This paper discusses the importance of the joy of learning in mathematics and some ways that teachers can foster this in mathematics education.

In this article, the authors present an approach to developing open-ended problems through capturing contextualised mathematics in photographs. They draw upon their research with the Problem Posing Research Project, a collaborative venture between an Australian and a Canadian university to broaden pre-service teachers pedagogical practices in the…

The role of the teacher in discovery teaching is discussed; examples of non-directed and of directed discovery methods are provided. (DT)

Questions which stimulate discovery learning are asked concerning polygons and curves drawn on an integral lattice. (DT)

Some examples for investigating shapes in the environment are given. Circular objects, triangulation, symmetrical designs, and further investigations are listed. (MNS)

A plea is made that mathematics should be taught the way that mathematicians do it, using an exploratory approach rather than rule learning. (MNS)

Activities suitable for use with primary school students are described. The author offers advice concerning expectations of the students, use of the vocabulary of probability, integration of activities with other classroom work, and related topics. (SD)

Graph theory is promoted as a vehicle for using the discovery method. A lesson is presented to illustrate the method, and activities and questions for further exploration are provided. (MNS)

The properties of the cube are explored. A set of activities is given that forms the basis of a class project on discovery. (MNS)

Activities used with seventh and eighth grade students in Western Australia are described. The instructor guides pupils towards experimental solutions and encourages discovery of solutions for similar and more general problems. Investigations include study and construction of polygons, polyhedra, and one and two-sided surfaces. Commercial kits are…

Several kinds of special dice are displayed and the various winning probabilities in games that could be played with them are discussed. Patterns for dice construction are provided. (MP)

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)

Samples of materials available to students from grades 4 through 12 at a Mathematics Center are reviewed. The examples are part of a collection of more than 200 mathematical tasks using solid materials in a new approach to problem solving. (MP)