answers to questions.…

Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)

Presents the problem of finding the maximum area of a quadrilateral when three of the four sides are given. Incorporates several parts of the secondary school precalculus curriculum into the solution. Develops the formula to solve the problem. (MDH)

An effective curriculum gives students the opportunity to perceive relationships among different topics in mathematics, use mathematics in their everyday lives, and apply mathematical thinking and problem solving to other curriculum areas. This book contains fun and creative ways to integrate mathematics across the curriculum with a diversity of…

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)

Presents 5 activities for the K-1, 2-3, 4-5, 6-8 grade levels and for in the home in which students explore the concept of combinations. Each activity includes a lesson plan to investigate a combinatorics problem appropriate for that grade level. Provides reproducible worksheets. (MDH)

Presents a hands-on mathematics task that can be investigated experimentally to produce a sequence of numbers. Describes ways to extrapolate values of the table of numbers by formulating and verifying a conjecture related to the pattern in the numbers. (MDH)

Describes the process of problem identification, data collection, and generalization in a mathematical experiment to find the speed at which a bug travels at the end of a fan blade. Presents the learning outcomes of the experiment and possible implications of using this teaching method. (MDH)