Describes the use of investigations for the purpose of assessment, teaching, and learning. Lists types of questions that can be included in investigations. Explains how to write an investigation and provides some examples. (ASK)

The difference between mathematical "investigations" and "investigating," used in two different British reports, is discussed. Investigations means an extensive project or extended exploration into a mathematical problem or topic. Investigating is promoted as an ongoing teaching method. (MNS)

Reports on rich mathematical activities that integrate different mathematics strands and learning. Describes how to introduce the task and the classroom setting, set up the task, and continue the investigation. Presents student work samples. (ASK)

Portions of the Cockcroft Report which seem confusing are discussed. The connections among problems, applications, and investigations are considered in sections on being a mathematician; open is in the mind; assumptions, rules and patterns; and learning not to be anxious. (MNS)

Topics for investigation in mathematics classes that arise from the Olympics are discussed. Activities with performance records leading to the development of graphs are illustrated. (MNS)

An investigation concerning the sum of square digits is described to show college mathematics students how mathematicians really work. A computer program is included. (MNS)

Three ideas are explored: (1) an improvement of the SSA congruence theorem for trigonometry; (2) a discussion of the failure of SSA in spherical geometry; and (3) an extension of SSA to spherical geometry and hyperbolic geometry. (MNS)

Defines and supports investigative mathematics for schools. Presents several results of an investigation of Fermat's Last Theorem. (PK)

A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)

Presents two proofs that only five regular polyhedra exist. The first is a geometric proof, and the second is based on graph theory, using the relationship between the vertices, edges, and regions of the graph model. (MDH)

Presents four investigations involving geometric sequences and series: folding a sheet of paper in half 8 times, stacking pieces of paper cut in half 50 times, snapping your fingers at intervals doubled in length for 1 year, and summing time intervals continuously cut in half. (MDH)

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…

Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)

Project questions are real-world problems with multiple solutions, no obvious solution sequence, requiring hands-on data collection, and investigation of topics within and outside mathematics. Discusses evaluation of solution processes, describes a detailed example involving the trajectory of a baseball, and suggests 19 other project questions.…