Conjecture and proof, as opposed to numerical calculation, are presented as being the primary focus for teaching mathematics. (MP)

Dialog from a filmed lesson that uses graphing to explain positive and negative numbers is presented. The material highlights the responses of children. The work was also presented to a class of low, mixed-ability pupils since the filming, and the work of two pupils from this group is noted. (MP)

The validity of the formula for the sum of the measures of the interior angles of polygon is explored using non-convex polygons. (SD)

Mathematical investigations pursued by two gifted students are presented. One is written by a boy age 9 with his follow-up at 11; he studied patterns to derive the factors for the difference of two squares. Another boy of 11 discovered formulas for slopes of tangent lines and areas under curves. (LS)

An intuitive approach to exponential functions is described. Microcomputers are used to aid discovery of derivatives. (MNS)

Different regular-polygon-shaped candles wound with a sheet of paper are cut through obliquely. When the papers are unwound, unique patterns are revealed. Investigation of these patterns leads to the discovery of geometric concepts. (JP)

An exploration approach with calculators that promotes student investigation and development of mathematical processes and concepts is highlighted. The presentation helps to highlight the enormous potential of calculators to facilitate new and imaginative approaches to certain areas of number work, and shows how student interest is promoted. (MP)

Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

Mathematical concepts occur spontaneously from many topics and can be developed in the framework of cross-curricular schoolwork. Consequently, students can gain knowledge of where mathematics arises and insight about its purposes. (Included are activities dealing with the reflectional and rotational symmetries of automobile hubcaps evolved from…

This article outlines a series of investigations in graph theory which simultaneously gives exercises in visualization. It is argued that one of the advantages of classroom investigations is that students can be lead to an intuitive grasp of advanced mathematics. (PK)

Cones as containers and envelopes are discussed with appropriate activities for middle grade children provided. (MP)

Describes activities in a mathematics class for six-year-olds. The article makes several points, including: working independently is very absorbing; investigative work is as important as algorithms; and children working in groups can achieve more than even the brightest child working alone. (PK)

A lesson involving moebius strips and geometric properties is reviewed. Specific activities are suggested. (MP)

A rationale is provided for the notion that mathematical games can be a valuable resource for the stimulation and support of student collaboration and cooperative classroom mathematical discussion. Included are examples of tangram games, people games, and board strategy games. (JJK)