In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

After stating that almost any topic could be generalized, the author was challenged to generalize the topic of polyominoes. His response is presented in this article. (SD)

Using the overhead projector, or overlays on an original pattern, a variety of tessellations can be generated. Several illustrations are included. (SD)

Examples of CLOPAK Networks, an approach to covering the plane with symmetrically arranged, close-packed geometric shapes, are given. Implications for the place of networks in geometry instruction are discussed. (MN)

Artistic configurations can be built using a rectangular array of points and number concepts or principles. (SD)

This pamphlet introduces the student to the basic ideas and procedures of transformational geometry through a series of worksheets. After developing intuitively the idea of rigid motion, vector diagrams are introduced, and translations are discussed in some detail. (SD)

A series of lessons in which the concept of symmetry is informally developed is described. Rotational and reflection symmetries are examined. Pictures and sample worksheets illustrate the article. (SD)

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…

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (SD)

The use of paper folding to demonstrate polygons which give plane tessellations, conic sections, and the solutions to several problems is described. (SD)

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)