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

In three experiments, three normal preschoolers were presented with sorting tasks ordinarily insoluble for four-year-olds. Found that, although the subjects had difficulty correctly sorting the pictures when told what criterion to sort by, they could provide correct answers when asked what they were looking for. This self-instructional effect was…

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Properties of a given array of numbers are discussed and some sample activity cards involving discovery of number patterns are presented. (MP)

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…

Examines the prospect of facilitating the discovery process for scientific researchers through anticipatory learning that is viewed as critical to the enhancement of intuitive abilities in pattern recognition among researchers. Discusses intuition, metaphorical thinking, and aesthetics as playing significant roles in the development of pattern…

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)

This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. A teaching procedure for this approach is presented, with questions, answers, and homework suggestions. (MNS)

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Alecia Ford, co-author of this article, had a problem that teachers everywhere face more and more frequently with the predominance of standardized testing--too much world history to teach in too little time. Her problem relates to how she can help her sixth-grade students develop an in-depth understanding of the Enlightenment, a period in history…

The focus of this article is patterns and pattern making using geometric figures. Included are sequentially planned activities for K-8 students that help them first to discover the attributes of various figures and later how to combine these figures into patterns. Finally, this information is applied to real world activities such as quilting and…

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)