Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

In a recent edition of "Mathematics Teaching" Midge Pasternack argued the case for the use of the 0-99 square with young children rather than the ubiquitous 1-100 square. In this article, the author would like to take the opportunity to mount a defence in favour of the much maligned 1-100 square. His main criticism of the 0-99 square (apart from…

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

Introduces students to nonperiodic tiling and allows them to construct their own sets of kites and darts through a series of explorations, conjectures, and discoveries. (ASK)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

Deriving all Pythagorean triples from simple patterns within an addition table is presented, with formulas included. (MNS)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

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…

Described are activities for thinking through patterns using toothpicks, paper strips, wooden cubes, and people patterns; thinking with attribute items such as geocards, namestrips, and treasures; and thinking with geometric materials such as geoboards and dot paper, cubes, and simple puzzle pieces. (MNS)

Programs (using Logo) developed by children to produce multiples, the Fibonacci series, and square numbers are presented, with graphical representations of functions introduced. Another investigation involves drawing a circle using turtle graphics. (MNS)

Patterns and relationships are shown between the Pythagorean theorem, Fibonacci sequences, and the golden ratio. Historical references also include the works of Euclid and Euler. These unexpected relationships can be used to motivate secondary students. (DC)

Patterns resulting from polygonal numbers are explored, with examples of triangular, square, pentagonal, rectangular, and other numbers. Tables and formulas to be developed are included. (MNS)

Described are: how teachers can use the computer language Logo, along with noncomputer activities, for teaching about linear and two-dimensional patterns and about combining shapes to create more complex shapes. Three computer program listings are included. (MNS)