The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

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)

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (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)

Activities involving estimation of the number of objects in a configuration can motivate students to consider parametric models. (SD)

Having students find and cut out of graph paper the 12 pentominoes can provide an enjoyable exercise in perception, discovery, and double checking. The pentominoes can then be used to illustrate informally several geometric concepts. (SD)

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)

The technique of organizing data in tables to solve counting problems in geometry is illustrated in the solution of five problems. (MN)

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)