Young children have been taught simple sequences of alternating shapes and colors, referred to as "patterning", for the past half century in the hope that their understanding of pre-algebra and their mathematics achievement would be improved. The evidence that such patterning instruction actually improves children's academic achievement…

This position paper is an extension of a presentation delivered to the National Council of Supervisors of Mathematics and the National Council of Teachers of Mathematics at their annual meetings in San Diego, 1978. Four limits in test design are discussed: focus on low-level skills, general adherence to randomness, filling in blanks, and right…

Games and activities, which are fun, practical, and related to the child's world, are presented. Suggestions are given for building skills in estimating lengths, guessing how many, recognizing patterns in counting, multiplying with "waffles," classifying by attributes, and adding and subtracting with special cards, relays, and play…

An activity similar to magic squares is described. (SD)

The use of dice and dominoes in the classroom is discussed as leading from counting activities to pattern recognition and discovery learning. (MP)

Some patterns resulting from certain operations on numbers are discussed, analyzed, and explained. A method for predicting the outcome of these operations for any number is developed.

Magic squares are developed beginning with square arrays of playing cards. (SD)

A unit on the peoperties of a kite can include many geometric concepts: symmetry, distance, relationships between diagonals, area, altitude, angles, and others. (SD)

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)

Patterns and relationships found in the multiplication table of the numbers zero through nine are discussed as a means to helping students understand certain concepts. (MP)

Upper elementary school students created their own algorithms for finding products of whole numbers. The algorithms were similar to familiar ones for finding products involving 9 and 11. (SD)

A set of geometric pieces is used to solve problems involving geometry, combinations, division, and money. (JT)

Playing with number patterns can lead students to discover some divisibility tests. (JT)

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)